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Evaluating the economic impact of cognitive radio with a three-player oligopoly model Kimmo Berg and Arttu Klemettil¨a

Mikko A. Uusitalo and Carl Wijting

Systems Analysis Laboratory, Aalto University School of Science P.O. Box 11100, FI-00076 Aalto, Finland E-mail: [email protected]

Nokia Research Center, P.O. Box 407, FI-00045 Nokia Group, Finland E-mail: [email protected]

Abstract—Cognitive radio provides an opportunity for more efficient use of spectrum and features that improve and increase services in mobile business. This paper analyzes the economic impact of cognitive radio with a three-player oligopoly model. The three players represent the three markets of the industry: devices, connectivity and services. We examine how the new technology affects the markets, and how the changes in one market affect the other markets. With the model, it is possible to estimate the players’ utilities under different parameters and scenarios. We also present a method to estimate the parameter changes in the model from the technological improvements of cognitive radio. The model can be extended to incorporate more specific issues like the running out of spectrum and the effects of coalitions, which are studied in this paper.

I. I NTRODUCTION Cognitive radio is a technology that is rapidly gaining interest in the wireless research community [1]. One of the drivers is to increase capacity in communication, as wireless traffic is increasing at exponential rates and as there is a limited amount of spectrum [2]. Cognitive functionalities can also be used in other ways for improving the communication between networks and nodes. This could result in new and innovative services and applications, including even potential for more sustainable communication systems [3]. For companies it is important to understand beforehand the economic implications of cognitive radio technologies in order to focus on right things in preparing their business activities. Also, the regulators and the society need economic information to regulate properly and to set incentives for the development. In this paper we describe a new approach for analyzing the economic implications of cognitive radio technologies. The mobile telecommunications and wireless industry consists of a large number of companies and their roles, such as network operators, chipset manufacturers, content and application providers, advertisers and device manufacturers. There are many ways to classify the roles of the players [4]–[6]; see Sabat [7] for a comprehensive list of companies for each role. Moreover, Camponovo and Pigneur [8] distinguish the general classes of technology, services, network, regulation and the end-user. The players’ relations in the mobile business environment have also been modeled with value chains and value networks; see [9], [10] and the references within.

Cognitive radio, as well as any other future technology, may affect the business environment by creating new players in the game or changing the roles of the current players. For example, Markendahl and M¨akitalo [11] and Smura and Sorri [12] analyze different scenarios for local area access, and Ballon and Delaere [13] propose different ownership structures over the cognitive pilot channel, which is a hypothetical central coordination entity for flexible spectrum use. In the future there may also be other new roles, like spectrum brokers or auctioneers, and database operators [14], [15]. Our analysis starts with the simplification of the mobile business ecosystem into three markets: mobile devices, network access and movile services. We construct an oligopoly model, where each market is controlled by a player who is able to set a price level for its market. The prices determine the demands for the markets and the players’ utilities. The parameters in the model, e.g., elasticities and marginal costs, are estimated for UK markets in the year 2015. The impact of cognitive radio can be evaluated by examining how the equilibrium changes in the model. We need to estimate how the parameters change, and we present a systematic method for doing this. As there are many uncertainties concerning what the cognitive radio implementation will be, we examine few scenarios for the demand growths and do sensitivity analysis with respect to the cost parameters. Moreover, it is possible to examine with the model how the running out of spectrum affects the markets and what happens if the business ecosystem changes, e.g., if some firms merge and form a coalition. This paper is structured as follows. The three-player oligopoly model is constructed in Section II. A method to estimate the parameter changes and the scenarios is presented in Section III. The parameter estimates and the numerical results for different scenarios, coalitions and limited spectrum are given in Section IV. Finally, Section V contains the discussion. II. O LIGOPOLY M ODEL In this section, we develop a three-player oligopoly model to evaluate the impact of cognitive radio in the mobile telecommunications and wireless industry. The three players are the

device manufacturer (dev), the network provider (net) and the service provider (ser). Cognitive radio will increase network capacity and enable new and better services, which change the parameters of the model, i.e., the demands and the costs. We evaluate the effects of cognitive radio by investigating how the equilibrium and the players’ utilities change in the model.

p∗ ∈ BR(p∗ ), where BRi (p−i ) = arg max πi (pi ; p−i ), pi

(2)

is the best response correspondence of player i given the other prices p−i . The best response function is then BR(p) = (BRdev (p-dev ), BRnet (p-net ), BRser (p-ser )). We assume linear costs and demands

A. Model We assume that the players are able to set a price level on their own markets. Thus, the players can be interpreted as three monopolies. This means that we do not consider the competition issues within the markets, but between the markets. Competition may have a significant influence on the price levels, and the level of competition may be quite different between, or even within, the markets. For example, there may be a small number of network operators and lots of competing services, or a service may be a monopoly in its own niche. The players set the prices independently and simultaneously, and the prices determine the demands and the players’ utilities. This timing describes the long-term equilibrium in the game, but we note that the timing could be different. For example, it is more realistic to assume that the users first purchase the device and the network access before they decide which services they subscribe to. This kind of situation could be modeled as a Stackelberg game, and it usually gives different prices than if the players set the prices simultaneously. Moreover, the time scales are different as the devices and the access are usually sold for years and the services only for days or months. Thus, it could be assumed that the service prices are set and are based on the number of potential customers that depend on the device and access prices. The prices can be interpreted as average spendings per user or flat rates, i.e., there is a fixed fee over a predetermined period, which can be a month for the access and the services, and two years for the device. The use of flat rates means that we leave different marketing and pricing issues, like quantity discounts and nonlinear pricing, out of this paper. It is really challenging to model the services as a homogeneous group as there are so many different kinds of services. Some services are completely free, e.g., due to advertising, some are one time payments, and some have monthly payments. These issues are important within each market but they are not, however, so relevant when we try to evaluate the overall effects of cognitive radio. The players set prices pi ≥ 0, where i ∈ I = {dev, net, ser} is the set of players. The demand of player i ∈ I, Di (p) is a decreasing function in all of the prices p = (pdev , pnet , pser ). The total costs of player i given the demand q = Di (p) is c(q), which is an increasing function in q. The players set the prices by maximizing their profits πi (pi ; p−i ) = pi Di (p) − ci (Di (p)), i ∈ I,

(1)

where p−i are the other than player i’s prices, i.e., −i = I\{i}. The Nash equilibrium of the game is the prices p∗ that satisfy

ci (q)

= cif + cim q, i ∈ I, X Di (p) = di0 − dij pj , i ∈ I,

(3) (4)

j∈I

where cif and cim are player i’s fixed and marginal costs, di0 is demand at zero price and the slopes dij tell how much player i’s demand changes as price j changes. We note that the real demand functions can be approximated linearly only around the current prices, and the demand can, for example, be much higher for small prices; see [16] for an approximate shape of demand functions. The slopes dij are estimated from the own-price and cross-price elasticities of demand Eij (p) =

pi ∂Di (p) , i, j ∈ I. Di (p) ∂pj

(5)

The demand estimation gives the elasticities Eij (p) and the demands Di (p) at price p, and with these we can solve the slopes dij = ∂Di (p)/∂(pj ) from Eq. (5) and the constants di0 from Eq. (4) for all i, j ∈ I. The exact parameters and the sources of elasticity estimates are given in Section IV-A. B. Coalitions Providing the mobile services to the end-users requires collaboration of a large number of players [8]. Network operators and device manufacturers are very important partners as the operators may sell the access in a bundle with a generous subsidy for the mobile device. In operator centric business model [5] the operators play the central role in forming the partnerships with the key players. The services build the customer base and bring revenues to the operator and, on the contrary, the network ensures a sufficient quality of services and offers the essential network services. The device manufacturers and service providers also benefit from their collaboration. The device vendors have started to expand their business in the service direction [12]; examples of such are the Nokia’s Ovi Store and the Apple App Store. The services are a good way to promote the new mobile devices and the new functionalities in the devices enable new kind of services. Moreover, the roles may not be so clear in the future, e.g., Google is offering beside the mobile services the devices, Android operating system and software. It has also shown interest in the US white spaces [15]. In this model we can determine rough estimates for the values of different coalitions in the game. We assume that if the players form a coalition then these players set their prices so that they maximize the total utility of the coalition. This means that there are no other benefits than setting the prices together; e.g., there could be cost benefits, increase in brand

Implementation

Enablers

Benefits and disadvantages

Affected groups

TV white spaces

New low frequency band

Longer range

Voice calls

Higher data rate

Positioning services

Better location information

Outdoor services

Mesh networks

Ultimate cognitive radio

New high frequency band

Parameter changes Device Demand Costs

Network

Sensing technology

Network constructor

Demand Costs

Services

Database costs Dynamic spectrum access

Active Internet access

Free short distance connections Fig. 1.

Demand Costs

Parameter estimation network

value and market power, and better working services. The coalitions here mean that the whole markets of mobile business are in collaboration, which is a highly unrealistic scenario and against the antitrust laws. The coalitions could be modeled better by splitting down the three players and analyzing more thoroughly these smaller coalitions. With the coalition analysis we can examine what is the most beneficial coalition in the game and how the players should share the profits created by the coalition. Although, we will not analyze them deeper in this paper. C. Limited Spectrum It has been estimated that the mobile data traffic will grow between twenty-five and fifty-fold within the next five years in the USA [2]. We examine what is the value of cognitive radio as a technology that increases the capacity of mobile data traffic and the efficiency of the spectrum use. We assume that the limited spectrum only affects the network operator and its demand. In reality, it also affects the services, especially the ones that require high bandwidth and quality of service, and this reflects back to the device sales. The limited spectrum is modeled as a capacity constraint for the network’s demand in the oligopoly model. We denote L as the limit of network’s demand when there is no cognitive radio. The demand function is then   X Dnet (p) = min L, di0 − dij pj  , (6) j∈I

which means that the network cannot sell more than L subscriptions no matter how low the price is. In cognitive radio scenarios there are no limits for the demands, and the demand functions are as presented in Section II-A. We note that this change also affects indirectly the device and the services through the players’ equilibrium behavior. Namely, if the demand limit is active then the network will increase its price and this means lower demands also for the device and the services.

III. I MPACT OF C OGNITIVE R ADIO To evaluate the impact of cognitive radio, we need to estimate different sets of parameters for the model. We use five scenarios to analyze the model: one without cognitive radio and four to represent different demand growths. In this section, we also present a method to estimate the parameter changes from the technological improvements and the benefits and disadvantages of cognitive radio. A. Parameter Estimation Network Cognitive radio is about technological advancements that will improve the wireless communications. The technical implementation and the exact form of cognitive radio is still an open issue. There are various technological and regulatory solutions for the problems of dynamic spectrum access, like interference management, sharing the spectrum among cognitive radio users and allowing coexistence. Even if we knew the technical solution, it would be a difficult task of estimating how it affects the parameters in the model. We present a method to evaluate the effects of cognitive radio by connecting the technological changes to the parameter changes through a network, as illustrated in Fig. 1. Different implementations on the left are connected to various cognitive radio enablers, e.g., a new frequency band, a database and a cognitive pilot channel. The enablers are further connected to various benefits and disadvantages. These are more concrete properties, like a long range transmission, a high data rate and the sensing chip costs, which can be connected to the three players in the model. Let us examine an example scenario of TV white spaces. TV bands have good propagation characteristics that allow signals to reach farther and penetrate walls and other structures [14], [17]. TV white spaces consists of 6 Mhz bands between 400 Mhz and 700 Mhz. The unlicensed usage originally required interference management in forms of primary database for TV channels and the sensing technology in the devices [18], but the sensing is no longer required [14]. Thus, the TV white

spaces implementation in Fig. 1 could be connected to new Demand low frequency band and sensing technology. Population growth The TV bands increase the network capacity, allow longer range in transmissions but incur database costs for the network and sensing chip costs for the device manufacturer. The longer range, e.g., may enhance positioning services by improving di0 reliability and operating area. This could attract more customers and result in 10 % growth in demand. If the positioning Trendy growth D(p0 ) services are used by 10 % of the total population, i.e., they represent 10 % of the service volume, the total increase in the service demand is 10 % · 10 % = 1 %. Similarly, we can p0 Price consider the database costs as part of the network operator’s costs, and these can be estimated to be 1 e monthly per user. Fig. 2. Different types of changes in demand function The impact of cognitive radio in each implementation can be estimated by creating the complete network, estimating the effects of each connection and adding up the changes for the three players. This method allows us a systematic way Beside the relative growths in demands, we can distinguish of estimating the parameter changes in the model. We note, two types of demand changes for the linear demand functions, however, that modeling the interdependecies in the network which are illustrated in Fig. 2. The demand can either grow may be a complicated task [19], [20]. We could also include by a constant or also the slope of the function may change. probabilities in the network and model the uncertainties of The former type is called as trendy growth, and it means that cognitive radio, but we leave these issues out of this paper. the constant di0 in Eq. (4) increases. The elasticity decreases Instead, we analyze how the model works by examining few and there will be a number of new customers no matter what basic scenarios, which are presented in the next section. the price is. The latter type is called as population growth. Here, the price of zero demand remains the same and for B. Scenarios all prices the demand is multiplied by the same factor. In the four scenarios we assume that the growths are equally We analyze the behavior of the model with four cognitive divided between population and trendy growths, but we will radio scenarios which represent different demand growths for also analyze the effects of the two types. the three players. The demand is the most uncertain factor in the model, since the marginal costs can be predicted according IV. R ESULTS to some guidelines and the fixed costs do not affect the equilibrium. We will, however, do sensitivity analysis with A. Parameter estimates respect to the marginal costs and compute upper bounds for The parameter estimation is very difficult because of the the fixed costs. high uncertainties in the business ecosystem. We will base our In the first scenario, we assume that there is an even estimates on data available from UK in the year 2015. We use growth in demand for all three players in the model. The the market data available from the British telecommunication new technology enables new services, improves the network authority Ofcom to estimate the parameters for Scenario 0, connections and makes the mobile devices more attractive to i.e., the one without cognitive radio. For the cognitive radio use. The customers will subscribe to new services and data scenarios it will suffice to estimate the changes from this basic plans and purchase new mobile devices. situation. The average price of a smart phone in 2015 could be In Scenarios 2-4, one player has clearly more advantage of 88 e. Ofcom predicts the amount of smart phones to be 50 the new technology and the demand growth for this player is million [21]. Typically, not all smart phone owners have a data significantly higher than for the others. The main idea is to examine how this boost in one demand affects the equilibrium subscription, and thus we estimate the amount of subscriptions and the other players. In Scenario 2, the new features in to be 25 million. Ofcom [21] reports the average monthly the devices make them more attractive and this results in subscription fee to be 10 e. For the services, we estimate an fast device replacement. The customers want to upgrade their average price of 1 e per service and consumers to use a total devices, which leads to increased device sales. In Scenario of 10 services per month. Several studies [16], [22], [23] report the price elasticity of 3, the network operator gains a boost in its demand, e.g., due to applications that require high bandwidth, such as video demand for home broadband connections to be approximately streaming. As these applications get more popular, more and 1.5-2. In Japan, a value of elasticity as high as 4 was estimated more people want to augment their mobile devices with the in 1999 [24]. Later, in the year 2005 the elasticity was new data capabilities. In Scenario 4, cognitive radio enables estimated to be 1.4−2.4 [25]. For wireless communication the new and innovative services, which results in explosion of elasticity is most likely higher than for broadband connections, but as in Japan, the elasticity will most likely be lower as service demand.

wireless communication becomes more common. Thus, we will use the value 2 for the elasticity of the network operator. We estimate that the elasticity for devices is lower than the elasticity for the connection, since consumers also buy devices for other reasons. Services, on the other hand, have the highest elasticity. They are more easily discarded if the prices go up. In conclusion, the elasticities are estimated to be 1.5 (device), 2.0 (network) and 3.0 (service). The cross-price elasticity to another player’s price is clearly lower than the own-price elasticity. We also assume the following relations in the elasticities: i) the pairs of players that influence each others’ demands are in order dev/net, net/ser and dev/ser, and ii) the first player’s price in those pairs affects the demand of the second player more than vice versa. Thus, we estimate the elasticities to be those in Table I, i.e., the elasticity of the device demand is 0.5 to service prices. Marginal costs are difficult to estimate due to the lack of publicly available data. The average marginal costs of smart phones could be 66 e, i.e. 66/24 = 2.75 e per month. For the network operator and service providers, we estimate the marginal cost to be 60 % of the initial price, that is 6 e for the network and 0.6 e for services. The most critical part in the parameter estimation is determining the changes induced by cognitive radio. The changes depend heavily on the implementation, technology and the business models. Ofcom reports annual growth rates of 5-10 % for mobile subscriptions [21]. We estimate the effect of cognitive radio to be approximately of the same magnitude for all sectors. In Scenario 1, all business sectors gain an equal 10 % growth. In the other scenarios, one of the sectors had an advantage over the others. The advantaged player will gain 20 % increase in demand. Changes in marginal costs consist mainly of adding cognitive functionality to the network infrastructure and the terminal devices. Although the infrastructure is a significant part of the network operators’ expenses, we estimate the influence of cognitive radio on the marginal costs per end-user to be very small. For the devices, adding cognitive functionality will most likely require a new radio chipset. Typically, this type of small changes have an extra cost of 1 e per device. Since there are many uncertainties in these estimates, we will examine them in the sensitivity analysis section. In addition to marginal costs, cognitive radio will require investments in development, production and other things that generate fixed costs. We can estimate their order of magnitude by assuming a level of total costs for each business sector. We estimate the device and network sectors to generate 10 % profits and the services 20 %. Considering the levels of marginal costs, this means approximately 15 %, 30 % and 20 % of the total revenue to be fixed costs for the device, network and services, respectively. Development costs for a single technology cannot form a significant part of the total costs, and thus the changes in fixed costs are only in the order of 0-5 % of the total fixed costs.

Demands \ Prices Device Network Service

Device 1.5 1.5 1.0

Network 1.0 2.0 1.5

Service 0.5 1.0 3.0

TABLE I E LASTICITY ESTIMATES

Device Network Service

Price 4.5 9.8 0.93

Demand 35.7 19.1 250.2

Profit 62.1 73.0 83.5

TABLE II NASH EQUILIBRIUM OF S CENARIO 0

B. Basic results for each scenario The Nash equilibrium in Scenario 0 is illustrated in Table II, which gives prices, demands and profits for each player. From these numbers, we see that the initial prices are not exactly the same as the prices at the equilibrium. The device prices are slightly higher, and network and service prices slightly lower. This means that the parameters are not totally consistent, but since we are mainly interested in the effects of cognitive radio, we will not be disturbed by this. We can calculate the Nash equilibria similarly for Scenarios 1-4. Comparing them to Scenario 0 yields the changes in prices, demands and profits listed in Table III. In Scenario 1, all demand parameters grow with a factor of 10 %. Even with these growths, the actual change in total demand is only around 6 %. This is because the elasticities get lower which enables the players to get higher profits by raising their prices. But as all players raise their prices the demands get a bit lower. The differences between the players are relatively small, and we cannot judge whether one player will gain a significant advantage over the others. In Scenarios 2-4, one player gains a significant advantage over the others. The player with the advantage has a growth factor of 20 %, whilst the others stayed at the 10 % rate as in Scenario 1. The player with the advantage gains, as could be expected, a clearly better profit than the other players. Surprisingly, even though the other two players’ demand parameters rise by 10 %, their profits only grow by factors as low as 4 %. The advantaged players, on the other hand, gain profits around 20 %. The higher demand allows the advantaged player to raise its prices and therefore lower the other players’ demands. The others, especially the network operator in Scenarios 2 and 4, cannot raise its prices. They might even have to lower their prices in order to prevent losing too much demand. As the others lower their prices, the advantaged player gains even more demand and profits. The advantaged player gains relatively more than the players do in Scenario 1, even considering the different changes in the demand parameters. We have not yet considered the fixed costs. As an example, let us look at Scenario 1. The players gain extra profits with absolute values of approximately 4.4, 4.6 and 6.9. The total

Scenario 1: Even growth Price Demand Profit Device +1.3 % +6.0 % +7.0 % Network +0.2 % +5.6 % +6.3 % Service +0.5 % +6.6 % +8.2 % Scenario 2: Fast device replacement Price Demand Profit Device +2.4 % +14.2 % +18.6 % Network -0.3 % +4.3 % +3.6 % Service +0.4 % +6.3 % +7.6 % Scenario 3: Bandwidth hungry applications Price Demand Profit Device +1.0 % +5.3 % +5.5 % Network +1.4 % +13.9 % +18.0 % Service +0.3 % +5.9 % +6.8 % Scenario 4: Service explosion Price Demand Profit Device +1.2 % +5.8 % +6.7 % Network +0.0 % +5.1 % +5.2 % Service +1.5 % +14.6 % +19.5 % TABLE III P ERCENTUAL CHANGES INDUCED BY COGNITIVE RADIO

amount of fixed costs for each player was estimated to be 15 %, 30 % and 20 % of the total revenues, i.e. 24.0, 56.3 and 46.7. This means that the generated profits are clearly over 5 % of the total level of fixed costs. Thus, the profit margin is high enough to cover the fixed costs even if they were as high as 5 %. Similar results can be achieved from the other scenarios. We can conclude that with these parameters, cognitive radio is profitable to all the players on the market. C. Coalitions When two players form a coalition, they can choose their prices together. This means that we are left with a two-player game with the coalition as one player and the third player as the other. All three players can also form a coalition and optimize their prices together. This coalition is called as the grand coalition. The percentual change in profits at the Nash equilibrium when forming each coalition in Scenario 1 is listed in Table IV. In general, coalitions should get at least the same profits as they would get without the coalition, as they can always choose the same prices as they would without the coalition. Now, two of the four possible coalitions actually gain less profits. This is because selecting the same prices as without the coalition is not the Nash equilibrium. We also note that the player that is not part of the coalition gains more profits, which is quite unexpected. For these reasons, the coalition game should be analyzed more thoroughly, e.g., change the game as a Stackelberg game. When two players form a coalition, the standard way to make more profits for the coalition is to lower one price while raising the other. This way the first one pumps up the demand for both markets, while the other collects the profits with the high prices. The player that lowers its price depends on the elasticities. As an example, in the device/network coalition, the

Coalition Device Network Service Coalitionists Non-Coalitionists

Dev/Net -70.2 % +84.7 % +21.6 % +13.2 % +21.6 %

Dev/Ser -18.4 % +37.4 % +7.0 % -3.8 % +37.4 %

Net/Ser +20.8 % -17.0 % +14.3 % -0.2 % +20.8 %

Grand -98.8 % +100.9 % +37.4 % +21.5 % N/A

TABLE IV E FFECT OF COALITIONS IN S CENARIO 1

Pop./trendy growth Device Network Service

20 / 0 15.5 % 9.0 % 8.9 %

15 / 5 17.2 % 6.3 % 8.2 %

10 / 10 18.6 % 3.6 % 7.6 %

5 / 15 19.6 % 1.0 % 6.9 %

0 / 20 20.1 % -1.7 % 6.2 %

TABLE V C HANGES OF PROFITS WITH DIFFERENT DEVICE DEMAND GROWTH TYPES .

device manufacturer lowers its price. Since the elasticity of the device to the network price is lower, the demand for devices is not affected as much as it would be the other way around. On the other hand, the network has a higher elasticity to the device price, so lowering the device prices raises the network demand relatively more. In general, the device manufacturer always lowers its price if it is part of the coalition. If the device is not in the coalition, then the network lowers its price. D. Demand change types Population growth multiplies the demand with a constant factor, while trendy growth adds a constant population willing to buy the product. Population growth does not affect the elasticity, while trendy growth lowers the elasticity beside increasing the overall demand. Let us examine Scenario 2. The network and service players gain +10 % increase in demand equally divided between both types of growths. The device manufacturer gains +20 %, but with a varying ratio of population and trendy growths. The changes in profits are listed in Table V. From the results, we can clearly see that the trendy growth is generally more profitable growth for the player receiving it. The device manufacturer’s profit ranges from 15 % to 20 %, which means that the trendy growth is clearly more beneficial than the population growth. From the other players’ point of view, the situation is the opposite. The sum of all growth percentages is approximately constant, so if the device manufacturer gains less profits, the network operator and service provider gain more. It is also notable that the network operator’s sensitivity to the ratio of the two types of growths is higher than the service provider’s. The reason for this behavior is that the trendy growth changes the elasticities and therefore causes notable shifts in the price equilibrium. In general, the trendy growth lowers the elasticity, which allows the player to raise its prices without losing too much demand. The effect is enforced when the other players must lower their prices to keep their current demands.

Dev Net Ser

30

Change in profit

25

20

15

10

5

10

12

14

16

18

20

Maximum demand

Fig. 3. Effect of limited spectrum on the change of profits by cognitive radio

E. Limited spectrum Cognitive radio was initially developed to solve the problem of limited spectrum. Without changing the current ways of doing, the spectrum will eventually run out, but it is uncertain when it will happen. Even if the amount of consumers is constant, the average usage of spectrum can vary significantly. If each user requires a lot of bandwidth, the maximum number of users is lower. In our model, the limited spectrum affects mainly the network operator. The other players are affected only indirectly via the increased network operator’s prices. The players’ profit changes to Scenario 0 are illustrated in Fig. 3 as a function of the network’s demand limit L. When the limit is not active, i.e., on the right, the constraint does not have any effect on the equilibrium. When the limit gets smaller and the network runs out of capacity, cognitive radio starts to be more beneficial to the device and the service, but not to the network. This happens because without cognitive radio the network should raise its prices, which results in greater profits for the network while the others’ profits decrease. When the limit is really low, also the network gets lower profits than it would get without the limit. We note, however, that the change to Scenario 0 is always positive, which means that cognitive radio is beneficial to all players regardless of the limit if the fixed costs are low enough. F. Sensitivity analysis As there is much uncertainty in the estimated parameters, it is important to study how the value of each parameter affects the end results of the model. We will focus on the sensitivity of marginal costs and elasticities. While studying the changes induced by cognitive radio, it is clear that the changes in parameters have the greatest influence on the outcome of the model. Also the initial levels affect the results, but the effect is very small compared to the changes of the parameters. We estimated that there will be no changes in the marginal costs for the network and service sectors. If the costs rose, it would not only reduce the profits but also shift the equilibrium point. We can analyze the sensitivity by determining how much can the marginal costs rise until the profits of one of the

players goes to zero. For the device, network and services, the marginal costs can rise 10 %, 4 % and 4 %, respectively. These percentages are rather high, as a single technological feature will typically add an extra cost of the order of 0.1 − 1 %. Of course, here we have not considered the fixed costs that need to be covered with the profits. If the fixed costs rose by 1 % on each sector, the respective maximal increases in the marginal costs would be 2.3 %, 1.4 % and 2.2 %. Note that the calculations were done under the assumption that only one of the costs rises. If all the prices rise simultaneously, the limits are lower. A key factor in the determination of the market equilibrium are the elasticities. In general, a low elasticity allows the player to raise its price without losing much demand. Thus, lower elasticity parameters result in lower demands but higher prices. The effect is not very strong, as changes in the parameters cause relatively small changes in the prices and demands. More important than the absolute values of the elasticity parameters is their relative order. With the parameters used in this paper, this is the reason why the device generates higher profits than the network operator. Although, the service sector has even higher elasticities, but it still generates higher profits. This is due to other reasons, such as the relative size of the population and the level of marginal costs, which also have an effect. In general, the model is very robust in the sense that changes in the parameters do not dramatically alter the equilibrium. The profits have a near linear dependency on the demand growth and marginal cost changes. V. D ISCUSSION We have constructed an oligopoly model to evaluate the economic impact of cognitive radio. We have examined the markets of devices, access and services together, and how the changes in one market affect the other markets. According to the model and the estimated parameters, cognitive radio will be profitable to all market players even if the parameters were to change by few percentages, which is actually quite much for the cost parameters. In the long run, the radio spectrum will run out and ultimately cognitive technologies are required to face the ever growing demands. When we know in the future what the cognitive radio implementation will be and the details become more certain, we can use the model to get better estimates for the markets. In this paper, we have also introduced the parameter estimation network that can be used to evaluate and compare different implementations and features of cognitive radio. Efficient use of the network will require extensive knowledge on each business sector and their properties. Then the network and the model can be combined and used to choose the optimal portfolio of features that should be developed and added to the final implementation of cognitive radio. The companies can also use this to select the features they favor and want to lobby. The studies of limited spectrum show that the capacity limit hurts the device and service profits but may be beneficial for

the network operator in the short run. This is because a little scarcity of spectrum will increase the access prices resulting in greater profits. As the limited spectrum is harmful to the other players, it might be beneficial for them to support the network operator, e.g. via subsidization or taking part in organizing some parts of the network infrastructure. For example, the TV white space database could be controlled by a group of service providers. The coalition analysis shows that the most beneficial twoplayer coalition in the game is between the device manufacturer and the network operator. The other coalitions, on the other hand, do not have that significant influence on the profits. This result can be seen in many countries today as phones and network subscriptions are sold in bundles. The coalition analysis of this paper is very rough and could be modeled more thoroughly, e.g., by changing the rules of the game when modeling coalitions and estimating the other benefits of coalitions. Moreover, cooperative game theory introduces different solution concepts, which satisfy different properties in the allocation; e.g., core, Shapley value and nucleolus [26]. With these concepts, we can determine how the profits within a coalition should be allocated. Currently, our model does not take into account the competition within a business sector. To properly analyze this, we could split the three players, e.g., model three network operators or two device manufacturers. We could also study coalitions between these smaller players, and examine if it is beneficial for one device manufacturer to join one network operator, while the others act independently. This way we get better economic information about the coalitions. Cognitive radio is still work in progress. In the end, the telecommunications business can be very different from what it is now. Cognitive radio can create new players, such as the database operator [15], or change the roles of the current players. The spectrum regulation may also see completely new forms of spectrum access methods in the future beside the current licensed and unlicensed usage [27]. The first steps have already been taken as FCC has allowed secondary usage of TV bands requiring only database guarantee for interference management [14]. R EFERENCES [1] I. Akyildiz, W. Lee, M. Vuran, and S. Mohanty, “NeXt generation/dynamic spectrum access/cognitive radio wireless networks: a survey,” Computer Networks, vol. 50, no. 13, pp. 2127–2159, 2006. [2] FCC, “Mobile Broadband: The Benefits of Additional Spectrum,” October 2010. [3] C. Wijting, M. A. Uusitalo, P. Alinikula, and H. Paloheimo, “Towards sustainable communication systems,” in WPMC2010, Recife, Brasil, 2010. [4] E. Faber, P. Ballon, H. Bouwman, T. Haaker, O. Rietkerk, and M. Steen, “Designing business models for mobile ICT services,” in Workshop on concepts, metrics & visualization, at the 16th Bled Electronic Commerce Conference eTransformation, Bled, Slovenia, 2003.

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