In this way some advantages are obtained: i) improve the network coverage by ... Wireless Sensor Network (WSN) is often termed a Shared Sensor Network ...
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Survey of Game Theory and Future Trends with Application to Emerging Wireless Data Communication Networks José Moura, David Hutchison
Abstract. Game Theory (GT) has been used with excellent results to model and optimize the operation of a huge number of real-world systems, including in communications and networking. Using a tutorial style, this paper surveys and updates the literature contributions that have applied a diverse set of theoretical games to solve a variety of challenging problems, namely in wireless data communication networks. During our literature discussion, the games are initially divided into three groups: classical, evolutionary, and incomplete information. Then, the classical games are further divided into three subgroups: non-cooperative, repeated, and cooperative. This paper reviews applications of games to develop adaptive algorithms and protocols for the efficient operation of some standardized uses cases at the edge of emerging heterogeneous networks. Finally, we highlight the important challenges, open issues, and future research directions where GT can bring beneficial outcomes to emerging wireless data networking applications. Keywords: Wireless data communication networks, resource management, multi-access, network periphery, emerging requirements, competition, theoretical games, players, stable equilibrium, convergence time, evolution, learning strategies, incomplete information, Fog / Mobile Edge Computing, Peer-to-Peer, device-to-device, Internet of Things, sensor networks, small cells, energy efficiency, vehicle communications, unmanned vehicles, tactile Internet.
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Introduction
Game Theory (GT) is a branch of applied mathematics which is used to study how rational players, aiming to have a satisfactory amount of common and scarce system resources, can interact among themselves to obtain a fair and stable distribution of useful services from a specific system. In this way, GT analyses the interaction among independent and self-interested players [1], [2]. More recently, there has been a considerable amount of research in wireless networks [3]– [5]. At the time of writing, there is an enormous interest in studying GT applications for emerging wireless data communication environments, such as cognitive radio [6] and sensor networks [7]. Data communication networks – especially wireless systems – are evolving, following a common and global trend: services and associated data, previously uniquely available at Cloud Data Centers, are also becoming directly accessible from the network edge (e.g. Base Stations, cloudlets) [8], [9]. Consequently, there is a smoothly change in the network model: from the centralized form based on cloud computing to a complementary one that is much more distributed and based on Fog or Mobile Edge Computing (FC or MEC) (see Fig. 1). Some advantages of adopting a system design that incorporates FC devices are to reduce the latency availability of both data and services to the end-users. The latency is reduced because both data and services are much nearer the final consumers (i.e. the system scope is changed from global to local management) and the Round Trip Time (RTT) is consequently diminished. In addition, the backhaul link overload can be decreased. Simultaneously, due to the appearance of the Internet of Things (IoT), which enables basically every device with a processor to communicate with the remainder of the network infrastructure; it makes possible the gradual integration of IoT into the network infrastructure. In this way, one can envisage that, very soon, new terminal devices show up inside each network domain in addition to the existing ones. These new terminal devices would be of distinct types, as shown in Fig.1: mobile devices (e.g. sensors), Unmanned Aerial Vehicles (UAVs), or domestic appliances. All these emerging changes cannot be supported in a satisfactory way by the main legacy components that form the network infrastructure, namely: switch, router, AP, BS, MPLS, OSPF, and SNMP. To illustrate the importance of preparing the legacy network infrastructure for some unexpected situations, we briefly present two pertinent scenarios. The first is related to the security aspect, e.g. DDoS attacks. The second is related to the variation of traffic load induced
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by IoT devices and multimedia mobile gadgets. These two scenarios should be correctly managed; otherwise, serious operational problems may occur within each network domain. We advocate that the infrastructure of a network domain needs to optimize the (heterogeneous) functional requirements of distinct entities (of the network operator, mobile smartphone, IoT devices, FC services, edge data caching, etc.). Consequently, GT should be revisited to check its adequacy for use inside each network domain by adjusting the configuration parameters of the network algorithms or protocols deployed within that domain. With these parameter adjustments, the network domain would hopefully react to unexpected situations (e.g. load variation). In this way, the question we would like to address is how GT could empower or inform new sorts of wireless data networking for the benefit of application designers, service providers, connectivity operators, and customers. These new forms of networking should be aware of the novel challenges imposed by FC services, energy efficiency, data storage and processing at the network edge. Cloud Computing @ Network core
How GT could empower new styles of networking?
Reduces both latency and scale; Mitigates backhaul congestion; but it creates novel challenges: energy efficiency, storage and processing additional demands at the edge
Fog Computing @ Network edge
Mobile Terminals, UAVs, Home Appliances, etc.
Fig. 1. FC Emerging Environment For answering this question, we need to identify and describe the most important technical aspects needed to bring about changes in the management of networks. These technical aspects are: mobile cloud computing [10], integration of Cloud Computing and the IoT [11], and the upcoming 5G access technology [12], [13]. In addition, driven by the rapid development of wireless terminal devices and the popular usage of bandwidth-hungry applications of mobile Internet, wireless data traffic has been increasing at an almost exponential rate during the last several years. The traffic load also changes very rapidly during each day. The current network infrastructures are lacking resources to support the large increase in data demand, the ubiquitous flow connectivity, extreme low latency, and very high-speed requirements of data transfer [14]. There are a few emerging design solutions to meet these new requirements. These solutions involve extending the network operator infrastructure with Femtocells and cellular relays or middle-boxes. In addition, with the upcoming appearance of IoT, mobile networks need to be extended at their edge with some capillary (multi-hop) networks, connecting a huge diversity of devices, namely: sensors, actuators, high-level peer-to-peer data caches, terrestrial vehicles, under-water sensors, under-ground sensors, and aerial vehicles. Further, the mobile operators are studying solutions where on the edge of their networks there are virtualized machines offering their customers some data storage and application housing, all with a lower RTT than the alternative based on remote cloud. The new solution is called Mobile Edge Computing (MEC) [15] (or Fog Computing as previously indicated). We can find already in the literature on GT some contributions, e.g. in [10], where the authors propose a three tier architecture for computation
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offloading from mobile devices. This comprises a local tier of mobile devices, a middle tier Cloudlet, and a remote tier of distant Cloud servers. It addresses the unmanaged scenario in which a user autonomously decides whether to offload to the nearby Cloudlet instead of the distant Cloud server. The Cloudlet in this framework offers a best effort service with no Quality of Service (QoS) guarantees but with a relatively small RTT. It assumes that each user is selfish in nature and decides following its own utility goals. The framework models the system as a queueing network and formulates the problem as a Generalized Nash Equilibrium Problem. It takes power consumption and user experience as inputs to optimize the problem. A distributed algorithm is then run to solve the offloading decision problem for each user. This approach, while theoretically feasible, has still not been applied in a real mobile environment. As an example (see Fig. 2) some heterogeneous small cells (e.g. picocell, femtocell) networks can be deployed within a macrocell (the users are not shown in Fig. 2). Each small cell is like a cluster entity with a Cluster Header and diverse cluster nodes (e.g. sensors). In this way some advantages are obtained: i) improve the network coverage by exploiting spatial/temporal reuse of the spectrum; ii) enhance the capacity of cellular network by offloading traffic from the BS, iii) managing data/service location at the network edge (i.e. FC) to diminish the network latency/jitter and increase the data rate, iv) load balancing among the diverse backhaul links, v) flow routing in the optimum conditions (e.g. low energy consumption, high rate, low delay, low interference, high robustness against fails). Other potential advantages can include [16]: i) combining wireless and backhaul resources in the network selection, ii) orchestrating flow admission and flow rate policing to guarantee end-to-end QoS/QoE. A further advantage of this emerging paradigm is enabling multiple applications running on the same underlying infrastructure. Within such an environment, multiple applications share the resources from the same sensing and communication infrastructure to increase the overall system utilization. This type of Wireless Sensor Network (WSN) is often termed a Shared Sensor Network (SSN) [17]. Once more the system lifetime is a very important aspect that urges to be maximized.
Cloud Center Internet Internet
Internal-Cluster Communication External-Cluster Communication
Access Point
CH
Base Station
CH CH
Cluster Header Sensor
Fig. 2. Design of a Heterogeneous Wireless Access Network
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As we already pointed out, GT is a very promising mathematical tool to identify the more suitable strategies to facilitate the network functional changes that we have discussed in the previous sections. Distinct game models have been designed and analyzed to study the behavior of networking entities to explore the network resources and obtain the game equilibrium (i.e. a game solution representing the behavior of the nodes at steady state). The games can be classified through different perspectives: classical/evolutionary; non-cooperative/cooperative; static/dynamic; single/repeated; complete/incomplete. Following this classification, we aim to survey the literature analysing the most powerful theoretical games to manage efficiently the new or emerging, novel wireless network infrastructures. This article has the following objectives: To refresh the literature review of GT applied to wireless networks; Discuss emerging networking scenarios such as heterogeneous networks, small cells, vehicular networks, IoT, energy consumption, and device localization; Point out open research issues in GT in the following directions: ICN, D2D, IoT, FC, local data storage/service, or green networks. Although there is some recent work related to edge computing [18], they are focused on economic and pricing approaches. By contrast, our work was developed to refresh the literature review for applying GT in wireless data communication networks, as well as to study how GT can be applied to emerging scenarios, including the analysis of a few standardized use cases related with MEC. To the best of our knowledge, the current survey is the first to discuss these aspects. Table I presents a comprehensive list of acronyms used throughout our survey. Table I Major Abbreviations Abbreviation 4G 5G Ad hoc Aloha BCG BG BOCF BS CDMA C-RAN CSMA/CA D2D DDoS DSA DSP DTN EGT ESS FBS FC FD FPGA GA
Description Fourth generation of wireless mobile telecommunications technology Upcoming generation of mobile networks Dynamic and decentralized wireless network Medium random access techniques in both WiFi and mobile networks Bayesian coalition game Bayesian game Bayesian overlapping coalition formation game Base station Code division multiple access Cloud radio access network Carrier sense multiple access / Collision avoidance Device-to-device cellular communications Distributed denied of service security attack Dynamic spectrum access Digital signal processor Delay tolerant network Evolutionary game theory Evolutionary stable strategy Femtocell base station Fog computing Full duplex Field programmable gate array Genetic algorithm
5 G-FQL GT GTE H2M HetNet ICN IoT LA LTE M2M MAC MDC MEC MG MIMO mmWave MPLS MPR NBS NC NE NFV NTU OFDMA OSPF PU QoE QoS RL RRH RTT SDN SNMP SP SSN SU TCP TI TU UAV VANET VI VM WiFi WLAN WSN UE
Game-based Fuzzy Q-learning Game theory Game theory explorer Human to machine communications Heterogeneous network Information-centric networking Internet of things Learning automata Long-term evolution mobile access technology Machine to machine communications Medium access control Multiple description coding Mobile edge computing Micro-grid network Multiple-input and multiple-output; it uses multiple transmit and receive antennas to exploit multipath propagation Millimeter wave band Multiprotocol label switching Multipacket reception Nash bargaining solution Non-cooperative Nash equilibrium Network function virtualization Non-transferrable utility Orthogonal frequency-division multiple access Open shortest path first Primary user Quality of experience Quality of service Reinforcement learning Remote radio head Round trip time Software defined networking Simple network management protocol Secondary user Shared sensor network Secondary user Transmission control protocol Tactile Internet Transferrable utility Unmanned aerial vehicle; idem Unmanned aircraft system (UAS) Vehicular ad hoc network Variational inequality Virtual machine Wireless fidelity (IEEE 802.11x) Wireless local area network Wireless sensor network User equipment
Section 2 of the paper briefly presents the more fundamental concepts and models of GT. In section 3, we review the literature related to the application of GT to wireless communications and networking. In Section 4, relevant research challenges related with GT in emerging networking scenarios, such as MEC are also outlined. Finally, section 5 concludes our survey.
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2 2.1
Background Selecting the Right Optimization Technique to Discover the Solution of a Network Problem
Before finding the optimum solution of a network problem, the researcher initially needs to select the right optimization technique to find that solution. For this, she (he) needs to verify if that optimization involves players with common or different objectives. In the case when the players share a common set of objectives, the researcher could select the most convenient optimization technique from the ones listed in the left branch of Fig. 3. Alternatively, if the problem involves players with different objectives and even with completely opposite goals, the researcher should choose the most suitable theoretical game for that problem, as further shown in the right branch of Fig. 3. Network Use Case
Players with similar objective functions
Players with different objective functions
Constrained Optimization
NonCooperative Game
LP and the Simplex Algorithm
Coalitional Game
Convex Programming
Matching Theory
Nonlinear Programming
Auction Theory
Integer Programming
Contract Theory
Dynamic Programming and Markov Decision Process
Bayesian Games with Imperfect Information
Stochastic Programming
Other Special Types of Games
Sparse Optimization
Evolutionary Games
Fig. 3. Taxonomy of Optimization Techniques 2.2
Game Theory Scope
Repeating what was already stated, GT is a mathematical tool that studies the interaction among the players participating in a specific use case. There are two distinct high-level perspectives within GT (see Fig. 4): classical and evolutionary. The classical GT essentially requires that all the players make rational choices among a pre-defined set of static strategies. Consequently, it is fundamental in GT that each player must consider the strategic analysis that the players' opponents are making in determining that her/his own static strategic choice is appropriate. By contrast, a more recent branch of GT - Evolutionary GT (EGT) - states that the players are not completely rational, the players have limited information about available choices and consequences, and the strategies are not static (the strategies evolve). The players have a preferred strategy that is continuously ranked with other alternative strategies. If a player finds a better strategy, then she/he prefers to change to that strategy to get a better reward (so-called fitness). The decision to change the preferred strategy can be also influenced by other neighbouring players belonging to the same population (by observation and learning). In this way, the strategy with the highest selection score inside a group of individuals forming a community will become the predominant strategy for that generation of individuals, and it will be transferred to the next generation of individuals (evolutionary aspect). During the previous transference, some individual characteristics can be changed through selection or mutation operations. A major potential advantage of evolutionary GT compared to the classical one is that the system’s equilibrium could be achieved more quickly. The system’s equilibrium (i.e. game solution) in both
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classic and evolutionary models means a stable system’s configuration, satisfying diverse system requirements and from which no player aims to deviate from. As a player deviates from the system’s equilibrium then that player would be penalized by some form of degradation on her/his payoff (classical game) or fitness (evolutionary game). Table II compares the main elements of a classical game with the corresponding facets of an evolutionary game.
Noncooperative
Pareto Optimality
Classical
Game Theory
Cooperative
Evolutionary
Nash Equilibrium
Evolutionary Stable Strategy
Fig. 4. Distinct Perspectives of Game Theory Table II Comparing Main Characteristics of Classical and Evolutionary Games Classical Game Players (They could be either system entities or optimization objectives with conflicting trends – e.g. delay vs. energy [19]) Strategies Player’s Strategy Set Payoffs The Player’s Strategy Set is static Rational-based Stable equilibrium strategy optimizes either individual payoff or group benefit
Evolutionary Game Individual Organisms Heritable Phenotypes Set of all Evolutionarily Feasible Strategies Fitness Players inherit their strategies and sometimes acquire a novel strategy as a mutation (i.e. Player’s Strategy Set is dynamic) Natural Selection of the fittest group of organisms Evolutionary group strategy ensures stable and high fitness
The GT classical approach can be divided into two dominant branches, namely non-cooperative and cooperative (e.g. coalitional). The essential distinction between these branches is that in non-cooperative GT the basic modeling unit is the individual player, while in cooperative GT the basic modeling unit is a group of several players sharing a common goal but in competition with other groups. The game benefit is also divided in different ways. In a non-cooperative game, each participant gains an individual benefit by default in a selfish way. By contrast, in a cooperative game the benefit obtained by a coalition group is shared among the diverse elements forming that group. In non-cooperative games some incentives to nodes normally selfish to collaborate among them to reach a common goal can be inoculated in those games by either pricing [20]–[23] or reputation [24]–[26]. This collaboration can be useful because the network resources for satisfying high loads are scarce, as is typically the case for wireless networks. In this way, the available resources can be distributed fairly among the diverse users (or competitive flows). Nevertheless, the fair distribution of network resources potentially becomes more difficult to achieve when interference among wireless nodes is also present. Reputation is defined as the amount of trust inspired by a particular node of a network in a specific community or domain [3]. Members with a good reputation, as they positively contribute to the community life, can use the network
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resources without any significant limitation, while nodes with a bad reputation, as they usually refuse to collaborate, are gradually constrained of using the network resources. Reputation systems can be classified as centralized or decentralized, depending where the node reputation is evaluated, respectively, at a central node or at each individual node. The reputation systems offer the main advantage of relying information from multiple sources to evaluate a node’s reputation. So, they are relatively resistant to the diffusion of fake information from a small number of lying/cheating nodes. A significant disadvantage is the considerable waste of node battery and communication bandwidth to support the continuous monitoring and reporting of node behavior. A very recent work [27] discusses further mechanisms besides pricing and reputation to motivate users to actively and persistently participate in a common strategy among them: auctions, lotteries, bargaining games, contract theory, and market-driven proposals. The authors of [28] study how the incentives are provided to the participants’ social friends to stimulate cooperation, rather than directly incentivizing participants themselves. 2.3
Definition of a Classical Game
A classical game can be represented in a normal-form way. This representation assumes a tuple with three elements, (N, A, u), where: N is a finite set of n players, indexed by i; these players make the relevant decisions (i.e. action choice) when the game is being performed; A=A1 x … x An, where Ai is a finite set of actions available to player i. Each vector a=(a1, …, am) is designated an action profile for that player; u = (u1, …, un), where ui is a real-valued utility (or payoff) function for player i. The payoff is a kind of reward a specific player will receive at the end of the game constrained by the decisions of other players. A very popular game is the Prisoner´s Dilemma, visualized in Fig. 5 (i.e. normal form representation). Here two players (namely 1 and 2) have each own two possible strategies: action 1 (to cooperate) and action 2 (to defect). Any payoff values respecting the following conditions, c > a > d > b, define an instance of that game. As an example, if during the current game player 1 chooses to cooperate and player 2 to defect then player 1 receives a benefit valued by b and player 2 receives a benefit valued by c.
Player2 Action 1
Player2 Action 2
Player1 Action 1
a, a
b, c
Player1 Action 2
c, b
d, d
Fig. 5. Prisoner’s Dilemma Using the normal-form representation, the game typically involves a single stage. There is an alternative representation, designated as the extensive form, where the game involves several stages, and each player chooses a strategy at each stage. Details of the extensive form are out of scope for this paper. The Game Theory Explorer (GTE) software, by means of a web interface, allows the creation of games in extensive or strategic form, and the computation of their Nash equilibria [29].
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2.4
Analyzing a Classical Game: from Optimality to Equilibrium
The question that now arises is how to reason about a normal form game. Depending on how the game outcomes are analyzed, there are two possible solutions: Pareto optimality and Nash Equilibrium (NE). As the game analysis is made by an external observer, who is interested in finding the strategy profile that maximizes the sum of players’ utilities, this analysis could return the game as a Pareto optimum. As an example, one can imagine a system allocating a specific resource among a set of players. Pareto efficiency, or Pareto optimality, is a state of allocation of resources in which it is impossible to make any one player better off without making at least one player worse off. Alternatively to the Pareto study, as the game analysis is made by the diverse game’s players, the Nash Equilibrium can be found when no player can improve her/his expected payoff by changing its current static (pure) strategy. The set of non-deviating strategies (one strategy per player) forms a strategy vector (i.e. strategy profile) with n positions, where n is the number of game players. Another way to validate whether a strategy profile is a Nash Equilibrium is to check that the strategy prescribed to each player is a best response to the strategies prescribed to the other players. Depending on the scope (more general or specific) of the equilibrium, the type of game, or the amount of available information about other players’ strategies, there are a few equilibrium types that could be considered as results of a game: these are the correlated equilibrium, Bayesian Nash equilibrium, and subgame perfect Nash equilibrium. Definitions of these are available in [30]. There is also an interesting solution, designated as Mechanism Design, to increase the NE efficiency. The mechanism design alters the original game, e.g. by applying an affine transformation on the utility functions and tuning the associated parameters, to obtain an NE that is more efficient than the one considered in the original game [31]. Comparing both NE and Pareto system designs, one can also conclude that, on the one hand, NE is typically obtained using the same algorithm but instantiated among diverse players. This design involves normally a high cost to obtain the required result due to players behave selfishly. On the other hand, Pareto evaluation requires a more centralized design and assumes a certain degree of cooperation among the players. Due to this cooperation, the cost to obtain the aimed result is minimized. So, there is a need to measure how inefficient is the NE solution in comparison to the Pareto scenario. This inefficiency measurement associated with NE is evaluated as the ratio between the costs of an NE over the optimum cost, i.e. the Price of Anarchy. 2.5
Discussion on Nash Equilibrium
The Nash Equilibrium can be evaluated in both game types: non-cooperative and cooperative [32]. The authors of [30] have studied the probability to find the NE in each game. Initially, in non-cooperative games with incomplete information about the strategies of the opponents, the probability to find the NE decreases as that available information shrinks. This occurs because the lack of available information means less data about the strategy space of the game opponents. Consequently, the moves of the other players are considered in a random way and it is more difficult to obtain probabilistically the game’s NE. In contrast, when a cooperative game is played, the probability of finding the more convenient set of NE increases. In fact, considering a cooperative model, each player has more complete information about the strategy space of others. In this way, a specific player can select the more suitable strategy almost without any conflict, which results in achieving the more convenient NE points with higher probability than in the initial case [32]. Another problem associated with a game’s NE is about its uniqueness. In fact, some games with static strategies have multiple NEs. A method to solve this problem and to guarantee a single equilibrium is by using a mixed-strategy game, i.e. each strategy has associated a specific probability that defines the odds of that strategy to be selected by a game player. For a comprehensive contribution discussing the uniqueness of NE on network games, see [33]. There is a generalization of NE designated as Correlated Equilibrium (CE) that describes a condition of competitive optimality. It requires observation of the history of decisions (or their associated outcomes) to naturally correlate players’ future decisions. This coordination among players in CE can potentially lead to their higher social welfare than making
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decision independently as in NE. Reaching a correlated equilibrium implies the capability of players to coordinate in a distributed fashion as if there were a centralized coordinating device that they all trust to follow. When a game is deployed at the network via a distributed algorithm there is always the need to tune it to find the right balance between network optimization and service fairness (e.g. among customers). A hybrid solution based on a Stackelberg game (network operator is the leader) combined with a coalitional game (each coalition is formed by local customers with similar service expectations is a follower) can be very useful to adopt in these scenarios. Computing an NE is generally hard in a repeated game. The main difficulty of this problem lies in computing the minimax profile because the strategy space of a repeated game is much more complicated than that of a one-shot game. In [34], the authors proposed a new refinement of NE in repeated games, namely the level-k equilibrium, in order to develop tractable and general algorithms to compute the NE of repeated games. Based on this concept, they show that specific Pareto optima of the convex hull of the feasible payoff profiles are NE payoff profiles. The minimax payoff profile is not needed in computing the level-k equilibria. In addition, they prove that there must be at least one level-k equilibrium in a repeated game. Further, according to the folk theorem and the concept of level-k equilibrium, they show that the Pareto front of the payoff profiles must be evolutionarily stable states in symmetric games. They compute the evolutionarily stable states of three repeated games by using their proposed methodology. To discover the solution of a game (often called an equilibrium), e.g. suppose a non-cooperative game, two classes of problem should be considered [35]. The first is the class of Nash Equilibrium Problems (NEPs) where the interactions among players take place at the level of objective functions only. The second is the class of Generalized NEPs (GNEPs) where in addition we have choices available to each player also depending on actions taken by her/his rivals. The NEP is, by far, better studied and “easier.” The GNEP has a wider range of applicability, but sparser results are available for studying it. In this context, the usage of Variational Inequality (VI) can be very useful. VI is a discipline in the field of mathematical programming which provides a unifying framework to study optimization and equilibrium problems [36]. Further information is available in [35]. Also, further information about game solution concept, analysis and algorithm design is available in the following tutorials [31], [37]. Fig. 6 summarizes how a classical game can be represented (strategic vs. coalition) to find a problem´s solution (NE, Pareto, Core, Shapley). Then, the set of available solutions can be studied from diverse perspectives (existence, uniqueness, characterization, efficiency). As a final step, from the previous model analysis, an algorithmic solution is designed to study its behaviour to solve the initial problem (e.g. Best-Response Dynamics).
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Game
Strategic Form
Coalition Form
Find Equilibrium
Find Stable Coalitions & Fair Allocation Within each Coalition
Nash Equilibrium
Pareto Optimality
Core
Shapley Value
Existence, Uniqueness, Characterization, Efiiciency
Best-Response Dynamics
Mathematical Representation
Solution Concept Solution Analysis Algorithm Design
Fig. 6. Diverse Solutions of Classical Games 2.6
Definition of an Evolutionary Game
We discuss evolutionary-game theory (EGT) to model dynamic games [4]. The term “dynamic” is applied to the strategy of each player. EGT has been developed as a mathematical framework to study the interaction among rational biological agents in a population. In evolutionary games, the agent revolves the chosen strategy based on its payoff. In this way, both static and dynamic behaviour of the game can be analysed [3]. In this way, on one hand, Evolutionary Stable Strategies (ESSs) are used to study a static evolutionary game. On the other hand, replicator dynamics is used to study a dynamic evolutionary game (see more about this below). EGT usually considers a set of players that interact within a game and then die, giving birth to a new player generation that fully inherits its ancestor’s knowledge. The new player strategy is evaluated against to the one of its ancestors and its current environmental context. Also, through mutation, a slightly distinct strategy may be selected, probably offering better payoffs. Next, the player competes with the other players within the evolutionary game using a strategy that increases its payoff. In this way, strategies with high payoffs will survive inside the system as more players will tend to choose them, while weak strategies will eventually disappear. In the following we present a mini tutorial about how EGT can be applied to wireless networks [4]. Formally, we should consider within an evolutionary game an infinite population of individuals that react to changes of their environmental surroundings using a finite set of m pure strategies S = {s1, s2, …, sm}. There is also a population profile, i.e. X = {x1, x2, …, xm}, which denotes the popularity of each strategy 𝑠𝑖 ∈ 𝑆 among the individuals. This means that xi is the probability that a strategy si is played by the individuals. For this reason, X is also designated as the set of mixed strategies. Consider an individual in a population with a profile X. Its expected payoff when choosing to play strategy s i is given by f (si, X). In a two-player game, if an individual chooses strategy si and its opponent responds with strategy sj, the payoff of the former player is given by f (si, sj). In a more generic way, the expected payoff of strategy s i is evaluated by 𝑚 𝑓𝑖 = ∑𝑚 𝑗=1 𝑥𝑗 . 𝑓(𝑠𝑖 , 𝑠𝑗 ), whereas the average payoff is given by 𝑓𝑥 = ∑𝑖=1 𝑥𝑖 . 𝑓𝑖 .
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2.7
Analyzing an Evolutionary Game: from Population Profile (game internal aspect) towards Evolutionary Stable Strategy (result obtained by an external entity)
To analyze an evolutionary game is fundamental for studying the behavior of a special function designated by replicator dynamics. The replicator dynamics is a differential equation that describes the dynamics of an evolutionary game without mutation [4]. According to this differential equation, the rate of growth of a specific strategy is proportional to the difference between the expected payoff of that strategy and the overall average payoff of the population, as follows, 𝑥̇ = 𝑥𝑖 . (𝑓𝑖 − 𝑓𝑥 ). Using this equation, if a strategy has a much better payoff than the average, the number of individuals from the population that tend to choose it increases. On the contrary, a strategy with a lower payoff than the average is preferred less and eventually is eliminated from X. Considering now the mutation issue, suppose that a small group of mutants 𝑘 ∈ [0,1] with a profile 𝑥 ′ ≠ 𝑥 invades the previous population. The profile of the newly formed population is given by 𝑥𝑓𝑖𝑛𝑎𝑙 = 𝑘. 𝑥 ′ + (1 − 𝑘) . 𝑥. Hence, the average payoff of non-mutants will be 𝑓𝑥𝑛𝑜𝑛−𝑚𝑢𝑡𝑎𝑛𝑡 = 𝑓(𝑥, 𝑥𝑓𝑖𝑛𝑎𝑙 ) = ∑𝑚 𝑗=1 𝑥𝑗 . 𝑓(𝑗, 𝑥𝑓𝑖𝑛𝑎𝑙 ) and the average payoff of 𝑓𝑖𝑛𝑎𝑙 ′ ′ mutants will be given by 𝑓𝑥𝑚𝑢𝑡𝑎𝑛𝑡 = 𝑓(𝑥 ′ , 𝑥𝑓𝑖𝑛𝑎𝑙 ) = ∑𝑚 𝑗=1 𝑥 𝑗 . 𝑓(𝑗, 𝑥𝑓𝑖𝑛𝑎𝑙 ). A strategy x is called ESS if for any 𝑥 ≠ 𝑓𝑖𝑛𝑎𝑙 𝑥, 𝑘𝑚𝑢𝑡 ∈ [0,1] exists such that for all 𝑘 ∈ [0, 𝑘𝑚𝑢𝑡 ], the following equation holds: 𝑓𝑥𝑛𝑜𝑛−𝑚𝑢𝑡𝑎𝑛𝑡 > 𝑓𝑥𝑚𝑢𝑡𝑎𝑛𝑡 . In this way, 𝑓𝑖𝑛𝑎𝑙 𝑓𝑖𝑛𝑎𝑙 when an ESS is reached, the population is immune from being invaded by other groups with different population profiles. In other words, an ESS is a mixed strategy that is “resistant to invasion” by new strategies. One can also conclude that the ESS is obtained after a successive set of payoffs analysis was made by an external observer of the game being studied. A very interesting practical scenario to use the ESS result is the one applied to the scenario of a network domain that the operator aims to keep protected from a DDoS attack. In case that domain is following a strategy very near to ESS, the network should continue to operate without problems following a DDoS originated in some compromised internal nodes.
2.8
Evolutionary Solution Performance
Discovering the evolutionary solution can have a huge impact on the system´s performance; this is related to the necessary time to find out the optimum solution of a problem, as well as the amount of energy depleted on each mobile device’s battery to discover the optimum solution in distributed network architectures. As an example, an evolutionary solution based only on a genetic algorithm (GA) to optimize either routing or localization function in a WSN is not a very efficient proposal to real-time applications due to both high delay and resource consumption (e.g. battery) induced by GA’s operation. In this context, other alternative learning techniques, such as the (unsupervised) Reinforcement Learning (RL) could perform better than GA, thus increasing WSN lifespan. On the other hand, a strong advantage of using GA is its easy deployment in digital signal processors (DSPs) or field programmable gate arrays (FPGAs) [38]. Aligned with this aspect, a recent contribution uses GA to enhance the network lifespan of a WSN, by employing a new rotated crossover combined with diverse mutation operators [39]. 2.9
Types of Game
This section briefly presents the most representative games found in the literature, organized in two distinct perspectives: classical and evolutionary ( Fig. 7).
13
Single turn Noncooperative
Classical
Multiple turns
Coalition
Game Theory Cooperative
Bargain Cooperation
Evolutionary
Games with Incomplete Information (Bayesian Games) Fig. 7. Taxonomy of Games Used in this Publication Classical Non-cooperative Games In non-cooperative GT, the fundamental modelling unit is the individual player, including her/his knowledge about the game status, expectations, and possible static strategies. In this game type, the main goal is to evaluate whether there exists a reasonable solution for that game. This solution implies a set of strategies that the players would rationally select for optimizing their own utility or payoff. At this point, it should be clear that a non-cooperative game is defined as a model in which any desired cooperation must be self-enforced. In addition, the players make their decisions in a simultaneous way. So, each player has no information about the decisions of others. Classical Repeated Games A repeated game is a non-cooperative game that is played through a finite number of turns. A historical log is also kept, with all the players’ decisions through the several iterations of that game. We can also classify repeated GT as an extensive form of GT, meaning a player has to take into account the impact of her/his current action on the future actions of others [40]. This special behaviour can enforce some cooperation level among the players, including in the players with no initial intention to cooperate (i.e. selfish players) with others. A repeated game is also sometimes designated as a dynamic game. The authors of [26] propose a taxonomy of applications of repeated games in wireless networks that we summarize in Table III. Table III Taxonomy of Applications of Repeated Games in Wireless Networks [26] Networking Scenario Cellular and WLANs Ad hocs Cognitive Radio Other Scenarios
Main Goals Multi-access; security; QoS Packet forwarding; energy efficiency; media streaming Spectrum sensing; spectrum usage; spectrum trading Wireless networking coding; fiber wireless access; and wireless multicast.
Classical Coalitional Games Coalitional games prove to be very appealing to design fair, robust, practical, and efficient cooperation strategies in communication networks. The main aim behind a coalitional game is that several players choose to form an alliance because they share a common objective and they can do better as a group than by acting alone. We can envision several
14
interesting applications of coalitional games, namely: heterogeneous wireless network access, small cells, D2D communications, Vehicular Networks, dynamic spectrum access, Cloud Radio Access Networks, delay-tolerant networks, and wireless sensor networks. A key design issue in coalitional games is the trade-off between the stability of the coalitions and the network efficiency [3]. Evolutionary Games In an evolutionary game, the game is played repeatedly among the elected agents from a large population. The two major mechanisms associated with the evolutionary process along the diverse population generations are mutation and selection. The mutation (static) mechanism is used to guarantee the diversity of the population. It is entitled Evolutionary Stable Strategies (ESS). The selection (dynamic) mechanism is used to promote the genetic code of agents with higher fitness over other agents with low fitness. In this way, the latter agents tend to disappear as the evolutionary process continues. The selection mechanism is described by replicator dynamics. Games with Incomplete Information (Bayesian) A Bayesian game (BG) is characterized by the fact that information about that game is not common knowledge, allowing concepts such as private information and secret information to appear [4]. Following John C. Harsanyi’s framework, a BG is modelled by introducing Nature as a player in that game. This framework changes the game type: from Incomplete to Imperfect Information, where Imperfect Information means the history of the game is not available to all players. These games are also called Bayesian because of the probabilistic analysis inherent in these games. Players have initial beliefs about others’ payoff functions. A belief is a probability distribution over the possible types for a player. Then, the initial beliefs might change based on the actions the players of the game have played. In a BG, it is necessary to specify the strategy spaces, type spaces, payoff functions, and beliefs for every player. Comparing a BG with a non-BG (both in normal form), the latter only requires the specification of strategy spaces and payoff functions. 2.10
MEC Foundational Aspects
The emerging MEC paradigm aims to support at the network periphery a ubiquitous and efficient access applied to a few number of operational resources, such as: data and/or service storage (e.g. distributed cache, proxies), computational capabilities, and message data transmission. Using MEC, the following aspects can be also addressed: enhance network coverage, enhance network capacity, performing load balancing at backhaul networks, orchestrating the usage of available network/computing/storage resources according the QoS/QoE of end-users, and increasing network lifetime by optimizing the energy consumption essentially at battery-operated devices. The models for distinct entities of MEC systems are comprehensively discussed in [15], including models for the computation tasks, wireless data communication channels and networks, as well as the computation latency, delay on data availability and energy consumption models of mobile devices and MEC servers operating at the network edge. Further advantages of using MEC are highlighted in [18]: It reduces the data traffic, cost, and latency and improves QoS/QoE since cloud resources and services are located close to users. It alleviates the major bottleneck and the risk of a potential point of failure since it relies on a decentralized computing. It enhances security since data is encrypted as the data is moved towards the network edge. It provides high levels of scalability, reliability, and automation. The reader can obtain further information about MEC from different perspectives, such as: standardization [41], industry [42], or academia [43].
15
3
Game Theory in Wireless Data Communication Networks
This section presents a comprehensive literature review on the applications of GT for resource management in wireless data communication networks, using usage scenarios well aligned with the current vision of MEC or FC, namely such as IoT, hierarchical cellular communications, vehicular networks, D2D communications, or smart grids. 3.1
Generic Perspective
We have found in the literature a significant number of surveys about GT being used as an analytical tool for enhancing notable networking features. These relevant publications cover the following areas: wireless networks [44][30][45][46][26][24][47][48][49][50], wireless ad hoc networks [51][52], Wireless Sensor Networks (WSNs) [53][54][40][55][7][56], MIMO systems [57], cognitive-radio [58][59][60], 4G networks [61], smart grids [62][63], telecommunications [64], vehicular networks (see section “Related Work”) [65], and D2D cellular communication [66]. Covering the area of wireless networks where GT is applied, we should mention the following surveys: a comprehensive discussion about GT usage is driven in a network-layered perspective [44]; multiple access games are analysed in [30]; GT models for random access with CSMA are covered in [45]; games about resource management and admission control are addressed by [46]; game theoretical contributions for network selection and resource allocation are available in [24][49][50]; opportunistic communications in hierarchical cognitive networks are the scope of [67]; and finally, evolutionary coalitional games for wireless networking and communications are the focus of the survey in [48], including a further recent related publication [68]. Discussed in [69][70][71][72][73][74] are several game theoretical models that are highly relevant for spectrum sharing. In [75] the authors outline a theoretical framework (taxonomy) to systematically understand and tackle the issue of economic viability of cooperation based on dynamic spectrum management. The authors of [76] propose a constrained coalition formation game, where each UE is a player whose cost is identified as the content upload time. The solution of the game determines the stable feasible partition for the UEs in the cell. Then, the proposed cooperative content uploading scheme guarantees lower upload delays than in the traditional cellular operation mode. In addition, the authors of [26] revise GT for existing cooperation stimulation mechanisms. They also discuss important issues in this field such as false judgment and node collusion. In addition, they argue that the root of these kinds of problem originates from the inability to evaluate accurately the behaviour of a node. In [55] we find a comprehensive revision of the literature discussing theoretical game contributions concerned with energy efficiency in WSNs. In scenarios with very high complexity where different types of agents with various characteristics and requirements want to interact with each other, the usage of conventional GT models can be very difficult to apply. There is an alternative called Matching Theory. For further information, the interested reader can consult [77][78]. A recent work presents a comprehensive multidisciplinary state-of-the-art review and taxonomy of GT models of complex interactions between agents [79]. A taxonomy and research challenges about the design of utility functions for strategic radio resource management games is available in [80]. For absolute beginners in GT, we refer to a recent lecture note [81] with nice MATLAB available code to reproduce some results discussed in that publication, whereas we invite those more interested in a thorough discussion on GT applied to wireless communications to consult specific textbooks [82][3][4][5]. Fig. 8 shows the amount of discussion dedicated to each type in terms of the relative number of publications of each game type in relation to the total number of publications covered by this survey. In the next section, we narrow our survey into the distinct types of games for optimizing the efficient operation of wireless data communication networks.
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Types of Game 11% 10%
NC
36%
Repeated Coalitional
32%
11%
Evolutionary Incomplete
Fig. 8. Types of Game 3.2
Non-cooperative Games
From the vast number of literature contributions in the scope of non-cooperative (NC) games, we have selected significant ones within the following aspects: network resource sharing [46][83][84][85][86], power control [87][88][89][90][91][36][92][93][94][95][96][97][98], medium access control [19][99][100][101][102][103], business model [20][22][23][104][105], routing [106], energy efficiency [88][89][92][93][96][107][108][109][110][111][112][19][113][114][115][116][117], micro-grid [118], proactive network resource reservation [119]. In Table IV all the NC games surveyed in the current publication are grouped in areas, describing their main goals. Additionally, we list in Table V the more important aspects of only some of these games due to limitations imposed by the current paper size. Table IV A Summary of the Area and Main Goals of Major Non-cooperative Approaches for the Resource Management in Wireless Networks Reference
Area
[46][83] [84] [85] [86]
Network resource sharing
[87][88][89][90][91][36][92][93][9 4][95][96][97][98]
Power control
[19][99] [100] [101] [102][103]
Medium access control (MAC)
Goals
[20][22][23][104][105]
Business model
Optimizing the usage of a common pool of constrained resources among a set of consumers, ideally in a fair way. Limiting the interference and increasing the Signal to Noise Ratio (SINR). Energy efficiency Schedule the access to a single communications channel shared among several users. Avoid collisions. External incentive to enhance cooperation. Increase profit.
[106]
Multirate opportunistic routing
Steering traffic through a network for maximizing end-to-end throughput
[88][89][92][93][96][107][108][10 9][110][111][112][19][113][114] [115][116][117]
Energy efficiency
[118]
Security
Study about data injection attacks on smart grids
[119]
Resource management
Advanced resource reservations for the expected number of users
Network’s green-operation
17
Table V Applications of Non-cooperative Games for Resource Management in Wireless Networks Objective
Player
Support inter-operator D2D communications
Among operators
Power control
Among primary and secondary users
They aim to support the distributed optimization of users’ transmission thresholds in queueing wireless networks, depending on the network interference level.
Among users
Strategy Operators make offers about the amount of spectrum committed to the spectrum pool without revealing information to others, and the offers are exchanged by an iterative strategy update algorithm Diminish power consumption of cognitive users with fast convergence of their iterative chaos algorithm Each source node can either transmit to its destination by selecting a frequency (if the corresponding channel gain is higher than a threshold) or be silent and enqueue any new packets. They propose a first algorithm based on a distributed bestresponse Jacobi iterative scheme that runs locally at each user node and ensures the convergence to NE despite real network problems, namely, congestion or asynchronous update. Nevertheless, it shows a poor performance for high levels of interference. Consequently, they studied some alternative
Payoff
Resource
RAT
Operator
Solution
Ref.
Utility Function
Spectrum pool
“5G RATs”
Multiple
NE, socially optimal solution
[86]
Cost function
Spectrum shared among primary and secondary users
Not Specified
Single
NE
[90]
Wireless spectrum (divided into frequency-orthogonal channels)
According to the authors, their model can be used in several scenarios, such as multihop wireless ad hoc networks, interfering multi-cells, and D2D 5G communications.
Not specified
NE
[22]
Each user dynamically (and selfishly) adjusts its threshold-based transmission policy for maximizing its expected throughput.
18
local cooperation among the users in the form of (pricing) message passing, which performs better than the former algorithm despite a high network overhead. Each node can assume a strategy They model the problem of two possible ones: following, of multirate opportunistic meaning the node follows the multi-hop routing as a protocol faithfully; or deviating, strategic game, and study meaning the node retransmits how to guarantee optimal The players of this forged probe messages. The end-to-end throughput game are the The game’s goal is to avoid misbehaving probe messages measure the link when deviating nodes intermediate nodes nodes in the network and maximizing loss probabilities. exist. The source node that are supposed end-to-end throughput. (always following the to forward packets. They use cryptography to protocol) computes the prevent probe messages from routing decision, and pays being forged, and carefully the forwarders for their design a payment scheme to service. enable non-deviating nodes. Each user aims at maximizing Power control for energy its individual EE while targeting Among users Utility Function efficiency (EE) its own power and rate constraint Distributed power allocation scheme for maximizing The actions available to each UE energy efficiency in the depend on the transmit power Utility function measures the energy uplink of OFDMA- based profile of all other users in the efficiency of the link; it is the ratio HetNets where a macroAmong UEs network; each UE maximizes its between the achievable rate and the user tier is augmented with individual link utility (energy equipment overall power consumption. small cell access points. efficiency) constrained by a Depending on the minimum rate requirement location of User Equipment (UE), as well
End-to-end throughput
Not Specified
Not Specified
NE
[106]
Signal-to-interference-plusnoise-ratio (SINR)
“5G RATs”
Single
NE
[88]
Energy efficiency
“5G RATs”
Single
Debreu equilibrium (i.e. Generalized NE - GNE)
[92]
19 as on the available links with their own “energy efficiency”, the UE can connect to either a small cell or the macro cell. It is a NC game with RL methods, in which all source nodes and relays act as players, adjusting their uplink transmit powers to approach an energy efficient data rate vector with maximum spectral efficiency
Source nodes and relays
Each source node has a minimum data rate demand, and individually tries to adjust its own transmitting power to achieve the highest channel capacity, while minimizing the transmit power consumption; each relay node individually adapts its own transmitting power to maximize the network sum-rate while guaranteeing each user’s minimum rate demand.
The utility function of a node is the ratio between the Shannon channel capacity and the total consumption power of that node. Nevertheless, there is a subtle difference in terms of the consumption power when we compare the utility functions of source and relay nodes. The utility of a relay node does not consider the transmission power, and the utility of a source node it does. It is assumed that the relay node has an “altruistic behavior” trying to optimize the network
They propose a beaconing control algorithm in drone small cells to optimize both rate and energy
Played between two UAVs
Each UAV is either in “idle mode” or “beaconing for mobile users on ground”
The UAV’s payoff is the difference between a reward and an aggregated cost. The reward is the probability of successful first contact with mobile users on the ground, while per slot consumed energy to send beacons and to switch the transceiver state are considered as costs
They deal with the problem of allocating the transmit powers at the users and relay for Energy Efficiency (EE) maximization
1 relay against the 3 source nodes acting as a single entity
Choose a transmission power to maximize its utility
The player’s utility is its EE. .
Resource allocation problem
Not Specified
Not specified
This game admits mixed-strategy Nash equilibria, and they propose a Q-learning-based algorithm to achieve one of these equilibria
[96]
[108]
[112]
EE while maximizing the likelihood of getting in contact with the mobile users on the ground.
Not Specified
Two operators
The NE point allows drones to efficiently optimize their energy consumption while maximizing the likelihood of getting in contact with the mobile users on the ground.
Channel
mmWave board-toboard communication system
Not Specified
NE
20
Each player has a cost function. To find the optimal trade-off solution, they define a bargaining problem in which each optimization problem represents a player (i.e., the energy player and the latency player). The bargaining problem is a problem of understanding how several agents should cooperate when noncooperation leads to Paretoinefficient results. The solution of this problem coincides to the solution that an external referee would recommend
They investigate the inherent trade-off The players are the between energy performance consumption metrics (energy and end-to-end delay and delay) instead from a GT perspective for of the individual duty-cycled MAC nodes protocols in low data rate wireless networks.
Each player threatens the other by using his best optimal point obtained from a NC game in which the player finds his best optimal operating point (e.g. the delay player obtains its lowest delay at the cost of increasing energy consumption)
They consider the uplink of a hybrid heterogeneous network with femtocells overlaid on a macrocell, and formulate a two-layer game theoretic framework to maximize the energy efficiency while optimizing the network resources. In the first game, each Femtocell AP (FAP) decides between mmWave and UHF frequency bands with the goal to optimise its data rate forming a NC game. The second game incorporates the user association to maximise the sum-rate and network energy efficiency.
FAPs aim to connect with the MUEs to reduce the interference The utility function of the mth FAP is the and maximize their rates. The sum-rate of the FUEs and the MUEs second game incorporates the connected to it. The users evaluate their user association to connectivity with the goal of maximize the sum-rate and maximizing their rates without affecting energy efficiency of the the network performance. network.
The first game is played among all FAPs. The second game is played among the users.
Channel access
Not Specified
Not Specified
Nash Bargaining Solution (NBS)
[19]
Choose access technology (UHF, mmWave); User association to FAP/MBS
“5G RAT”
Not Specified
NE
[113]
21 They study the problem of energy charging using a robust Stackelberg game approach in a power system composed of an aggregator and multiple electric vehicles (EVs) in the presence of demand uncertainty.
They consider a network where multiple unmanned aircraft systems (UASs) collect data from ground sensor nodes as the formers fly in annular trajectories.
They propose a clusterbased approach for maximizing the energy efficiency of wireless small cell networks.
The aggregator and EVs are respectively the leader and followers of the Stackelberg game.
The aggregator seeks to maximize its utility by setting an appropriate price to sell its available energy to plug-in hybrid EVs when guaranteeing the energy demands of the plugin EVs. Each EV chooses its own demand strategy to maximize its own benefit selfishly.
The aggregator sets its optimal price in response to the Variational Equilibrium energy demands of the SEVs, which represents the optimal global solution (RSE) of the proposed robust game. As the price is above the pay-off threshold of the EV k, then the EV k will stop charging the energy from the aggregator without buying the amount of energy.
Battery charging
Not Specified
Not Specified
Robust Stackelberg Equilibrium (RSE)
[115]
It is formulated a theoretic game to maximize the energy efficiency with fairness among cluster heads (CHs). They also use adaptive modulation. It enables transceivers to transmit more data for the same transmission power under the condition that the channel conditions are favorable, i.e., SNR level is high.
Each CH aims to increase its individual utility function.
The utility function of each CH is the throughput per energy
Energy efficiency and throughput
Not Specified
Not Specified
NE
[116]
Among clusters
Due to the lack of intercluster communications, clusters compete with one another to improve the overall network’s energy efficiency. This intercluster competition is formulated as a NC game
The clusters seek to minimize their respective cost functions. The cost function captures the individual energy consumption and the flow level performance in terms of the fractional time required to transfer the traffic load
Game captures the tradeoff between energy efficiency and flow level performance.
“5G RATs”
Single
NE
[117]
22
They propose a model for data injection attacks with multiple adversaries and a single smart grid defender
They propose a model to reserve in a proactive way network resources for the expected users
The defender’s goal is to reduce A Stackelberg the effect of potential attacks on game is proposed the system while optimizing a in which the utility function that captures defender acts as a both the benefits and costs of the leader that can chosen defense strategy. In anticipate the response to the leader’s strategy, actions of the the attackers play a NC strategic adversaries, that game in which each attacker act as followers, chooses its optimal attack before deciding on scheme to maximize the tradeoff which between the benefits, obtained measurements to from prices’ manipulation, and protect. costs associated with the attack.
They consider a random number of players (users)
Each user decides whether to make Advance Reservation (AR) or not based on her own lead time and on statistical information about others
The defender aims to minimize a cost function that captures the variation between the day ahead (DA) and real time (RT) market locational marginal prices (LMPs) in the system. The payoffs of the different attackers are interdependent. In fact, an attacker can collect financial benefit or endure loses due to the strategies played by other attackers.
Understand the interdependencies among multiple attackers and their impact on the power-grid’ s performance
Not Applicable
Single (grid’s owner)
Stackelberg equilibrium
[118]
The user’s payoff that gets service is 1−C if she chooses AR and 1 if she does not choose AR. The cost (C > 0) reflects all aspects of making reservation. A user that does not get service in her desired slot leaves the system with zero payoff.
Connectivity service
Not Specified
Not Specified
NE
[119]
23
Discussion about recent work using NC games In the following text, we discuss selected literature in diverse use cases with selfish players. The discussed work is related with spectrum sharing [86], power control in either one-hop [90] or multi-hop [96] uplink cellular communications, media access protocol [19][22], multirate opportunistic routing [106], energy efficiency [88], scheduling of beacons (discovery signals) for competing drones [108], and supporting resource reservations according to expected load [119]. The communications on the network edge requires mitigating the interference not only within a cell but also among cells. This interference mitigation is very important to optimize the usage of network resources. In [86] they study spectrum sharing for D2D communications in scenarios such as public safety and vehicular communications. The pool of shared spectrum is obtained from distinct mobile operators involved in a NC game that analyses possible negotiation strategies among them. The mobile operators submit proposals to each other in parallel until a consensus is found. The authors reach the following conclusions: i) the existence of a unique equilibrium point will occur when every mobile operator has a concave utility function on the box-constrained region and all eigenvalues of derivatives of iterative response process are less than unity. In the case a mobile operator does not fulfil the previous conditions then it cannot be accepted within the network since its participation could cause the existence of multiple equilibria which is undesirable; ii) the iterative algorithm based on the mobile operator’s best response might not converge to the equilibrium point due to myopically overreacting to the response of the other mobile operators; iii) alternatively, when the Jacobi-play iterative algorithm for updating the mobile operators’ strategies is used with a proper smoothing parameter, then all mobile operators experience performance gains compared with the scheme without spectrum sharing. The Jacobi-play strategy update assumes that all players adjust access probabilities in a specific direction, depending on the measured congestion level of the network, and towards the best-response strategy; iv) In this game asymmetric mobile operators could contribute with an unequal amount of resources to the spectrum pool; v) The authors also assume that the iteration converges much faster than any change detected in the channel. At the network edge is also relevant to control the transmission power of cognitive nodes. In [90] they propose a new chaos based cost function to design power control algorithm and analyse the dynamic spectrum sharing issue among secondary users for their uplink communications through cellular cognitive radio networks. They specify utility/cost functions considering the interference from and the interference tolerance of the primary users. They show that their power control game rapidly converges to a single NE. This result is obtained in parallel with a reduction on the power consumption of cognitive terminals at the expense of small drift (1–3%) from the target SINR in comparison with other existing game algorithms. The authors of [96] use NC game theory paired with RL methods, to investigate the problem of power allocation in the uplink communication at both source and relay nodes on a multiple-access multiple relayed wireless scenario. The main goal of this model is to achieve a good performance in terms of both energy efficiency and overall data rate. We have assisted to a significant increase on the number of wireless networks operating at the network edge. This requires a more intelligent and flexible MAC that could tune MAC system parameters (e.g. sensor wakeup period) to reach a fair equilibrium point that minimizes both the system latency and energy consumption [19]. This also means a denser spectrum usage that requires more innovative ways to reuse that spectrum and minimize the interference among the wireless transmitters in case of competitive transmissions [22]. In [19] they use a theoretical game formed by two players. Interestingly, these are related to performance network metrics, such as energy and delay. These performance metrics have conflicting operational trends among them. On one hand, the delay is minimized at the cost of increasing energy consumption. On the other hand, the energy consumption is minimized at the cost of increasing delay. Consequently, these two metrics have been modelled as the players of a NC game to solve a conflicting multi-objective optimization problem in energy-constrained, delay-sensitive wireless sensor networks. Increasing the sensor wakeup period reduces the energy consumption but increases the end-to-end (e2e) delay. They tried to solve their game over a duty-cycled MAC protocol with the length of the wake-up period as the single parameter to be optimized. They have found the Nash bargaining solution (NBS) to assure energy consumption and e2e delay balancing. As a final game result, given the two performance requirements (i.e., the maximum latency tolerated by the application and the initial energy budget of nodes), the proposed game framework allows to set MAC tuneable system
24
parameters (e.g. sensor wakeup period) to reach a fair equilibrium point that minimizes both the system latency and energy consumption. The authors of [22] studied the scenario of Network Utility Maximization (NUM) applied to a mobile cell with interference among the terminals within that cell, when some cooperation among the users in the form of (pricing) message passing is allowed. The NUM is a distributed algorithm for the resource allocation in a constrained network with the global objective of maximizing the total utility of users connected to that network. Using NUM, they aim to maximize the sum-throughput of the users with respect to the transmission thresholds. In this way, they propose a distributed pricing-based algorithm that converges to a stationary solution of the NUM while requiring only limited signalling among the users. This algorithm is more suitable in “collaborative” contexts, where users are willing to exchange some (limited) information (e.g. accepting some overhead and privacy loss) in favour of better performance. From their experiments, they have also concluded that in networking scenarios with “high” interference, the cooperation among the users via pricing enhances the network performance. Further work is envisaged by the authors such as multi-hop wireless networks. Article [106] explores the combination of two possible features of wireless networks: multi-rate and opportunistic routing. The multi-rate feature is related with the multiple transmission bit rates specified by IEEE 802.11 protocols. The opportunistic routing allows any node that listens to a previous packet transmission to participate actively in packet forwarding. Aggregating these two features and as everyone follows the routing and incentive protocol, the system performance gets optimized and each node gets its payoff maximized. Specifically, the incentive protocol works as follows. They added to the network some probe messages, which measure the link loss probabilities, with a cryptographic component to prevent the probe message from being forged, and design a payment scheme to guarantee that the nodes cannot benefit from manipulating the link loss probability measuring process or deviating from the routing decision. So, the spirit behind this incentive protocol is by accepting some network overhead due to the extra probing traffic among the nodes, and maximizing the global network performance. Further work is required to protect this proposal from collusion among diverse nodes. In [88] the authors have proposed a framework to develop centralized and decentralized power control algorithms for energy efficiency optimization in multi-cell massive MIMO networks with the presence of relay nodes involved in multicarrier communications. From their results, they have concluded that centralized algorithms are quite robust to the enforcement of demanding rate constraints. Instead, the distributed algorithms are more sensitive to rate constraints, especially for increasing maximum feasible powers, due to the lack of centralized interference management. Also, the centralized algorithms perform better than their distributed counterparts, both with and without rate constraints, at the expense of a higher computational complexity and feedback requirements. A challenging problem still needs to be solved. It is necessary a suitable optimization framework to effectively determine the global solution of energy-efficient optimization in interference-limited networks. In [108] we find a study about the scheduling of beacons (discovery signals) from an energy efficiency perspective and a algorithmic model based on a NC GT for competing drones. From the literature, a vast number of games from the literature assumes that the number of players is fixed and known by everyone. However, in some networking scenarios when it is necessary to reserve resources in advance, users typically do not know how many other users will compete for those same resources. Therefore, to model this situation, the authors of [119] propose a NC game where at the beginning of that game the number of players is completely random. This game studies the strategic behavior of users in systems supporting advanced reservations and the impact of the network provider’s decisions on the behaviour of its users. The authors considered several aspects of this model, including pricing, information sharing, and learning, on the economic equilibria and the dynamic behavior of the system. This work as novelty incorporates the fact that the strategic behavior of customers in making advanced reservation is driven not only by their prices, but also by their beliefs about other customers’ decisions. In addition, this game has several NE, where in some of these the provider could obtain a null profit. To avoid this, the provider may opt to be risk-averse and set a price yielding sub-optimal but guaranteed revenues.
25
Summary A system designer before choosing a NC game to support the more correct operation of wireless networks should be aware that this choice offers advantages but it could also imply some disadvantages. On one hand, the main advantages are, namely: Wireless nodes compete for a limited set of network resources Obtain a more robust distributed control algorithm in comparison with the centralized game option Diminish the signalling network traffic due to local processing in each node On the other hand, the main issues that the same system designer should be aware of, namely are as follows: Absence of learning as the game is played simultaneously by all the users during a single interval of time Selfish user behaviour can be naturally induced by the lack of information about other players Difficulty in attaining a global system optimization due to the distribution From all the NC games surveyed in the current publication, we highlight the following because they are associated to emerging usage scenarios: WSNs [19], 5G modelling [22][86][88][92][112][113][117], UAVs [108][116], and powergrid [115][118]. Some fundamentals about NC games that can be used in wireless and communication networks can be found in [3], [4]. The next sub-section reviews the existing repeated (learning) games for cognitive cellular networks where namely energy efficiency is a main concern. 3.3
Repeated Games
A repeated game (RG) is an effective tool to avoid potential conflicts among wireless nodes. The occurrence of these conflicts leads to selfish behaviors, resulting in poor network performances and detrimental individual payoffs. Contrary to static one-shot games that model interactions among players during a single time interval, in RGs, interactions of players repeat along multiple time intervals. Thus, the players become aware of other players' past behaviors and their future benefits, and they can adapt their strategies accordingly, resulting in better system performance in a long-term basis. In wireless networks, conflicts among wireless nodes can lead to selfish behaviors, resulting in poor network performances and detrimental individual payoffs. To address this problem, the use of RGs with the aid of a convenient incentive mechanism can encourage wireless nodes to adopt more cooperative strategies, thereby improving network performance and avoiding network disruption due to selfish behaviors. Aligned with these goals, the authors of [26] survey a considerable number of RGs in different wireless networks. A very important advantage of using a RG is to enforce learning at cognitive nodes in a NC game with incomplete and imperfect information [120]. With this learning, the game evolves to a state where the interference is mitigated and QoS requirements are fulfilled. In addition, [7] also revises RGs but within a more specific scope related to security. From the literature in the scope of RGs, we have surveyed and divided it in two parts, namely: non-cooperative and cooperative, as discussed below. Discussion about recent work using Non-cooperative repeated games From the literature in the scope of NC RGs, we have selected some recent contributions with the following main goals: cognitive radio access channel among nodes with imperfect information [121]; spectrum oligopoly market where each primary individually defines a channel-price based on its quality [23]; adaptive popularity-based video caching algorithm at the network edge [122]; spectrum trading scheme based on supply and demand trends for both service providers and D2D users [123]; multi-flow multicast scenario in cellular networks [124]; beaconing control algorithm in drone small cells to optimize both rate and energy [108]; resource allocation enabling D2D communications to reuse the available cellular primary spectrum [125]; a new solution to develop tractable and general algorithms to compute NE of RGs [34].
26
The NC RGs we have selected are discussed more comprehensively as follows. In [121] the authors propose a RG to model a distributed algorithm that enables an opportunistic channel selection by cognitive wireless nodes under imperfect observations, limited memory, and without any centralized coordination. The authors of [23] show that price competition does not lower the payoff of primary players (that uses licensed spectrum) in a repeated subgame. Article [122] considers two cognitive aspects regarding the problem of distributed caching with limited capacity in a content distribution network. Firstly, a nonparametric learning algorithm is proposed to estimate the request probability of videos from past user choices. Secondly, using these estimated request probabilities, the adaptive caching issue is elaborated as a NC RG in which servers autonomously select which videos to cache. The utility function makes a tradeoff between the placement cost for caching videos locally and the latency cost associated with delivering the video to the users from a neighbouring server. The game is nonstationary as the preferences of users in each region evolve over time. The authors then propose an adaptive popularity-based video caching algorithm that has two timescales: i) slow timescale corresponds to learning user preferences; ii) whereas fast timescale is a regret-matching algorithm that provides individual servers with caching prescriptions. It is shown that, if all servers follow simple regret minimization for caching, then the network achieves a correlated equilibrium. This means servers can coordinate their caching strategies in a distributed fashion similarly to a centralized coordinating device that all they trust to follow. In [123] the authors have investigated a cellular network consisting of a BS, multiple cellular users and a D2D pair of users that communicate using licensed spectrum resources. They have introduced a new spectrum trading scheme based on supply and demand curves for service providers (SPs) and D2D user. The game model has been formulated and it has been shown that the game has a unique NE point under a certain condition. Furthermore, a gradient based learning method has been proposed for decision making of the SPs and the D2D user in incomplete information case, when they only have the historical information of the price. In fact, the stable point of the learning dynamics is the NE point of the game. Simulation results show that increasing the channel quality results in more profit for SPs. This is a suitable incentive for SPs to offer bandwidth in high quality channels to improve their economic performance and satisfy their users. It is also shown that the higher learning rates may lead to faster game convergence. Moreover, increasing the learning rate from a specified threshold will result in the instability of the game. Furthermore, the authors have extended their model to the multiple D2D case. The authors of [124] address the resource allocation problem in the multi-flow multicast scenario in a cellular networking environment. To configure the multicast and achieve optimal resource allocation, the BS requires the feedback of the channel-quality information (CQI) from the users. There is an incentive mechanism to users report the channel quality in a truthfully way. This mechanism is based on both a pricing scheme and a weighted water-filling resource allocation. In [108] the authors aim to fix the beaconing time period of two UAVs acting as airborne access points to optimize both energy efficiency and rate. They study the scheduling of beacons transmitted by two UAVs acting as drone small cells for two distinct scenarios, temporary events and disaster-relief activities. To study the first scenario, they proposed a NC game and characterized the equilibrium beaconing period durations for the competing drones. Next, for studying the second scenario, they described a fully distributed mechanism that allows each drone to self-discover its equilibrium beaconing strategy without any knowledge of its opponent’s scheduling decision. The equilibrium point of each game allows drones to efficiently optimize their energy consumption while maximizing the likelihood of getting in contact with the mobile users on the ground. Some aspects of this work that can be enhanced are as follows: i) the UAV backhaul is a satellite link with high latency and limited rate; ii) they not discuss the energy consumption in each UAV associated to the satellite interface. Article [125] proposes a game-theoretic resource allocation scheme to address inter-cell interference with multiple cell settings in a mobile networking environment. The authors study the coexistence of D2D and cellular transmissions that can mutually interfere when D2D reuses the available cellular spectrum. They characterize Base Stations (BSs) as players
27
competing for resources allocation quota of D2D demand, and define as a novelty the utility of each player as the payoff gained from both cellular and D2D. The authors of [34] have proposed a new solution to develop tractable and general algorithms to compute NE of RGs. This new solution appears as a more viable alternative when compared with the solution that computes the minimax profile, which is an NP-hard problem in RGs, such as the iterated Prisoner's Dilemma. In Table VI are summarized the advantages and disadvantages of major approaches for NC RGs. Table VI Advantages and Disadvantages of Major Approaches for Non-cooperative Repeated Games Reference [121]
[23]
[122]
[123]
[124]
[108]
Advantages -Support non-homogeneous channel usage by the primaries. -Support imperfect private monitoring and limited memory for secondaries sensing/access the channel. -Proposal evaluated with real values of spectrum occupancy. -Primary selects a price depending on channel transmission rate. -Guarantees NE uniqueness. -Price competition does not lower payoff in a repeated game. -Propose an adaptive popularitybased video caching algorithm in servers at the network edge with two adjustment timescales: slow related with learning from past user preferences, and fast related with server load, behaviour change. -It is reached a correlated equilibrium which implies a coordination among the distributed edge servers like a centralized coordinating device. -Proposal evaluated using real data from YouTube. -The convergence of the learning decisions to the NE (only for the complete information case) is analyzed using Lyapunov theory, meaning this analysis is based on the perceived players’ utilities. Consequently, it does not require knowledge of the past decisions. -Results illustrate that higher learning rates may lead to faster network convergence. -It is proposed a multicast resource allocation mechanism with the designs of the accesscontrol pricing scheme and the weighted water-filling resource allocation. These guarantee users report quality in a truth way. -They study the scheduling of
Disadvantages -The statistics of primary user duty cycle are assumed to be known to the autonomous CNs.
-Channel parameters, transmission power and channel gain, are static for all the secondaries.
-Assumes non-misbehaving players. -Require coordination traffic among the edge servers which could be difficult as a multi-operator scenario is being used. -Other types of traffic distinct from video are not supported. -Energy efficiency was not considered.
-It is restricted to multiple D2D communications within a single cell. -All the coordination work is done at the BS which is a bottleneck as the users scale up. -When devices aiming to establish a D2D session send spectrum requests to the BS, these requests could create interference in others and increase the cell’s load. -Increasing the learning rate from a specified threshold results in instability of the game.
-To configure the multicast and achieve optimal resource allocation, the BS requires the feedback of the channel-quality information from the users. This feedback can produce network overhead and expose user privacy.
-The UAV backhaul is a satellite link with high latency and limited rate.
28
[125]
[34]
beacons transmitted by two UAVs acting as drone small cells. They aim to optimize both energy efficiency and rate, for both UAVs and mobile ground devices. -They proposed a fully distributed mechanism that allows each drone to learn its equilibrium beaconing strategy without any knowledge of its partner’s scheduling decision (i.e. due to issues in obtaining data from the other). -It proposes a game for resource allocation to address inter-cell interference with multiple cell settings in mobile networks. It studies the coexistence of D2D and cellular transmissions that can mutually interfere when D2D reuses the available cellular spectrum. -It is proposed a novel utility for each player as the payoff gained from both cellular and D2D. -It is proposed a novel refinement of the NE of repeated games, when evolution techniques are also applied. This novel proposal, level-k equilibrium, means not only does any individual player not have incentive to unilaterally change their strategies but also a group of k players has no incentive to deviate from it collectively. It finds a repeated game equilibrium in a simpler way by searching in a less complex domain (payoff) than a more complex domain (strategy).
-They not discuss the energy consumption in each UAV associated to the satellite interface.
-The scenario of multiple cellular users in each cell was not studied.
-The novel proposal is only discussed in terms of symmetric repeated games. -To analyse the game evolution neither mutation nor crossover are considered.
Discussion about recent work using cooperative repeated games From the literature in the scope of cooperative RGs, we have selected some recent contributions with the following goals: To guarantee the optimization of load balancing and energy efficiency optimization for intra-domain routing and, energy efficiency for inter-domain routing [126]; To share available spectrum among LTE-A relay nodes [127]; To schedule network access among mesh nodes [128]; A Bayesian coalitional game with incomplete information was proposed for delay tolerant networks [129]. The cooperative RGs we have selected are discussed more comprehensively as follows.
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In [126] the authors have suggested a multi-objective optimization problem, which solves the trade-off between load balancing and energy efficiency. They use a repeated Nash bargaining game between two players, representing each a system objective (e.g. load balancing, energy) to optimize. The model also considers a threat mechanism among the players to not only guarantee an agreement but also generate a fair solution. Article [127] considers a repeated cooperative game that shares the available bandwidth among diverse relay nodes using LTE-Advanced. The authors of [128] propose a game-theoretic MAC based on an incompletely cooperative game. This model can easily be implemented in mesh nodes. They propose a MAC access model called V-CSMA/CA that operates like CSMA/CA but only manages virtual frames. In this way, as a node decides to transmit a virtual frame, no real frame is transmitted. V-CSMA/CA estimates the collision probability by assuming real transmission of virtual frame. Collision of a virtual frame is detected when other nodes transmit their real frames in the same time slot. In the case of collision, VCSMA/CA goes into back-off mode. Since no real frame is transmitted in V-CSMA/CA, it has no effect on contention of other nodes and no consumption of bandwidth and extra energy occur. If the node has no real packet to transmit, it estimates the game state through V-CSMA/CA. Therefore, nodes have always packets, either real or virtual, to transmit. This means the nodes are always in the saturation mode and they can use the above-mentioned relations to estimate the number of competing nodes and to adjust their strategies of a dynamic BG state to compete for accessing the channel with optimal strategy when transmitting their real packets. With this method, nodes are always ready to transmit their real packets and use the channel efficiently. In [129] a Bayesian coalitional game with incomplete information is considered. The current proposal is a nontransferable utility coalitional game since the individual payoff of each mobile node (i.e., utility as a function of packet delivery delay minus cost of helping other nodes to deliver packets) cannot be given or transferred arbitrarily to other mobile nodes. The main objective of the current coalitional game is to find a stable coalitional structure in a distributed way that despite the lacking of information (real scenario) the actual payoff of each mobile node is close to that when all the information is completely known (theoretical scenario). The formation of coalitions was studied in the context of delay tolerant networks (DTNs). Each node decides to form a specific coalition as it expects the other nodes of that coalition will cooperate with him, forwarding his packets; otherwise, the previous coalition is terminated. In this way, the coalitions in the network vary dynamically. To discover stable coalitions, they also used a discrete Markov chain model. The BG model was also extended to a dynamic game model. In this dynamic game, each mobile device refreshes its beliefs about other mobile devices’ decisions as the cooperative game is played in a repeated way. These beliefs in other devices’ behaviour (e.g. selfish, available to cooperate) are pertinent to a device assume its choice of staying or leaving its current coalition. For this game, the actual payoff of each mobile device is very similar to that when all the information is well known. In addition, the payoffs of the mobile devices when these are organized in several coalitions are, in the worst situation of limited information, equal to the payoffs of the case with no coalitions at the network. In Table VII are summarized the advantages and disadvantages of major approaches for cooperative RGs. Table VII Advantages and Disadvantages of Major Approaches for Cooperative Repeated Games Reference [126]
[127]
Advantages -They study the multiobjective optimization problem for green network routing. -They use a repeated Nash bargaining game between two players. The two players negotiate how traffic should be routed to optimize both objectives. There is a threat mechanism to enhance cooperation among the players and a fair game solution. -It enhances spectrum
Disadvantages -The results of this proposal can be affected as some players deviate from the strategy of changing their threat value (performance thresholds) to improve their performance. -To model the two objectives for green network routing they assume convex, continuous and nondecreasing functions.
-They assume only constant bit rate traffic.
30
[128]
[129]
utilization in two hop cellular networks. -They employ two kinds of games to further strengthen cooperation to optimize spectrum sharing between the different entities, including relays, as follows: punishmentbased RG, cooperative game. -They adapt the basic mechanism of RGs to the bandwidth sharing problem in relaying networks using appropriate utility functions. -They propose new rules to build a stable coalition formation game among all the nodes that improves both the radio capacity per node and in the entire system. These improvements in relation to the NC scenario are more relevant in a loaded cell. -It is proposed an incompletely cooperative game for wireless mesh networks. CSMA/CA is used as a channel access mechanism. -The proposal is initially formulated as a finite RG because a packet can be retransmitted for a few times. -The number of opponents are estimated by using conditional collision probability and transmission probability. These probabilities are computed by the node using two local counters of transmitted data frames (total number of both successfully and unsuccessfully ones). -The cooperation among the nodes is also considered. In a two-node case, one node adjusts its transmission probability to help the other to achieve the optimal payoff. -They studied how cooperative coalition under uncertainty is formed among the players of the game. -They developed a model for dynamic coalition formation among the nodes. -They have achieved the NE condition for the stability of the coalitions using the discrete Markov chain model.
-They assume static values for transmission power.
-The estimation (made about the total number of mesh nodes is accurate only under system saturated conditions (i.e., nodes always have frames to transmit either real or virtual).
-They assume that there is a coordinator at the central application server to collect information about the mobile nodes.
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Summary In this sub-section, we have reviewed the literature of RGs and divided it in two groups: NC and cooperative. A very important aspect that remains to be solved is how to mitigate the negative impact on the network performance imposed by misbehaving players. Other remaining issue is finding a stable and optimum network configuration. In the following sub-section, we review the current coalitional games for diverse aspects of wireless access networks, including resource management in a scalable way after enforcing some level of collaboration among the players. 3.4
Coalitional Games
Coalitional games (CGs) have been applied in wireless networks to design fair, reliable, and efficient cooperation algorithms. One should be aware that to incentivize cooperation among the players of a game, this does imply the usage of a CG. In fact, as an example, a NC game in conjugation with an incentive (or punishment) mechanism can also be used to enhance a cooperative behaviour among the players of that game. In [130] is studied the problem of local cooperative application execution for mobile cloud computing in opposition to the case of moving the task execution to a remote cloud. The main expectation behind the local execution of a task is to reduce the latency associated to the complete execution of that task by diminishing the RTT in comparison with it being processed remotely (at cloud). To encourage mobile devices to share their unused resources, they design an incentive scheme, which benefits both the tasks’ owners and mobile devices helping in the execution of those tasks. To model this scenario, they formulated a NC Stackelberg game that enables task owner (leader) to decide the price that can be offered to mobile devices for application execution and the amount of execution units that each mobile device (follower) is willing to provide. This depends on the follower’s battery autonomy, which is a model constraint. Notably, there are important differences in how the payoff is allocated to each player depending on whether the game is either a NC game with a specific incentive to cooperation or a CG. In fact, on one hand, as a NC game is used, each player receives his own payoff. On the other hand, in a CG the payoff of a coalition (i.e. group of players forming a single cluster) is alternatively divided among all the elements of that group as the game has a Transferrable Utility (TU) [131], [132]. Alternatively, the payoff is not divided among the coalition members because the game has a Non-Transferrable Utility (NTU). This means that the individual payoff of each player cannot be given or transferred arbitrarily to other players due to practical impairments [129][70][133]. Regardless of this, each agent of a specific coalition gets a benefit that depends on the actions chosen by the remainder agents of that coalition. There are three types of coalitional (cooperative) games. The first is designated by canonical games. The main goal of this game is to get the grand coalition of all users. The major potential problem is how to stabilize that grand coalition. The second type is designated by coalition formation games. These games assume that forming a coalition brings advantage to its members but the gains are limited by a cost for forming that coalition. So, the key question is how to form an adequate coalitional structure (topology) and how to study its properties? In addition, the algorithm used by a coalition formation game has typically two functions, i.e. to merge and split coalitions. The convergence time of these functions is very critical for the game scalability. In the third and last type, we have coalitional graph games. In these games the players’ interactions are ruled by a communication graph structure. The key question associated with this game type is how to stabilize the graph structure. In this game, the interconnection between the players strongly affects the characteristics as well as the outcome of the game [134]. In what follows, we discuss recent contributions of CGs to diverse aspects of wireless access networks, such as: small cell networks [69][135][136][137][138], D2D communications [70][76][131][133][139][140][141][142][143][144][145][146], vehicular networks [32][147][148][149], wireless sensor networks [128][150][151], cooperative cellular communications [129][152][153][154], and cloud computing [155][156][157].
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Small cell networks A possible solution to satisfy the problem imposed by high demands of multimedia data over an already deployed mobile cell is to use a deployment choice commonly proposed in 3G and beyond systems, essentially in areas with a huge concentration of mobile users. This choice is based on the usage of femtocells sharing the same spectrum of the macro cells, which raises new challenges, such as interference mitigation and spectrum reuse. CGs could be useful in these scenarios. In [136] the performance of cognitive femtocell networks was enhanced through the hybrid overlay/underlay paradigm. This hybrid paradigm combines the benefits of both the overlay and underlay techniques. More exactly, the hybrid overlay/underlay paradigm utilizes both the non-utilized and under-utilized spectra. In addition, as a novelty from prior work, the authors aim to explore the potential of spatial and frequency reuse of the network to improve the performance of cognitive femtocell networks. They formulate the sub-channel allocation problem as a coalition formation game among femtocell users under the hybrid access scheme with negative externalities, to effectively characterize and mitigate the interference. They also propose an algorithm based on the solution concept of recursive core, and achieve a stable and efficient allocation. The authors in [135] suggested a solution based on an analogy of uplink user association as an admission game between mobile users and BSs who have conflicting interests. They solved the previous conflict using matching theory [78] and CG [158]. In [137], the authors propose a canonical and a CG model as a technique for co-tier interferences mitigation among cooperative small cells. In addition, the authors of [69] propose a CG for the mitigation of both co-tier and cross-tier interferences as well as the resource allocation in dense heterogeneous networks that allows in case of congestion the traffic offload from macrocell base station to small cell base stations. Article [138] considers a dynamic clustering and social-aware user association mechanism in D2D enabled small cell networks to optimize the network throughput considering both network status and social-ties among the users. Their simulation results show that the proposed social-aware user association approach yields significant performance gains, reaching up to 26%, 24%, and 31% for 5-th, 50-th and 95-th percentiles for UE throughputs, respectively, as compared to the classical social-unaware baseline. In Table VIII are summarized the advantages and disadvantages of major CGs applied in small cell networks. Table VIII A Summary of Coalitional Games in Small Cell Networks Reference [69]
Problem -They aim to mitigate cotier and cross-tier interference in operator networks with small cells.
[135]
-Uplink user association in small cell networks.
[136]
-It was proposed a hybrid overlay/underlay solution that utilizes both the nonutilized and underutilized spectra for enhancing the performance of cognitive femtocell networks.
Advantages -Their proposal allows the macrocell base station in case of congestion to offload data traffic to the dense small cell tier. -It is proposed a distributed algorithm that combines notions from matching theory and CGs. -They formulate the subchannel allocation problem as a coalition formation game among femtocell users under the hybrid access scheme with negative externalities, to effectively characterize and mitigate the interference. -They propose an algorithm based on the
Disadvantages -Their work does not support mobility. -The current contribution lacks an admission control mechanism to block users who fail to obtain the minimum requirements, and redistribute the network resources in a more efficient way among the accepted users. -User mobility not supported. -User multi-homing not supported. -They only considered a single macrocell base station. -The cognitive small cells act as secondary users and have a higher priority than primary users but the collaboration between the two tiers is not investigated. -The priority applied can result in a deterioration of the macro-tier performances.
33
[137]
-They aim to mitigate cotier interference among cooperative small-cell base stations
[138]
-They propose a dynamic clustering and socialaware user association mechanism in D2D enabled small cell networks to optimize the network throughput considering both network status and social-ties among the users.
solution concept of recursive core, and achieve a stable and efficient allocation. -They propose operations research game for resource and power allocation in cooperative femtocell networks. -They utilize the notion of social distance to identify sets of socially important nodes acting as the best serving nodes for other nodes within proximity range.
-Cross-tier interference (i.e. from the macro base station to the small cell base stations) is not analysed.
-Their work assumes no power control and the bandwidth is equally shared between the served user devices.
D2D communications Only recently, GT and CGs have been also successfully applied to address the new challenges imposed by D2D communications in mobile scenarios (i.e. these challenges also involve 5G, IoT and mobile edge computing use cases). In particular, in [133] game-theoretic models are applied to D2D radio resource allocation and numerous open issues are identified. They study a coalition formation game with Non-Transferable Utility (NTU), and the mobiles are partitioned into many coalitions, each of which applies a cooperative scheme to maximize their profit. In [140] the authors propose a CG in a scenario of wireless content distribution as an effort to minimize the overall energy consumed whenever a number of mobile terminals seek to download a common content of interest. Article [141] investigates the scenario of uplink radio resource allocation when multiple D2D pairs and cellular users share in an optimized way the available resources, considering a cross-tier interference among primary and secondary users. In [142] a simple CG is studied for energy-efficient D2D communications in public safety networks. In [76], a constrained coalition formation model considers the content uploading time and also includes the coverage constraints for the D2D links so that only feasible coalitions are formed. The authors of [70] introduce a new Bayesian non-transferable overlapping coalition formation (BOCF) game model to study spectrum sharing by D2D communications in cellular networks. This work was extended in [152] to the case in which a mobile device can belong simultaneously to multiple coalitions. Article [143] develops a coalition game-theoretic framework to devise social-tie-based cooperation strategies for D2D communications, which can achieve significant performance gain over the case without D2D cooperation. The authors of [144] design and evaluate a dynamic distributed resource sharing scheme that jointly considers the mode selection, resource allocation, and power control in a unified framework, with the goal of maximizing the available rate under a series of practical constraints in a mobile D2D cellular network that has multiple potential D2D pairs and cellular users. In addition, the authors of [145] are concerned with diminishing the energy consumption on the cellular network with D2D communications. In [146] they proposed a trust-based and social-aware coalition formation game for multi-hop data uploading in 5G systems. A survey of interference management for D2D communication and its challenges in 5G networks is available in [159]. Article [133] comprehensively revises game-theoretic resource allocation methods for D2D. In Table IX are summarized the advantages and disadvantages of major CGs applied in D2D communications. Table IX A Summary of Coalitional Games in D2D Communications Reference [70]
Problem -It is proposed a Bayesian non-transferable utility
Advantages -In this game the D2D users associated with the same
Disadvantages -They assume the conflict-solving rules of the operators and the D2D links with vacant sub-bands for exclusive use are fixed. A possible
34 overlapping coalition formation game for spectrum sharing between the D2D and cellular communications in the network with multiple operators.
[76]
-They investigate relaybased schemes in cellular systems, where multihop D2D communications are exploited for content uploading toward the eNodeB.
[131]
-It is proposed a cooperative game with transferable utilities (TU) to share the idle capacity at the edge of cellular and WiFi networks, helping the users to find the most suitable (multi-hop) path to the Internet.
[133]
-They discuss in a comprehensive way how GT can be applied to study the resource allocation problem for D2D communications. -Cooperative packet delivery in hybrid wireless mobile networks.
[139]
[140]
-The mobile terminals decide autonomously on group formation and content download via locally exchanged information.
operator are regarded as a coalition. -It is assumed (due to complexity of the considered interference management) that each sub-band can be occupied by at most two users (either two D2D peers or one D2D peer and one cellular subscriber). -To find a stable coalition structure in this game, the authors introduce a hierarchical method based on matching theory. -Their main novelty is in the sense that previous multihop routing proposals aimed to optimize a given path metric (e.g., minimize the number of hops, the links cost, etc.), and now in their proposal the multihop path selection considers the presence of self-interested UEs concerned about their own payoff when they act cooperatively (e.g. reducing the upload time). -It departs from similar solutions as it is very flexible, adaptive, scalable, and can be directly extended to include operator controls, e.g., for accounting. -The solution was implemented in a testbed. -Using a CG, they show the D2D communications enable a more efficient (i.e. fewer data message collisions) content distribution among many users. -For multi-hop cellular networks is proposed a distributed algorithm to form coalitions and a Markovchain-based analysis validates the most stable coalitions. -It is proposed a CG in a scenario of wireless content distribution as an effort to minimize the overall energy consumed whenever several mobile terminals download a common content of interest.
improvement on this could be using a two-sided matching market, which enables the operators to adjust their conflict-solving rules to further improve their benefit.
-They do not consider downward traffic.
-The choice of right time intervals to send the network status to the SDN controller via periodic heartbeat messages is very critical: if the periodical interval is too low then it overloads the network; if too high the system is slow to react. In addition, there are significant differences among the system measured parameters, some are slow to change its state, others change more frequently. To avoid these problems an eventtriggered update system could offer better performance than a periodic one does. -As the central SDN controller (central decision engine) fails the system does not work. -They did not discuss the additional time delay and message overhead that need to be considered as extra costs due to the signalling exchange for the formation of coalitions.
-Misbehaving mobile nodes could affect the proposal performance.
-The issues of interference, collisions and mobility support were not covered.
35 [141]
[142]
-The uplink radio resource allocation is studied when multiple D2D pairs and cellular users share in an optimized way the available resources, considering a cross-tier interference among primary and secondary users. -They propose a CG to minimize the energy consumption both in the upstream and downstream cellular LTE communication.
[143]
-They developed a coalition game-theoretic framework to devise social-tie-based cooperation strategies for D2D communications that achieves significant performance gains over the case without D2D cooperation.
[144]
-They design and evaluate a dynamic distributed resource sharing scheme which jointly considers the mode selection, resource allocation, and power control in a unified framework. -They propose a cooperative game framework supporting D2D communications that deals with the content dissemination through a self-organized infrastructure organized in several coalitions. -They propose a trust-based
[145]
[146]
-It achieves the close optimum solution by enhancing the system sum rate by about 20% to 65% without loss of resource sharing fairness compared with other strategies.
-The used resource sharing model only allows the D2D pairs to reuse all the resource of a cellular user.
-It uses an iterative algorithm that decides about the joining of coalitions (i.e. between the coalition with the highest energy consumption and the coalition that guarantees after their eventual join the lowest energy consumption in the current round). This join operation only effectively occurs if after its occurrence the value of consumption energy of that merged coalition is lower or equal than the sum of the consumptions of both individual coalitions. -They proposed an overlay architecture where in the top layer are considered the available “link” connections based on either social trust (e.g. family members at home) or social reciprocity (e.g. passengers of a scholar bus) “connections” and at the bottom layer are considered the physical links and network devices limited by their physical impairments. -Their main goal is to maximize the available rate in a mobile D2D communication cellular network with multiple potential D2D pairs and cellular users.
-Intercell interference was not considered.
-Their results show that using the proposed solution, significant energy savings can be achieved compared with the cellular multicasting case and the NC case.
-They assume that the channel conditions on the D2D links and the cellular links remain approximately constant during the distribution of part of the content (i.e. a low mobility scenario is adopted).
-Up to 86% reduction in
-They assume the eNodeB should store a player trust matrix (PTM)
-A critical task here is to identify the social relationships among device users. To this end, they adopt a network-assisted approach such that two device users carry out the identification process through the cellular communications. This seems to expose private information to the public domain, that can raise some security issues.
-They do not consider link selection for D2D links and sub-band assignment optimization for cellular links.
36 coalition formation game to design opportunistic hopby-hop forwarding schemes, relying on cellular D2D communications, to enhance content up- loading services.
terms of data loss is obtained with respect to the case where the proposed trust model is not implemented.
containing reliability, reputation and trust information to be used by the trust-based coalition formation algorithm. This is a centralized solution with some potential limitations on scalability and robustness.
Vehicular networks The main aspect of a vehicular network is the great difficulty (due to vehicles mobility and limitations on the network coverage) in always maintaining a high-quality coverage by means of the most popular access technologies, e.g. cellular and WiFi. Consequently, a way to mitigate the previous limitation is to enable multi-hop communications in this emerging scenario. To enable multi-hop communications in an efficient way, the cooperation among the vehicles needs to be improved. In this way, coalitional formation games can be very useful to attain those goals. The authors of [147] proposed a cooperative Bayesian Coalition Game (BCG) as-a-service for content distribution amongst vehicles using Learning Automata (LA). The previous work is complemented in [32] by proposing a NC Bayesian coalition game. The last two contributions [147] [32] have convergence time issues due to a exponentially increasing complexity (i.e. number of iterations) in the algorithm to form the coalitions of vehicles. Alternatively, in [148] the algorithm to form the coalitions only requires a single iteration, making it a scalable solution in terms of the number of vehicles, each of which searching for the best access network. The limitation imposed by this proposal is that at a given time, a vehicle is only allowed to use one single network interface. The authors of [149] investigated a reliable message delivery in Vehicular Ad Hoc Networks (VANETs). They model the cooperative service-based message sharing problem in the VANET as a coalition formation game among nodes. Some nodes within a coalition can work as a relay, which is modeled to select exactly one relay among a group of potential relay nodes to improve efficiency of the network in terms of improved packet reception rate and reducing transmission delay. In Table X are summarized the advantages and disadvantages of major CGs applied in vehicular networks. Table X A Summary of Coalitional Games in Vehicular Networks Reference [32]
[147]
Problem -They complement previous work [147]. They also propose NC Bayesian coalition games, using learning automata. -They proposed a Bayesian coalition game as-a-service for content distribution amongst vehicles. The vehicles are the players of this game. The coalitions of this game are formed with several vehicles. A Markov decision process controls how vehicles leave or join a coalition.
Advantages -They assume players could be either cooperative or not.
Disadvantages -The security is an open issue because the contents are exchanged among the vehicles.
-They propose two algorithms to optimize the problem in “two-steps”. The first one is a coalition formation among the automata of three-possible (keep current coalition, move to a new one, rollback to an older coalition) decisions for each vehicle in each game step with the expectation of increasing its payoff. This algorithm creates a set of coalitions. The second algorithm is concerned with how to distribute the content in an effective way inside each
-They assume all the players are cooperative. -The complexity of the coalition formation algorithm is in the order of O(n^N), where n=3 decisions, and N is the number of vehicles. Clearly, this algorithm has issues on the convergence time because this raises exponentially in terms of the number of vehicles.
37
[148]
-They proposed a cloudbased network selection approach to allow performance optimization for vehicles for enabling advanced services.
[149]
-A distributed model is proposed for the cooperative service-based message sharing problem in VANETs.
coalition. -They propose a coalition formation game model for vehicular networks, achieving fairness via built-in utility division rule in the game instead of hand-tuned weighted fairness metric in utility function. -They propose a fast convergence algorithm (i.e. one iteration) for solving a coalition formation game, making possible optimization for larger scale networks and enabling practical implementation of coordinated algorithms in vehicular networks. -A coalition formation game is used together with a network formation game to solve some problems, namely to improve message reception rate and reduce delay.
-At a given time, a vehicle is only allowed to use one single network interface.
-In the proposed model they do not consider the effect of delay in transmission due to a slow server generating a service-message. They also assume that all service-messages have the same transmission delay.
Wireless sensor networks We have found in the literature several CGs to enhance the performance of wireless sensor networking environments. The authors of [55] review the recent literature about using GT, including cooperative and cooperation enforcement games, in wireless sensor networks to achieve a trade-off between maximizing the network lifetime and providing the required service. In [150], a game theoretic method is introduced, namely cooperative Game-based Fuzzy Q-learning (GFQL). G-FQL adopts a combination of both the game theoretic approach and the fuzzy Q-learning algorithm in WSNs. It is a three-player strategy game consisting of sink nodes, a base station, and an attacker. The game performs at any time a victim node in the network receives a flooding packet as a DDoS attack beyond a specific alarm event threshold in WSN. The proposed model implements a cooperative security to mitigate attacks for the sink node and the base station to operate as rational decision-maker players through a GT strategy. Article [151] suggests a security strategy to predict the attacks and their effect using cooperating camera sensors. The model is based on a threshold for the probability of error of the captured scene. This approach provides a solution for false alarm, energy conservation, early attack prediction, and selfish behavior detection. The authors of [128] use incompletely cooperative GT in wireless mesh networks to model the behavior of a hybrid CSMA/CA protocol. Their results suggest that their solution can increase the throughput of a mesh network, as well as decrease both delay, jitter, and packet loss rate. Table XI summarizes the advantages and disadvantages of major CGs applied in wireless sensor networks. Table XI A Summary of Coalitional Games in Wireless Sensor Networks Reference [128]
Problem -They use incompletely cooperative GT in wireless mesh networks to model the behavior of a hybrid CSMA/CA
Advantages -Their results suggest that their solution can increase the throughput of a mesh network, as well as decrease both delay, jitter,
Disadvantages -The estimation (made about the total number of mesh nodes is accurate only under system saturated conditions (i.e., nodes always have frames to transmit either real or virtual).
38
[150]
[151]
protocol. -It is proposed a mechanism designated by Game-based Fuzzy Qlearning (G-FQL). It combines both a CG and the fuzzy Q-learning algorithm in WSNs.
-It analyses the detection performance of eventdriven wireless visual sensor networks that utilize attack-prone scalar sensors in addition to low-complexity image processing.
and packet loss rate. -It is a three-player strategy game consisting of sink nodes, a base station, and an attacker. The game performs at any time a victim node in the network that receives a flooding packet as a DDoS attack beyond a specific event threshold in WSN. The proposed model implements a cooperative security to mitigate attacks for the sink node and the base station to operate as rational players through a GT strategy. -A security strategy is introduced to predict the attacks and their effect using cooperating camera sensors. The model is based on a threshold for the probability of error of the captured scene. This approach provides a solution for false alarm, energy conservation, early attack prediction, and selfish behaviour detection.
-The authors plan to extend the proposed Game-FQL mechanism by incorporating data from various attack types and sources to further enhance its decision-making capabilities to thwart existing or new attacks, potentially also using an evolutionary algorithm.
-They assume that the main source of scalar sensor error is attack rather than harsh environmental conditions, wrong calibrations or component defects.
Cooperative cellular communications Cooperative packet transmission can enhance the throughput in wireless networking infrastructures by taking advantage of the mobility of the users’ devices, essentially at networks with intermittent connectivity, high delay and error rates such the typical case of delay-tolerant networks (DTNs). For such type of network, the authors of [129] investigate the issue of rational coalition formation among devices to transmit packets in a cooperative way to other mobile devices within the same coalition. Each coalition is formed by mobile devices which can be either well behaved or misbehaved. The well-behaved devices always help others for packet transmission. In opposition, the misbehaving devices act selfishly and they do not relay packets originated in other devices. The authors of [152] investigates a cooperative game to study spectrum sharing by D2D communications in cellular networks. This work offers the novelty of a mobile device can belong simultaneously to multiple coalitions. In [153] a CG theory is proposed for determining the rate region of multiple description coding (MDC). MDC introduces enough diversity at source coding level to mitigate packet losses by adding description information. Each description provides a coarse reconstruction of source information at destination. As the number of received descriptions increases, the reconstruction quality would be improved. They show that the non-empty core exists for multiple description coalition game. Moreover, Shapley value is utilized to determine each description's rate. Thus, a fair rate adjustment is obtained that comprises entropy and mutual information of original and reconstructed descriptions. The authors of [154] develop a distributed coalition formation algorithm and analyze the stability of the coalition structure using a Markov chain model for vehicular networks. Simulation results show that, compared with the noncoalition and grand coalition, their distributed coalition formation can improve the Cloud Radio Access Network (C-
39
RAN) throughput by at least 20% and 80%, respectively. They also define the conditions needed for Remote Radio Heads (RRHs) to form a coalition and obtain higher throughput. Table XII summarizes the advantages and disadvantages of major CGs applied in cooperative cellular communications. Table XII A Summary of Coalitional Games in Cooperative Cellular Communications Reference [129]
[152]
[153]
[154]
Problem -They propose a Bayesian CG model to study how the mobile devices should behave in coalition formation for DTNs. These devices can be either altruistic or selfish. -They investigate a cooperative game to study spectrum sharing by D2D communications in cellular networks. -They propose a CG with transferable utility for determining rate region of multiple description coding.
-They study the cooperative interference management among remote radio heads (RRHs) in the cloud radio access network (C-RAN). For this, a coalition formation game is formulated to model the situation in which RRHs of C-RAN can make an individual decision to cooperatively serve their vehicular users (VUs) if the throughput of the RRH can be improved. To obtain the solution of the proposed game, they develop a distributed coalition formation algorithm and analyze the stability of the coalition structure using a Markov chain model.
Advantages -They present a stable coalitional structure for their CG with limited information.
Disadvantages -A Markov chain analyzes the coalition formation. This option has the drawback of being applicable only for the coalition formation with few players.
-A mobile device can belong simultaneously to multiple coalitions.
-They assume that all players in a coalition abide by the entire coalition decision, but this does not hold in real scenarios if we have the same mobile device belonging to two distinct coalitions with non-compatible decisions.
-They show that the nonempty core exists for MD coalition game. -The rate of each description is determined by Shapley value. -A fair rate adjustment is obtained that comprises entropy and mutual information of original and reconstructed descriptions. -The RRHs can form coalitions to mitigate intrainterference and jointly serve their subscribers. To characterize RRH performance under the coalition, this paper develops two signal-tointerference-plus-noiseratio (SINR)based downlink throughput models of RRH, where one adopts tools from stochastic geometry to capture the interference from vehicular users (VUs) belonging to NC RRHs and another one ignores the VU interference.
-They do not support multi-hop cellular communications.
-The convergence of their algorithm follows the complexity of the merge-and-split operations over the coalitions. The complexity of merge operations is (in the worst case) given by R*(R-1)/2, where R is the initial number of NC remote radio heads which for R=20 gives 190 iterations, which is acceptable; the complexity of split operations follows the bell number which has a value smaller than (0.792*R1/ln(R1+1)) ^ R1, where R1 is the number of previously formed coalitions. Analysing the two convergence cases, the worst case in terms of the convergence time of the current algorithm is related with the part that evaluates how the coalitions should be divided to optimize the rate because this last time raises exponentially. As an example, for R1=(5, 20) we have respectively (52, 2*10^14) iterations in the loop for evaluating all the possible split combinations, which shows the solution can be impossible to deploy when R1 increases.
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Cloud computing To support cloud computing (CC) services, which are dynamic and crossing several datacenters, novel challenges have been imposed to the network infrastructures mainly at the datacenters and network edge, such as balancing the user load [160][161]. CGs also seem a good tool to use on CC services. The authors of [155] establishes the incentives for cooperation among the relays and the cloud centralized decoder by formulating a coalition game, leading to a joint optimization of physical layer network coding and enabling simultaneous multi-operator communications in a FC environment [8], [9]. The authors of [155] also presented some simulation results showing that their proposed strategy leads to an improvement of at least 1.5 dB for the sum rate of the network, compared to previous results in the literature. Furthermore, the profit of the players is increased up to 21%, while the solution provided by the proposed algorithm has no profitable deviation, guaranteeing the stability of the partitioning of the players. Article [156] proposes a coalition formation game enabling the cloud providers to dynamically form a stable cloud federation, maximizing their profit. In [157] the authors model the datacenter bandwidth allocation as a cooperative game, toward VM-based fairness across the datacenter with two main objectives, namely: i) guarantee bandwidth for VMs based on their base bandwidth requirements, and ii) share residual bandwidth in proportion to the weights of VMs. Through a bargaining game approach, they propose a bandwidth allocation algorithm to achieve the asymmetric Nash bargaining solution (NBS) in datacenter networks. In Table XIII are summarized the advantages and disadvantages of major CGs applied in cloud computing. Table XIII A Summary of Coalitional Games in Cloud Computing Reference [155]
Problem -They aim to optimize a heterogeneous mobile environment belonging to several operators.
[156]
-They model the cloud federation formation as a hedonic game, a type of CG, satisfying fairness and stability properties.
[157]
-They propose a bargaining game to address the rate allocation for VM-pairs in data centers.
Advantages -They study the incentive for cooperation among the relays and the Cloud-RAN infrastructure by formulating a coalition game to maximize both the sum upload rate of the users and the operators’ profit, allowing nonsymmetric rates. -They design a cloud federation formation mechanism which allows the cloud providers to make their own decisions to form a stable federation yielding the highest total profit. -The VM-pairs, i.e., buyers, participate in an iterative bargaining game to negotiate the rates with the servers, i.e., sellers. Their results show that the proposed approach can satisfy bandwidth demands of VM-pairs up to 99%.
Disadvantages -They impose a strong constraint on players’ mobility.
-The maximum number of iterations on the coalition join/split functions is respectively O(m^3) and O(2^m), where m is the total number of cloud providers.
-It could have a slow convergence speed.
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Summary In this sub-section, we have reviewed the existing literature of CGs at the network edge. The covered topics were the following: small cell networks, D2D communications, vehicular networks, wireless sensor networks, cellular communications, and cloud computing. Some challenging issues for coalition games are how to discover the correct strategy of each player (collaborate, defect) and the necessary time to reach the more efficient formation of coalitions among the players. We have also found in the literature some important contributions that revise game-theoretic models, including CGs, applied to several distinct wireless scenarios, as follows: wireless and communication networks with evolutionary games [43] and without this natural selection perspective [158], cognitive radios [60], radio resource allocation in D2D communication [133], energy efficiency [55] or clustering protocols [56] in wireless sensor networks, and to enhance the collaboration among players via either pricing [128], [162] or reputation [127]. In the following sub-section, we review the available evolutionary games in very diverse networking scenarios. 3.5
Evolutionary Games
Applying evolutionary algorithms to theoretical games allow players with limited-rationality to learn from the environment and take individual decisions for attaining each game’s equilibrium with minimum control exchange. We have found in the literature some important contributions that illustrate how evolutionary game-theoretic (EGT) models may be successfully applied to model a huge variety of networking functional aspects. The authors of [4] review the literature concerning the applications of EGT to distinct network types such as wireless sensor networks, delay tolerant networks, peer-to-peer networks and wireless networks in general, including heterogeneous 4G networks and cloud environments. In addition, [3] discusses selected applications of EGT in wireless communications and networking, including congestion control, contention-based (i.e. Aloha) protocol adaptation, power control in CDMA, routing, cooperative sensing in cognitive radio, TCP throughput adaptation, and service-provider network selection. A comprehensive discussion about finding stable states on evolutionary games is available in [34]. In [61] they discuss the stability of a RL-based distributed mechanism for strategy and payoff learning in 4G networks based on evolutionary game dynamics. Further, a broader perspective in how evolutionary games can be very useful in future wireless networks are available in [48][163]. We have found in the literature games that use evolutionary algorithms in very diverse networking scenarios. From these, we have selected a few with the following main goals: developing strategies for wired [164] or wireless [165][48] cases to use the available resources in the more efficient way, distributed management of networking environments with small cells for optimizing the usage of radio capabilities [68][166], distributed learning to mitigate interference in wireless topologies with Femtocells [66][167], and enhancing cooperation in VANETs [168]. The evolutionary games we have selected are now comprehensively discussed as follows. Developing more efficient strategies for wired/wireless networks Evolutionary algorithms have been proposed for either wired [164] or wireless [165] [169][48] use cases to use the available networking resources in a more efficient way. In [164] they use evolutionary theoretical games to study the necessary network conditions to concurrent transport protocols might either coevolve or not for dealing with the congestion problem. In the latter case, a dominant protocol would be operating at the network. In addition, the authors propose some directions in upgrading the protocols to enable the network operation at an optimum stable state. In [160] they discuss several typical caching scenarios and apply corresponding game theoretical models to illustrate how the selfishness of different parties may influence the overall wireless proactive caching. Efficient caching strategies can be designed by carefully considering the relations and interactions among these parties by using GT. They also outline possible future research directions in this emerging area. The authors of [169] consider NC mobiles, each faced with the problem of which subset of WLANs access points (APs) to connect (and multi-homing) to, and how to split its traffic among them. Considering the many users’ regime,
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they obtain a potential game model and study its equilibrium. They obtain pricing for which the total throughput is maximized at equilibrium and study the convergence to equilibrium under various evolutionary dynamics. They also study the case where the Internet Service Provider (ISP) could charge prices greater than that of the cost price mechanism and show that even in this case multihoming is desirable. Article [48] offers a comprehensive literature revision in evolutionary CG theory applied to wireless networking and communications use cases. Table XIV summarizes the advantages and disadvantages of major evolutionary games in developing more efficient strategies for wired/wireless networks. Table XIV A Summary of Evolutionary Games in Developing More Efficient Strategies for Wired/Wireless Networks Reference [164]
Problem -They study how several congestion algorithms engage on a serious competition among them to use the available network resources..
[165]
-They discuss an evolutionary Game for vehicle-to-vehicle (V2V) caching. In the V2V caching, only users who actively participate in this caching can obtain cached contents from others, and users who participate in V2V caching must keep the contents in storage after watching/using/consuming them.
[169]
-They study user multihoming in a Wireless LAN (WLAN) usage scenario modelled as an evolutionary game.
[48]
-They use evolutionary games for modeling wireless networks, such as opportunistic and cognitive radio networks.
Advantages -They study the cases whether a protocol will be the dominant solution to mitigate the negative effects imposed by congestion or whether two distinct congestion protocols could coexist after some selfadaptation on them. -The choice on this solution is to find evolutionary stable strategies. An evolutionary stable strategy is a mixed strategy for the whole population (i.e. the winner strategy), such that the turbulence of a small proportion of other strategies will gradually disappear in the long-term trend. Examples of these minority strategies are related with a reduce number of users leaving or joining the system. -The authors analyzed the user performance of UDP/TCP throughput with varying frame lengths over WLAN. -They propose a dynamic (evolutionary) spectrum access game. They also explain the open issues and trends in the field.
Disadvantages -They have identified some pertinent model parameters that guarantee, with some set of proper values, the network converges to a stable state. The question to answer is, how to implement these set of parameter values in a real system?
-No results from the proposed evolutionary game were presented and discussed.
-They assume only a single Internet Service Provider (ISP).
-They assumed a homogeneous wireless network.
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Distributed management of networking environments with small cells Evolutionary games have been proposed for optimizing the management of radio resources in networking environments with small cells [68][166]. In [68] they study the spectral coexistence between a macrocell and Femtocells using tools from evolutionary GT and RL. These tools are investigated in diverse scenarios. In the first scenario, Femtocell Base Stations (FBSs) exchange information through a central controller, and adapt their strategies based on their instantaneous payoffs and average payoffs of the Femtocell population. In the second scenario, when information exchange among Femtocells is no longer possible, each Femtocell gradually learns by interacting with its local environment through trial-and-error means, and adapts its strategies. In addition, a variant of the evolutionary game approach (referred to as replication by imitation) is also investigated where Femtocells probabilistically review their strategies and imitate other Femtocells in the network. They finally conclude that the spectral efficiency and convergence to a system stable state are shown to be driven by the type of information available at Femtocells. The authors of [166] propose a new game theoretic framework, where fast interference suppression is decoupled from the relatively slow frequency allocation process to tolerate the delayed control. The key idea is to cast Femtocell clustering as an outer-loop evolutionary game coupled with bankruptcy channel allocation, which drives the cells to spontaneously switch to less interfered clusters. Within each cluster, they design an inner-loop NC power control game, such that the requirement of prompt control is eliminated. The two loops interact recursively with an analytically confirmed stability. Simulations show that their framework can improve the throughput by 13.2% in a network of 200 cells, compared to the prior art. Table XV summarizes the advantages and disadvantages of major evolutionary games in distributed management of networking environments with small cells. Table XV A Summary of Evolutionary Games in Distributed Management of Networking Environments with Small Cells Reference [68]
[166]
Problem -They propose an evolutionary game theory (EGT)-based distributed resource allocation scheme for small cells underlaying a macro cellular network.
Advantages -They develop a distributed algorithm that can be executed individually at every player in an asynchronous manner and with a linear time complexity.
-They propose a NC evolutionary game based on stochastic geometry analysis for small cells resource allocation.
-They propose a new game theoretic framework, where a fast interference suppression algorithm is decoupled from the relatively slow frequency allocation process to tolerate the delayed control. These two processes interact recursively with analytically confirmed stability.
Disadvantages -The performance of the evolutionary-game-based algorithms under information delay is highly subjective to the system and network parameters such as channel gains and number of devices in the network. Nonetheless, evolutionary game models may not be capable of modeling uncertainty and the stochastic nature of parameters such as queue dynamics and non-guaranteed energy supply. Moreover, evolutionary games assume homogeneity of players. Therefore, modeling the interconnection of different types of mobile devices may be difficult. -They assume the signalling exchange between the service gateways (S-GWs) is delay-free.
Distributed learning to mitigate interference in wireless topologies with Femtocells Evolutionary solutions have been proposed for enhancing distributed learning to mitigate interference in wireless topologies with Femtocells [66][167].
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In [66] they introduce two mechanisms for interference mitigation, inspired by evolutionary GT and machine learning to support the coexistence of a macrocell network under-laid with self-organized Femtocell networks. In the first approach, stand-alone Femtocells choose their strategies, observe the behavior of other players, and make the best decision based on their instantaneous payoff, as well as the average payoff of all other Femtocells. They formulate the interactions among selfish Femtocells using evolutionary games and demonstrate how the system converges to equilibrium. In contrast, in the Reinforcement-Learning (RL) approach, information exchange among Femtocells is no longer possible and hence each Femtocell adapts its strategy and gradually learns by interacting with its environment (i.e., neighboring interferers) through trials-and- errors. Their investigations reveal that through learning, Femtocells can selforganize by relying only on local information, while mitigating the interference towards the macrocell network. Besides, a trade-off exists where faster convergence is obtained in the evolutionary case as compared to the RL approach, at the expense of more side information. Finally, it is shown that Femtocells face an interesting trade-off exploration versus exploitation in their learning processes. Article [167] studies the strategic coexistence between macro and Femtocell tiers using tools from evolutionary GT and RL. In the first case, Femtocell base stations (FBSs) exchange information through a central controller, and adapt their strategies based on their instantaneous payoffs and average payoffs of the Femtocell population. A fictitious play formulation is also examined where FBSs maximize their payoffs given the empirical frequency of other Femtocells’ actions. In the second case, when information exchange among Femtocells is no longer possible, each Femtocell gradually learns by interacting with its local environment through trials-and-errors, and adapt its strategies. Variant of the evolutionary game approach (referred to as replication by imitation) is also investigated where Femtocells probabilistically review their strategies and imitate other Femtocells in the network. Finally, the overall performance of the network in terms of spectral efficiency and convergence is shown to be adamantly driven by the type of information available at Femtocells. Table XVI summarizes the advantages and disadvantages of major evolutionary games in distributed learning to mitigate interference at wireless topologies with Femtocells. Table XVI A Summary of Evolutionary Games in Distributed Learning to Mitigate Interference at Wireless Topologies with Femtocells Reference [66]
[167]
Problem -They aim to mitigate interference in a twolayered network environment formed by a macrocell underlaid with self-organized small cells. -The problem of subcarrier and power allocation for small cell networks underlaying a macrocell is formulated as an evolutionary game.
Advantages -They propose a solution that combines both evolutionary GT and machine learning. This adjusts the transmit powers of Femtocells and attenuate the interference. -The authors propose two techniques to attain the evolutionary equilibrium. One is based on replicator dynamics and the other is based on RL. They also study the ‘replication by imitation’ approach to reach the equilibrium and the spectral efficiency.
Disadvantages -This proposal requires that instantaneous information should be exchanged among Femtocells, which is hard to achieve in practice.
-The effect of information exchange delay on the convergence performance of the distributed resource allocation algorithm is not studied.
Enhancing cooperation in VANETs The authors of [168] suggest an evolutionary game to support cooperation in VANETs. They analyze how networking properties can impact the diffusion of cooperation. Simulation results show that higher network connectivity induces higher clustering in the network. This influences the probability of nodes receiving common packets from the
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neighbourhood. The average path length proportional to clustering impacts the benefit sharing in the neighbourhood. Results show that cooperation diffusion in these networks cannot be forced but evolves with different networking conditions. Table XVII summarizes the advantages and disadvantages of major evolutionary games for enhancing cooperation in VANETs. Table XVII A Summary of Evolutionary Games for Enhancing Cooperation in VANETs Reference [168]
Problem -They propose a public goods game (PGG) group interaction model for vehicular networks. They aim to analyse how networking properties can impact the diffusion of cooperation.
Advantages -Results show that higher network connectivity induces higher clustering in the network. This influences the probability of nodes receiving common packets from the neighbourhood. The average path length proportional to clustering also impacts the benefit sharing in the neighbourhood. They conclude that cooperation diffusion in these networks cannot be forced but evolves with different networking conditions.
Disadvantages -They assume a minimum number of twenty seeders to ensure a correct operation of the network.
Summary In this sub-section, we have reviewed the existing literature of evolutionary approaches at the network edge. The covered topics were the following: efficient usage of network resources, small cells, distributed learning to mitigate the interference issue, and enhancing cooperation in VANETs. Some puzzling issue in this game type is how the players should evolve in their actions to allow the network reach in a polynomial time a stable and optimum operation. The most part of the games previously discussed in the current publication are models were the players have access to a complete set of information about the game they are involved in. However, in a significant number of practical scenarios, it is only possible to the players have access to a limited amount of information. Consequently, there is a strong demand to infer in a correct way the missing data. To support this, a new type of game is required. This game is discussed in the next sub-section for diverse scenarios, including hierarchical small cells with D2D communications. 3.6
Games with Incomplete Information (Bayesian)
This section discusses BGs for wireless networking environments. These are games of incomplete information. These scenarios with limited information occur namely, due to the absence of a centralized coordination mechanism. In this way, the dissemination of channel gain information among the cognitive nodes is unavailable or difficult to deploy [170]. Because of this, there is a significant need to players learn the correct weights to calibrate their utility function for optimize the network. The players in BGs select their strategies according to Bayes’ Rule [171]. In [172] is available a comprehensive contribution that is meant to serve as an introduction to Bayesian mechanism design for a novice, as well as a starting point for a broader literature search for an experienced researcher. In the case a game with incomplete information is repeated, the folk theorem [173] can be very useful to find a stable solution for that repeated game. This theorem proves
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that individual rational payoffs of a one-shot game (repeated infinitely) can be approximated by sequential equilibrium payoffs of a long but finite repeated game of incomplete information, where players' payoffs are almost certainly as in the one-shot game. A typical requirement in a networking scenario where players have a limited amount of knowledge about the game status is the most (as possible) correct assessment by a specific player of other players’ choices and their impact on the network performance. From the literature was found very recent games that use Bayesian algorithms in very diverse networking scenarios. From these, we have selected a few covering the following aspects: hierarchical small cells [36][110][121][170][174], D2D communications [123][129][175][176], vehicular scenarios [115][147][177], and efficient resource allocation for IoT / wireless mesh networks [128][178]. The BGs we have selected are discussed more comprehensively as follows. Hierarchical small cells We discuss now some GT proposals that have been proposed to enable the performance of cognitive small cells in scenarios with limited information about the network context. To enhance the performance of a mobile cell, the main idea is to reduce the on-air distance between the mobile terminal and the radio-equipment of mobile operator. As this distance is reduced, the quality perceived by the users about the network connection is enhanced as well as there are significant gains on the autonomy of terminals’ battery. Nevertheless, as small cell base stations (i.e. Femtocells) are densely deployed in the same area already covered by macro cell base stations, the case of interference raises its priority to be successfully controlled and mitigated, as well as the spectrum reuse and finally the practical inexistence of complete information about the state of channels is urgent to be addressed by the algorithms that control the network edge. In [168] they formulate a Bayesian Stackelberg game to model and analyze behaviors of macrocell and Femtocell base stations (MBS and FBSs, respectively). In this game, the MBS is the leader, whereas the FBSs are the followers. The channel information between an FBS and its associated Femtocell user is unknown to the other FBSs. The leader issues the price of interference charged to the followers first to maximize its own profit. Based on the price, the followers decide the strategies to maximize their payoffs defined as the difference between the transmission capacity and the cost of interference (CoI) paid to the leader. Using backward induction, they first analyze the follower game. The existence and uniqueness of the Bayesian Nash equilibrium (BNE) are examined, and the methods to obtain the BNE for a symmetric case are provided. Then, the leader game is analyzed. Finally, some numerical results illustrate the transmission capacity of the Femtocell networks is optimized while the interference experienced at the MBS is ensured not to exceed an interference constraint. Further Bayesian Stackelberg games have been discussed to maximize the capacity of a hierarchical cellular network, considering both imperfect channel state information and interference power constraints [36] [110]. Article [170] studies a power allocation BG for hierarchical small cells. The authors of [121] investigate the issue of how autonomous cognitive nodes (CNs) can arrive at an efficient and fair opportunistic channel access policy in scenarios where channels may be non-homogeneous in terms of primary user (PU) occupancy. In their model, a CN that adapts to its environment is limited in two ways. First, a CN makes imperfect observations (such as due to sensing and channel errors) of their context. Second, a CN has imperfect memory due to constraints in computational tasks. For efficient opportunistic channel access, they present a simple adaptive win-shift lose-randomize (WSLR) strategy that can be executed by a two-state machine (automaton). Using the framework of repeated games (with imperfect observations and limited memory), they show that the proposed strategy enables the CNs (without any explicit coordination) to reach an outcome that: 1) maximizes the total network payoff and ensures fairness among the CNs; 2) reduces the likelihood of collisions among CNs; and 3) requires a small number of sensing steps (attempts) to find a channel free of PU activity. They compared the performance of the proposed autonomous strategy with a centralized strategy and tested it with real spectrum data. In [174] is modelled the dynamic spectrum access (DSA) problem of the secondary users (SUs) as a BG, referred to as the DSA game. They model the primary user (PU) network as a forest where the roots represent the operators and the
47
leaves represent the operators’ sub-bands. This forest analogy is useful to model the market interaction between the SUs and the PU network. In this market, a set of SUs can be first matched to a set of operators and the SUs matched to the same operator can then be associated to the corresponding sub-bands. In this scenario, the SUs cannot exchange information among them or know the PUs’ preferences. The authors of [174] propose a distributed algorithm that results in a stable forest matching structure, which coincides with the optimal Bayesian Nash equilibrium of the DSA game. They prove that the Bayesian hierarchical mechanism associated with the proposed algorithm incentivizes truth-telling by SUs. Table XVIII summarizes the advantages and disadvantages of major BGs for hierarchical small cells. Table XVIII A Summary of Bayesian Games for Hierarchical Small Cells Reference [36]
[110]
Problem -They aim to address simultaneously several distinct network constraints: power (e.g., total and spectral mask), interference (e.g., individual and global), and diverse uncertainty models (e.g., columnwise and ellipsoidal).
-They address both problems of resource allocation and interference management in hierarchical cellular networks, also considering the energy efficiency.
Advantages -They assume a NC setting where the macro base stations (MBSs) and small cell base stations (SBSs) compete to maximize their own capacities considering imperfect channel state information. A robust Stackelberg game (RSG) is formulated to model this hierarchical competition where the MBSs and SBSs act as the leaders and the followers, respectively. They show how the different constraints and uncertainty models change the property of the game (e.g., Nash equilibrium problem (NEP) or generalized Nash equilibrium problem (GNEP)) and accordingly impact the choice of analysis method (e.g., GT or variational inequality (VI)), solution (e.g,. closed-form or numerical), and the design of algorithms and their distributive properties (e.g., totally distributed, semi-distributed, and centralized). -They formulate a Stackelberg game with incomplete channel state information. A backward induction method is used to analyze the proposed game. A closed-form expression of the Stackelberg equilibrium (SE) is obtained for the proposed game with
Disadvantages -The uplink communications are not considered.
-The authors state that a more robust proposal is required against channel estimation errors. To achieve this, the uncertainty associated to a parameter could be modelled as the sum of its estimated value and the uncertain part.
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[121]
-They study the problem of how autonomous cognitive nodes (CNs) can arrive at an efficient and fair opportunistic channel access policy in scenarios where channels may be nonhomogeneous in terms of primary user (PU) occupancy
[170]
-They aim to control the allocation of downlink power in a two-tier cellular network that consists of a macrocell network underlaid by multiple Femtocells.
[174]
-They model the dynamic spectrum access (DSA) problem of the secondary users (SUs) as a BG where SUs cannot exchange information among them or know the PUs’ preferences.
various interference power constraints. -The proposed solution enables the CNs (without any explicit coordination) to reach the following outcomes: 1) maximize the total network payoff and ensure fairness among the CNs; 2) reduce the likelihood of collisions among CNs; and 3) require a small number of sensing steps (attempts) to find a channel free of PU activity. -They formulate a Bayesian Stackelberg game to maximize the transmission capacity of the Femtocell networks while guaranteeing that the interference experienced at the macro base station does not exceed an interference constraint. -They model PU network as a forest where the roots represent the operators and the leaves represent the operators’ sub-bands. This forest analogy is useful to model the market interaction between the SUs and the PU network. -They propose a distributed algorithm that results in a stable forest matching structure, which coincides with the optimal Bayesian Nash equilibrium of the DSA game. -They prove that the Bayesian hierarchical mechanism associated with the proposed algorithm incentivizes truth-telling by SUs.
-They order the channels by the increasing probability of the PU being present. How to obtain this order in a real system? -The authors state that the statistics of PU’s duty cycle are assumed to be known to the autonomous CNs. In practice, the autonomous CNs may obtain the statistics of PU’s duty cycle using geo-location databases. This could overhead the CNs and the network with extra control traffic.
-The scalability of this solution was not addressed.
-They assume that each sub-band (either occupied or unoccupied by a PU) can be accessed by at most one SU.
D2D communications We discuss now some BGs proposals that have been proposed to enable D2D communications. A mobile operator has the opportunity to increase the profit from his mobile infrastructure, including the allocated spectrum, if some mobile traffic is offloaded from the channels established between users’ terminals and macro base stations to other channels that allow a direct communication among user’s terminals, avoiding any intervention of macro base stations [175]. In this way, a mobile cell can support sporadic high loads without any cost/overload increase. The authors of [176] study a cooperative spectrum sharing scenario by allowing secondary users (SUs) to dynamically and
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opportunistically share the licensed bands with primary users (PUs). For rewarding this, a SU relays PU’s traffic to improve the PU’s effective data rate. In this way, they propose a dynamic NC bargaining game with incomplete information. This lack of information occurs because the PU does not have complete information of the SU’s energy cost. Their results indicate that the proposed scheme can lead to a win-win situation, where both the PU and the SU obtain data rate improvements via a bargaining-based mechanism. They assume that the channel gains remain fixed across time slots. In this simplistic way, they only need to consider the average channel condition. Article [123] proposes a spectrum auction where a D2D transmitter bids a demand price-bandwidth curve and each SP offers a price-bandwidth supply curve. In addition, a repeated game enables players to learn despite they have access to only a limited set of information. In [129] a Bayesian CG with incomplete information is suggested in the context of delay tolerant networks (DTNs). Each node decides to form a specific coalition as it expects the other nodes of that coalition will cooperate with him, forwarding his packets; otherwise, the previous coalition is terminated. In this way, the coalitions in the network vary dynamically. Their results show that it is possible to discover a Nash-stable coalitional structure. In addition, the payoff of each mobile device is like that when all the entire game information is available. Table XIX summarizes the advantages and disadvantages of major BGs for hierarchical small cells. Table XIX A Summary of Bayesian Games for D2D communications Reference [123]
Problem -They consider a macro cell base station trading its spectrum with D2D capable users.
[129]
-They propose a Bayesian CG with incomplete information to study the formation of coalitions in the context of delay tolerant networks.
[175]
-They propose a model
Advantages -They formulated an auction game where a D2D transmitter bids a demand price-bandwidth curve and each service provider offers a pricebandwidth supply curve. The NE of the auction game with complete information is obtained analytically. Then, a learning method is proposed for the decision making of the players in the incomplete information repeated game. Moreover, the convergence of the proposed learning method to the NE is studied through the converse Lyapunov theorem. -They propose a method to mitigate the absence of information about other players’ decisions; each mobile device updates its beliefs (cooperate or defect) about other mobile devices when the cooperative game is played in a repeated way. Their results show the payoff of each mobile device is like that when all the entire game information is available. -This game offers a main
Disadvantages -They assume static channels. -All the auction activities are conducted by a central entity, called the broker which is located at the base station. This solution has some weaknesses: bottleneck, low reliability, because a single node decides how the spectrum should be allocated.
-They use a discrete-time Markov chain for coalition formation among mobile nodes. This solution is not scalable.
-To avoid causing interference to the neighbouring cell, they
50 called Bayesian NTU overlapping coalition formation (BOCF) game among nodes with enabled D2D communications. They also assume each D2D link cannot know the instantaneous decisions of others but can observe the decisions of other D2D links in previous time slots. Each D2D link can exploit these observations to establish a belief function about these unknown parameters.
[176]
-They study a cooperative spectrum sharing scenario by allowing secondary users (SUs) to dynamically and opportunistically share the licensed bands with primary users (PUs). In return, an SU will relay a PU’s traffic to improve the PU’s effective data rate. -In this way, they propose a dynamic NC bargaining game with incomplete information. This lack of information occurs because the PU does not have complete information of the SU’s energy cost.
novelty that enables two or more nodes to share their sub-bands between each other for D2D communications and without consulting the macro cell operators. -They propose a hierarchical matching algorithm which can detect whether the sufficient condition is satisfied, which coincides with the overlapping coalition agreement profile in the core of the BOCF game. -Different from previous work, they assume each D2D link should not only choose a specific mode to operate in but also decide a specific operator and sub-band that can maximize its performance in its chosen mode. -Their results indicate that the proposed scheme can lead to a win-win situation, where both the PU and the SU obtain data rate improvements via a bargaining-based mechanism.
assume each D2D link can only share spectrum with the subscribers in its local cell.
-They assume that the channel gains remain fixed across time slots. In this simplistic way, they only need to consider the average channel condition.
Vehicular scenarios We discuss now some BGs proposals that have been proposed in the context of vehicular environments. The main characteristic of a vehicular environment is the great difficulty in maintaining all the time a high-quality coverage by means of the current access technologies available via a heterogeneous (typically cellular and WiFi) network infrastructure. Consequently, a way to mitigate the previous limitation is to enable multi-hop communications in this emerging scenario. Other very interesting and related aspects with this emerging use case are how to dynamically manage the network locations where data (computation power) is stored (available) (at cloud, cloudlet, access points, base
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stations, each vehicle) to optimize the system performance, and how the electrical grid should be controlled to energize the batteries of electrical vehicles in the most efficient way. In [147] they proposed a new Bayesian coalition game (BCG) as-a-service for content distribution amongst vehicles using support from cloud. They have addressed the problem of content distribution to vehicles from the perspective of BCG and learning automata (LA). Content are assumed to be located at the cloud, which is accessed by the vehicles through Internet even on-the-fly. Vehicles are assumed to be the players in the game and form a coalition amongst them using Markov decision process (MDP). For each action taken by an automaton, it may get a reward or a penalty from the environment which updates the action probability vector. Their results show the data distribution among vehicles could be optimized. The authors of [115] study the energy charging in a power system composed of an aggregator and multiple electrical vehicles (EVs) in the presence of demand uncertainty. They propose a Stackelberg game, where the aggregator is the leader and EVs are the followers. They propose two different approaches under demand uncertainty: a NC optimization and a cooperative design. In the robust NC case, they present the energy charging problem as a competitive game among self-interested EVs, where each EV chooses its own demand strategy to maximize its own benefit selfishly. In the robust cooperative model, they formulate an optimal distributed energy scheduling algorithm that maximizes the sum benefit of the connected EVs. They theoretically prove the existence and uniqueness of robust Stackelberg equilibrium for the two approaches and develop distributed algorithms to converge to the global optimal solution independently on the demand uncertainty. Moreover, they extend the two robust models for handling slow variations on the system power. In [177] they investigate a Bayesian Coalition game as-a-service for intelligent context-switching of virtual machines (VMs) in a vehicular cloud for reducing the energy consumption, so that the clients of VMS can execute their services without a performance degradation. In the proposed scheme, they have used the concepts of learning automata (LA) and GT in which LA are assumed as the players such that each player has an individual payoff based upon the energy consumption and load on the VM. Players interact with the stochastic environment for acting such as the selection of appropriate VMs and based upon the feedback received from the environment, they update their action probability vector. The performance of the proposed scheme is evaluated by using various performance evaluation metrics such as contextswitching delay, overhead generated, execution time, and energy consumption. The results obtained show that the proposed scheme performs well with respect to the previous performance metrics. Specifically, using the proposed scheme there is a reduction of 10 percent in energy consumption, 12 percent in network delay, 5 percent in overhead generation, and 10 percent in execution time. Table XX summarizes the advantages and disadvantages of major BGs in vehicular scenarios. Table XX A Summary of Bayesian Games in Vehicular Scenarios Reference [115]
Problem -They studied an emerging system designated by vehicle-togrid. It is based on an electric power system consisting of one aggregator (electrical grid supplier) and several electrical vehicles (EVs) requiring the charging of their batteries. -They designed a Stackelberg game to optimize charging of EVs’ batteries in scenarios where is difficult to anticipate the total energy demand in a
Advantages -In their Stackelberg game, the leader of this game is the aggregator unit of the system and the followers are the diverse EVs requiring battery charging. They differentiate the followers between “heavy” and “light” electrical consumers, giving higher priority in terms of charging to the former ones. -They propose two distinct ways to model this system: the first is based on the selfish strategy of each
Disadvantages -They considered “all possible energy variations using the robust game optimization technique” to obtain (NC and cooperative) games results. But according to the original authors of robust games [179], these can only produce stable results only for a bounded payoff uncertainty set. How accurate could be the game solution of [115] (obtained from a limited set of possible decisions the opponents could choose) for assuming the most correct adversarial realizations of uncertainty in a real application?
52 complete accurate way.
[147]
-They study the content distribution amongst vehicles using support from cloud.
[177]
-They study a cloud scenario where virtual machines are running on the vehicles
EV, and the second one is based on a distributed scheduling algorithm where all EVs actively cooperate among them to obtain the highest amount of energy from the leader. -They designed both solutions to be immune against the situation where some of the parameters used by the optimization algorithms cannot be precisely sampled and/or are time-varying. -They proposed a new Bayesian coalition game (BCG) where the decision of a vehicle to enter or leave a coalition is coordinated by a Markov decision process (MDP). -They propose a hybrid solution, formed by a Bayesian coalition game and learning automata, asa-service for intelligent context-switching of VMs in a vehicular cloud for reducing the energy consumption, so the clients of VMS can execute their services without a significant performance degradation
-The scalability of this proposal was not addressed.
-The data privacy is an open issue to be addressed.
Efficient resource allocation for Internet of Things We discuss now some BGs proposals that have been proposed in the context of Internet of Things (IoT) With the advent of the IoT, the algorithms and protocols that are used in the network edge need to be revisited to rapidly learning how to adapt to the emerging context that is very dynamic and heterogeneous. An example of an algorithm that requires urgent intervention is the one that controls the access to the communications media for the efficient use of network capabilities. The authors of [128] present a novel concept of incompletely cooperative GT and use it to improve the performance of MAC protocols in WMNs. In this game, first, each node estimates the current game state (e.g., the number of competing nodes). Second, the node adjusts its equilibrium strategy by tuning its local contention parameters (e.g., the minimum contention window) to the estimated game state. Finally, the game is repeated several times to get the optimal performance. To use the game effectively in WMNs, the authors present a hybrid CSMA/CA protocol by integrating a proposed virtual CSMA/CA and the standard CSMA/CA protocol. When a node has no packet to send, it contends for the channel in virtual CSMA/CA mode. In this way, the node can estimate the game state and obtain the optimal strategy. When a node has packets to send, it contends for the channel in standard CSMA/CA mode with the optimal strategy obtained in virtual CSMA/CA mode, switching smoothly from virtual to standard CSMA/CA mode. At the same time, the node keeps adjusting its strategy to the variable game state. In addition, the authors propose a simplified game-theoretic MAC protocol (G-CSMA/CA) by designing an auto backoff mechanism based on the incompletely cooperative game. G-
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CSMA/CA can easily be implemented in mesh nodes. Finally, simulation results show that the incompletely cooperative game can increase system throughput, decrease delay, jitter, and packet loss rate, and support the game effectively. In [178] they propose a Bayesian coalition game in an IoT environment. The players of this game have variable learning rates to optimize the decisions they need to take in relation to the most suitable coalition they need to stay. This leads to the achievement of Nash equilibrium in the game quicker than previous proposals when static learning rates were used. Table XX summarizes the advantages and disadvantages of major BGs in efficient resource allocation for IoT. Table XXI A Summary of Bayesian Games in Efficient Resource Allocation for IoT Reference [128]
[178]
Problem -They aim to enhance the performance of MAC protocols in WMNs.
-They aim to study a networking edge scenario with diverse devices forming an IoT environment.
Advantages -They proposed a repeated cooperative game with limited information. Their simulation results show the network performance can be improved. -They propose a hybrid solution formed by a Bayesian coalition game and a learning automata (LA) framework. -They assume the players of this game (i.e. automatons of the LA framework) have variable learning rates in terms of the more suitable coalitions they choose. -The automatons try to harmonize in this stochastic modelled environment two distinct “spaces” (knowledge obtained via learning vs. strategical decisions).
Disadvantages -The payoff was not specified.
-Their proposal can be enhanced for supporting the collection of data from various RFID tags deployed in the IoT environment.
Summary In this sub-section, we have reviewed the existing literature of Bayesian approaches at the network edge. The covered topics were the following: hierarchical small cells, D2D communications, vehicular communications, and efficient resource allocation for wireless mesh networks with sensor devices. Some challenging issues for limited information games are learning and solution scalability in scenarios at the network edge with limited capabilities of connectivity, processing, and data storage. In the next section, we steer our survey into future solid perspectives at the network edge. More particularly, we discuss in how GT can bring positive outcomes to the new paradigm designated by FC or MEC.
4
Future Trends in Applying Game Theory to Fog or MEC
In the last few years, the huge popularity of mobile devices and the exponential increase in mobile Internet traffic have been pushing many innovations in wireless communications and networking. More precisely, the deployment of more dense wireless cells and the advent of 5G [13][14] access technology promise to offer mobile users a gigabit wireless access to data stored at the cloud infrastructure. However, as an illustrative example, this remote access to data has an
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inherent limitation due to propagation delay values in the range of 50-200ms. These delay values are very high for latency-critical mobile applications, such as real-time and interactive ones. Recently, a new model has emerged that aims to diminish the latency to values around 1ms or less. This new research area is called “Fog Computing” [8] (as proposed by CISCO) or “Mobile Edge Computing” (MEC) [15] (proposed by ETSI). In this paper, we use the term MEC. Both proposals aim to integrate the concept of Cloud Computing, namely both storage and computation (virtualized) elastic aspects, into the edge of the network infrastructure and offering a low latency to applications where time-efficiency is very critical. Article [15] presents a research outlook consisting of a set of promising directions for MEC research, including its deployment, cache-enabled, computation offloading, mobility management, green computing, as well as privacy-aware services. The remaining part of this section discusses the same concept from two distinct perspectives: standardization (three initial parts) and academia (fourth and last part). The first part presents diverse categories extracted from the current MEC standardization. Then, we proceed to a second part that outlines distinct use cases associated to the previous categories. In the third part, we also identify some (constrained) functional aspects being disputed by multiple entities that need to be optimized. Some of these optimizations can potentially be performed by GT in future research activities. Finally, the current section is concluded by highlighting the most prominent theoretical game contributions found in the literature which have goals very well aligned with those of MEC. These theoretical game contributions can be a strong basis for further interesting enhancements to develop disruptive MEC services. 4.1
MEC Usage Categories from Standardization
ETSI has defined several main categories for use cases [41]. The potential benefit of the existence of these categories is that the requirements on the architecture are generally quite similar for use cases within the same category, and quite different between the categories. However, [41] argues that all these categories need to be supported to empower MEC as a robust methodology to be deployed across a heterogeneous set of use cases to support a global seamless operation with more capabilities, speed and energy efficiency than current networking solutions. The heterogeneous set of use cases are as follows: connected vehicles including unmanned aeronautical ones, satellite networks, railway backhaul communications, future smart offices, remote real-time health services and maintenance of industrial factories controlled by robots, ultra-dense networks for smart cities, smart metering in the grid obtained via sensors, home automation, and media & entertainment services. There are a few very recent contributions discussing the use cases where MEC can have a significant positive impact [41][42] . As an example, three MEC categories are proposed in [41]: consumer-oriented services, operator and thirdparty services, network performance and QoE improvements. First, the consumer-oriented are innovative services that generally benefit directly the end-user, i.e. the user using the mobile equipment device. Secondly, the operator and thirdparty are innovative services that take advantage of computing and storage facilities close to the edge of the operator's network. Third, the services of network performance and QoE improvements are usually not directly benefiting the enduser, but can be operated in conjunction with third-party service companies. These services are generally aimed at improving performance of the network, either via application-specific or generic improvements. The user experience is generally improved, but in a way, completely transparent to the end-users. 4.2
MEC Use Cases from Standardization
The purpose now is to describe the more relevant use cases of each MEC usage category to derive useful requirements and system design constraints. These constraints will be useful in the next sub-section to identify the MEC challenges that could be addressed applying theoretical games. After that, we continue our discussion by segmenting each MEC usage category.
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Consumer-oriented services The MEC use cases grouped in the consumer-oriented services are listed in Table XXII. We also highlight the system design constraints associated with each use case. Table XXII System Design Constraints Imposed by MEC Consumer-Oriented Services Use case Gaming and low latency cloud applications Augmented reality, assisted reality, virtual reality, cognitive assistance
System design constraints Latency, jitter, computing capacity, storage, host mobility support, transfer of user session Latency, jitter, dynamic virtualization, dynamic contents, user’s location, environment sensorial data, response time, transfer of user session
By placing game server applications closer to the radio equipment, at the edge of the network, a new kind of low latency-based games will become available to end-users. For that, the network device where the game server is running should have enough resources in terms of storage and computing power. While the game is running, one or more users might move around, and be connected to a different radio node (handover). As this is occurring, the connectivity between the UE and the application needs to be maintained. As the user moves away from the original location, the latency between the UE and the application is likely to increase and pass over the maximum delay value. To avoid this, the user session might have to be relocated to another game server located at a shorter distance from the current user location than the initial game server. Augmented reality permits end-users to have additional information from their environment by collecting sensor data, device location, and/or camera information. This information is sent to a server, located at the network edge. This server then derives the semantics of the scene, augments it with additional knowledge provided by databases, and feeds it back to the user device within a very short time. Assisted reality is like augmented reality, but its purpose is to actively inform the user of any matter of interest to her/him. This might be used, for example, to support people with disabilities or the elderly to enhance the interactions with their environment. Virtual reality is similar to augmented reality, but its purpose is to render the entire field of view with a virtual environment either generated or based on recorded/transmitted environments. This might for example be used to support gaming implementations or remote viewing while using the most natural input device available. Cognitive assistance takes the concept of augmented reality one step further, by providing personalized feedback to the user on any activity the user might be performing. As an example, the server located at the network edge can send to the user some useful advice or information helping him performing his activity in a more effective way. In this way, the analysis of the scene and the advices to the user need to be fulfilled within a very short time. For all these cases, i.e. augmented reality, assisted reality, virtual reality and cognitive assistance applications, the session between the user and the application needs to be personalized, and continuity of the session needs to be always maintained as the user moves. In addition, users are not necessarily going to be permanently using the mobile network environment for running their applications. In some cases (e.g. in their home or at work), they might access their applications located in a cloud environment through the local WiFi. However, when a user moves away from her/his indoor environment to an outdoor environment, the session needs to be exchanged from the cloud to the MEC server colocated with the mobile cell covering the outdoor position of that user, and without any disruption. Operator and third party services The MEC use cases grouped in the operator and third party services are listed in Table XXIII. We also highlight the system design constraints for each use case. Table XXIII System Design Constraints Imposed by MEC Operator and Third Party Services Use case Vehicle-to-infrastructure communication Unified enterprise communications
System design constraints Latency, vehicle mobility support, reliability Latency, throughput, reliability, elastic service, location and other environment data
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MEC can be used to extend the connected vehicle cloud into the highly distributed mobile base station environment, and enable data and applications to be placed close to the vehicles. This can reduce the RTT of data. MEC applications can run on MEC virtualized servers that are deployed at the cell radio base station to provide the roadside functionality. The MEC applications can receive local messages directly from the applications in the vehicles and the roadside sensors, analyse them and then propagate (with extremely low delay and in a reliable way) hazard warnings and other latencysensitive messages to other cars in the same geographical area. This enables a nearby car to receive data in a matter of milliseconds, allowing the driver to react immediately. MEC opens services to consumers and enterprise customers as well as to adjacent industries so that they can deliver their mission-critical services over the mobile network. The goal is to develop favourable market conditions that create sustainable business for all players in the value chain, and to facilitate global market growth. To this end, a standardized, open environment needs to be created to allow the efficient and seamless integration of such applications across multivendor MEC Computing platforms. These real-time applications should be offered with low latency, high throughput, in a reliable and elastic ways, and with a proficient awareness of location and other users’ environmental information. The fulfilment of all these requirements ensures that the clear majority of the customers of an enterprise can be served in a highly satisfactory way. Network performance and QoE improvements The MEC use cases grouped in the service category “Network performance and QoE improvements” are listed in Table XXIV. There are also highlighted the system design constraints associated with each use case. Table XXIV System Design Constraints Imposed by MEC Network Performance and QoE Improvements Use case Video analytics Mobile edge host deployment in dense-urban network environment
System design constraints Computational power, latency, security, Latency, compute resources, storage resources, throughput, D2D Communication, traffic offloading, relaying
The video management application transcodes and stores captured video streams from cameras received on the mobile cell uplink. The video analytics application running at the MEC server processes the video data to detect and notify specific configurable events e.g. object movement, lost child, abandoned luggage, etc. The application sends low bandwidth video metadata to the central operations and management server for database searches to fulfil the needs of certain applications. Applications may range from public security to smart cities, respectively from human authorized access (e.g. with face recognition) to car park monitoring. The dense-urban network deployment can be useful to support services in the following areas: eHealth, Media & Entertainment, factory, and Enterprise [42]. First, the area of eHealth will require remote monitoring of health or wellness data, smarter medication, and grid access. Second, the area of Media & Entertainment will require on-site live event experience and collaborative gaming. Third, the factory will require non-time-critical optimizations to realize increased flexibility and sustainability, and to increase operational efficiency. Fourth, in Enterprises we expect seamless intra-/interenterprise communication, allowing the monitoring of assets distributed in larger areas, the efficient coordination of cross value chain activities and the optimization of logistic flows. The final goal is to facilitate the creation of new value added services. As a partial conclusion, the use case of dense-urban network requires low latency and the mitigation of wireless network congestion. To satisfy these requirements, MEC can support D2D communication or traffic offloading. Another useful deployment is the use of Relay Nodes as mobile edge hosts. The MEC can manage these Relay Nodes similarly to other mobile edge hosts, allowing the system to have further options to fulfil the application requirements (notably latency, compute resources, storage resources, and of course throughput).
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4.3
GT Future Trends Aligned with MEC Standardization Use Cases
We present now some thoughts about possible future GT research directions related to the MEC standardization use cases discussed in the previous section. We can resume the challenges in the following areas: augmented/assisted/virtual reality, cognitive assistance, dynamic and fair (virtual) resource allocation, seamless session transfer, and congestion control. The augmented/assisted/virtual reality as well as cognitive assistance have a strong demand on location and other environmental information obtained via camera/sensors. The dynamic and fair (virtual) resource allocation has a prominent demand on elastic system capabilities such as storage and computing power. The seamless session transfer has a strong demand on an efficient support of host mobility as well as the life cycle of virtualized resources. The congestion control has a strong demand on two distinct aspects: technical and business. On the one hand, for the technical aspect, the relevant features are traffic offloading [180][10][181], D2D communication [125][82][133], and relaying [182][127][96]. To achieve all these, the usage of CGs can be also very useful to enhance the cooperation among the devices [175][141][183]. Nevertheless, according to our current knowledge only a small number of papers have proposed cooperative strategies among users or providers considering the cost for cooperation [145]. The cost can be the power required and the terminal battery energy for negotiation, the additional delay because of the information exchange, the security threats, and the fairness aspect among edge/core nodes. In a practical scenario, it is not reasonable to neglect this cost for spectrum management especially in a resource constrained environment like future networks dealing with the near-exponential increase in data traffic. Therefore, investigating the overhead, delay, security threats and fairness issues caused by the communication to form coalition groups for cooperation can be an interesting direction for future research. Trust and security are key issues for future networks. The presence of malicious (or colluding) entities and their possible attack against incentive mechanisms for cooperation need further research. For investigating different issues such as how to detect and counteract such attacks, and how the reliability of network can be maintained despite the presence of misbehaving nodes, using GT can be a very fruitful research area [184]. On the other hand, for the business aspect, the relevant aspect is to use a dynamic congestion-sensitive tariff, where prices are set in real time according to current load or interference to maximize efficiency and fairness [185]. A survey on interference management for D2D communication and its challenges in 5G networks is available in [159]. In [186] the authors discuss the latest developments and novel distributed resource allocation algorithms for Full Duplex (FD) communication systems that can optimize, as an example, the performance of 5G networks. A FD communications system allows a node to send and receive the signals at the same time and frequency resource. These features can potentially double the spectral efficiency. Using both GT and matching theory, the authors have studied centralized and distributed FD communication networks. 4.4
MEC Main Requirements from the Literature
In our opinion the emerging paradigm of MEC seems very well aligned with a set of existing networking use cases in the available literature. These scenarios are: cognitive small cells, wireless sensor networks, unmanned vehicles, vehicular networks, power-grid, and tactile Internet. For each of these scenarios, we discuss below some main requirements to be fulfilled. To fulfil these requirements, we think GT can be a very useful tool to analyze and optimize the network infrastructure involved in each one of those use cases. We also pointed out from the current literature further contributions that can be used as solid references to future exciting developments on the novel paradigm of MEC. Cognitive Small Cells The deployment of low-cost and high-capacity cognitive small cells over existing cellular networks has been discussed as a promising solution to offload the macro cellular traffic to small cell networks. To achieve this, some problems induced by this hierarchical design needs to be successfully addressed, such as: share of spectrum among macro base stations and Femtocell base stations, as well as among macro-cell users and Femtocell users [187][188][189][190][191]; energy consumption [192][193][194][195]; signalling overhead; control of power transmission / mitigate interference
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[196][197][198][199]; security [200][201]; enhance cooperation via pricing [202]. In [6] is available a comprehensive literature revision on applications of Model-Free strategy learning in cognitive wireless networks. In [203] they discuss relevant trends and challenges in the deployment of millimetre wave, massive MIMO, and small cells to prepare the evolution of current mobile networks towards fifth generation (5G) wireless networks. During this evolution, the capacity of mobile networks should increase to support the exponential growth on data traffic. Several deployment strategies at mobile networks can increase their capacity [204]: i) use of larger bandwidth by exploiting higher spectrum frequencies [113] (i.e. more spectrum available); ii) increasing spectrum efficiency by exploiting multi-antenna transmission/reception [111] (i.e. MIMO, cooperative communications); and iii) spatial reuse of spectrum by deploying D2D communications [175], small cells [189], and heterogeneous access networks [110]. Wireless sensor networks Wireless sensor networks (WSNs) have profound significance towards environmental surveillance and remote monitoring by placing sensors in places of difficult access to humans. However, the limited network lifetime is a major deployment barrier for the traditional battery-operated WSN. Consequently, energy-efficient algorithms and protocols should be developed [205][206]. In addition, the data need to be disseminated with low-latency because most of the cases are used to signalize a faulty situation in the monitored environment that urges to be solved [207][208]. In [209] they propose a localization scheme named Opportunistic Localization by Topology Control (OLTC), specifically for sparse Underwater Sensor Networks (UWSNs). In [7] they use GT to mitigate security threats in WSNs. In [61] [62] are studied economic and pricing models associated to WSNs. In [17][210] are available research future trends in WSNs. Unmanned vehicles Some examples of unmanned vehicles are aerial [108][211][65] and maritime [212][213] ones. UAVs were initially developed for military monitoring and surveillance tasks but found several interesting applications in the civilian domain. A promising application/technology is to use drone small cells (DSCs) to expand wireless communication coverage on demand [108]. This requires for wireless communication links with sufficient QoS metrics (e.g. throughput, delay, jitter), satisfying security requirements (e.g. avoid fake DSCs), and the support of energy consumption optimization [116]. An interesting idea is to use UAVS to deploy a crowd surveillance system [211]. Other tantalizing scenario is using unmanned vehicles to maritime tasks [212][213], such as surveillance and patrolling, aquaculture inspection, or wildlife monitoring. There is a clear need for a completely distributed solution to allow each vehicle to learn (e.g. in an evolutive process) how to engage in a more effective way with other vehicles to all these can fulfil a specific mission. To support the system scalability, the vehicles organization in terms of clusters (i.e. coalitions) could be a possible option. Vehicular networks The interest of intelligent transportation systems and vehicular ad hoc networks has increased in recent years. As a fundamental building block for the development of applications for vehicular networks, the resource management and sharing problem for bandwidth and computing resources should be revisited to support mobile applications in cloudenabled vehicular network [214]. The challenges to solve are namely: find in an intelligent and efficient ways the more suitable communication link (i.e. with adequate data rate, low jitter and errors), support multi-hop communications, ensure data privacy, give incentives to vehicles cooperate and either relay traffic from others or cache data that can be used by others, support distinct patterns of mobility, use the parked cars as Serving nodes (i.e. like BSs or APs) for the cars circulating on the road, and increase the comfort of the passengers of self-driving vehicles by giving them all the Internet contents they need (e.g. streaming movie, live festival concert). Finally, new techniques and solutions are needed to handle data appropriately in the vehicular networks [215]. Power grid Recently, electric vehicles (EVs) and plug-in hybrid EVs have been considered as natural components of future electricity power systems, due to their efficient integration, cost savings, and significant environmental advantages. This will lead to
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new significant challenges in the design of power systems. These challenges include proposing energy charging scheduling plans for connected EVs, guaranteeing energy demands of EVs during peak hours, and managing information exchange between EVs and the grid (or aggregators). Other interesting area to investigate is the security of these systems. In fact, intrusion detection/prevention and mitigation of distributed denial-of-service attacks are pertinent security requirements to be addressed in power-grid systems. Some recent literature about power-grid are available in [216][217][218][219][220][221]. Tactile Internet The Tactile Internet (TI) involves human-to-machine (H2M) communications for remotely supervise tactile/haptic devices. These devices have local sensors and actuators and are required to be controlled via the Internet in a completely reliable and deterministic ways [222]. The TI seems to converge towards a well-defined list of design goals [223]: • Very low latency on the order of 1 ms; • Ultra-high reliability; • Very high availability; • H2H/M2M coexistence; • Integration of data-centric technologies with an emphatic focus on WiFi; • Security. Other important challenges for the TI are, as follows [223][224]: • Resource management and task allocation schemes (optimal online/offline scheduling); • Failure handling; • Mobility of robots; • Haptic feedback (multimodal or multisensory) based remote robot steering and control applications; • Flexible service coordination among robots. The authors of [43] report on the first initiative in designing LANs to facilitate the converged delivery of latencysensitive TI traffic and bandwidth-intensive applications.
5
Conclusions
This paper has summarized the recent developments in GT for optimizing the usage of network resources in emerging or future wireless networking environments with the aim of offering innovative applications/services with perceived high quality to end-users with multimode and more powerful handsets. Our discussion was focused on identifying important areas where further work needs to be performed for enhancing the performance of future wireless networks in the face of heterogeneity, novel flow requirements, a lack of network connectivity resources, and spectrum management issues. In our view, cooperation and learning aspects will be most relevant to use a common pool of network resources in the most efficient way among the diverse network players. The future games that potentially could be used in MEC use cases should have the following characteristics: incentives to cooperate (e.g. pricing, reputation, auctions, lotteries, bargaining games, contract theory, mechanism design, and social interactions) among the players; the players should play the game in a repeated way to enable the usage of additional learning algorithms; one should assume realistically that, in order to make a decision, the players have access to only a limited part of the total game status, and the use of evolutionary algorithms could speed up the process to find the optimum status of a networking infrastructure. In terms of the deployment of theoretical games at the network edge, we assume that the usage of a single game to control the operation of such a heterogeneous data communication system is very difficult, because it shows a dynamic behaviour, constrained resources, uncertainty information, as well as there are several simultaneous critical trade-offs to
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balance, namely: available energy vs. relaying traffic, computation offloading vs. channel interference, and data consistency vs. latency. So, we envision a more simpler way, breaking an original high complex problem in several lower complexity sub-problems. To support this, at the MEC servers, we point out the existence of several virtual machines or “lighter” namespaces where each one can run its own theoretical game with very specific goals. In this architecture, the terminals should also have some namespaces to play the games in which those terminals need to be involved. The architecture would require – at the edge of the network – some coordination among the distinct games played by the same terminal. A strong advantage from this coordination is the fully-integrated distribution control of both network, computational, and storage resources at the network edge. SDN [225] and NFV [226] can operationalize this coordinated control in quicker and more effective ways, trying to solve the various trade-offs in the best way possible [227].
ACKNOWLEDGMENTS
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