Proc. of the 3rd International Conference on Application and Development of Computer Games (ADCOG 2004), HKSAR, pp. 12-17, Apr. 2004.
Application of the Artificial Society Approach to Multiplayer Online Games: A Case Study on Effects of a Robot Rental Mechanism Ruck Thawonmas and Takeshi Yagome Intelligent Computer Entertainment Laboratory Department of Human and Computer Intelligence, Ritsumeikan University Kusatsu, Shiga 525-8577, Japan
[email protected]
Abstract This paper discusses a case study where the artificial society approach is used to examine effects of a robot rental mechanism in a multiplayer online game, under development at the authors’ laboratory. Simulation results show the effectiveness of the proposed rental mechanism, namely, better game balance and inflation control. These results also indicate that the artificial society approach has high potential for use in multiplayer online game applications in order to systematically predict effects of each service or component.
1. Introduction
Development of multiplayer online games involves high costs. A major reason for this is that effects of each service or component are hardly known before launching of beta versions. To remove unwanted effects or add more wanted effects, ad hoc development is forced to continue after releasing of the games. This paper aims to present a solution to the above issue. Our solution is to use the artificial society approach [1, 2] for analyzing each service or component in advance. In the artificial society approach, computer simulation is used to explore and understand social and economic issues. The approach has been widely used since 1990s among social scientists. In this paper, based on the artificial society approach, we study effects of introducing a robot rental mechanism into a multiplayer online game called ”The ICE”.
2. Game concepts of The ICE Here we describe the game concepts of The ICE. This game is under development at the authors’ laboratory using a customized middleware of Community Engine Inc [3]. Besides educational purpose, it will be used as a platform for examining various data mining techniques in [4-6], recently proposed by the authors’ group and tested on a multiplayer online game simulator called Zereal [7]. In The ICE, each player is initially given a programmable robot. A major role of the player is that of programming the robot and participating with it in a snow battle at a battle field against the team of another player and his robot. A reward is distributed to the winner player of the battle. The fun of this game is the in-game programming. Though they might have difficulty in programming their robots in the beginning, through trial-and-error processes and advices from virtual friends or Game Masters, players should gradually overcome such hurdles step by step. They should also become more and more attached to their own robots. However, there might be some players who have a relatively low programming ability. Rather than preventing this type of players from playing the game, we propose below a robot rental mechanism for balancing the player status, in terms of the amount of virtual money in hand versus the robot performance. This should result in higher player satisfaction.
3. Robot rental mechanism and its economical perspective The proposed robot rental mechanism is outlined as follows:
0.70
PROGRAMMING 0.33
C:1.00
A:0.80
0.30 B:0.33
0.33
BATTLING
CHATTING 0.50 0.33
B:0.33 B:0.33
0.50
Table 1. Evolution of player ability state evolvable ability PROGRAMMING pi , si BATTLING pi , si , ci CHATTING pi
A:0.20 0.50
WATCHING
REGISTERING 0.50
Figure 1. State transition diagram of the players
1. A player who wishes to rent out a clone of the current version of his robot must register that version at the robot shop of the corresponding game zone. 2. To use registered clones besides his own robot in a snow battle, a player must go to the robot shop, specify the number of clones he wants, and pay a rental fee to the shop owner, a non-player character. Upon receiving the fee, the shop owner randomly reproduces clones from the list of the registered versions of the robots and rent out the clones to the customer. At the end of each snow battle, all clones are voided. 3. If the team of a clone wins a snow battle, a part of the rental fee is given to the programmer of the robot, from which the clone is reproduced. From an economical perspective, we divide the players into the following two categories. Producer who is good at programming and thus programs his robot for not only winning a snow battle but also renting out its clones. Consumer who is poor in programming and hence needs to additionally use clones in a snow battle for increasing the chance to win. By having both producers and consumers in the game, an economy [8] is formed where virtual money, consisting of the battle rewards and the robot rental fees, is circulated. In this economy, the cost of X is represented by time, the number of simulation cycles in the simulator discussed below, required to complete X. For example, the programming cost of a robot is the number of simulation cycles required to program the robot.
We expect that the proposed rental mechanism will weaken the power-law relation between the robot performance and the amount of money in hand of the players. Namely, with the proposed rental mechanism, players having higher performance robots do not always get richer in the game. Another more evident effect of the proposed rental mechanism is that of controlling inflation in the game. Without this mechanism, the system can not absorb the money from the players. Hence, the amount of money in hand of each player keeps on growing, causing inflation.
4. Game simulator In this section, we discuss how we simulate The ICE and the proposed robot rental mechanism. In our simulator, a player is modeled by an agent, and the ability of player i at a given simulation step, abilityi , is defined by abilityi = floor(pi + si + ci ), (1) where floor() is the floor function, and pi , si , and ci are the degree of programming ability, the degree of skillfulness, and the degree of concentration of player i at the current simulation step, respectively. The above pi , si , and ci evolve according to the state transition diagram of the players shown in Fig. 1, where the ovals represent states and the arrows represent transitional probabilities between states. Table 1 shows the states at the end of which each corresponding ability is slightly increased by a small random number α. The initial state of a player can be one among PROGRAMMING, BATTLING, and WATCHING with the same probability. The description of each state in Fig. 1 is given in detail as follows: PROGRAMMING indicates the state where the robot of the player is programmed. The performance of the current version of the player i’s robot (and its clones), performi , that can be achieved is defined by performi = opi + dpi + spi + pri ,
(2)
where opi , dpi , spi , and pri are the offense power, the defense power, the speed, and the precision
of the player i’s robot, respectively. These four parameters are calculated by the nearest integer not larger than the result of pi added by a random value from 0 to si . The cost, i.e., the number of simulation cycles required to complete this state, depends linearly on the robot performance and inversely on the degree of concentration of the player. It is calculated by floor(performi /ci ). At the end of this state, the version of the player i’s robot is incremented by 1. BATTLING indicates the state where the player together with his robot and the rented clones are engaged in a snow battle. Player i rents clones for battling if the performance of the current version of his robot is not larger than a threshold θi , i.e., performi ≤ θi . Here θi is defined by the average performance of the former versions of his robot and the rented clones that player i previously used in the lost battles. If performi ≤ θi holds, player i rents up to τ clones at the robot shop. The total rental fee is the sum of the rental fee of each rented clone, where the rental fee of a clone is defined as the rental fee of the registered version of the robot from which the clone is reproduced. The out-going branches from this state depend on the following three conditions: Condition A: where the player’s team wins the current battle,
used to wait for the availability of a battle field and/or the availability of an opponent team. CHATTING indicates the state where the player chats with his friends. This state requires five simulation cycles. REGISTERING indicates the state where the player registers the current version of his robot at the robot shop. This state requires one simulation cycle. WATCHING indicates the state where the player merely watches a snow battle between another two teams. This state requires one simulation cycle.
5. Simulation results In our simulation, the main variables are as follows: • 40 game zones • 8 battle fields per one game zone • 50 players per one game zone • 1000 simulation cycles • 100 money units as the initial amount of money in hand for each player
Condition B: where the player’s team loses the current battle, and
• The initial degrees of pi , si , and ci are uniformly assigned a random integer value from 1 to 6, and α is randomly selected from 0.0, 0.1, and 0.2.
Condition C: where the player’s team skips the battle because his robot has not been programmed yet.
• θi is initially set to 0. For simulating the game without the proposed rental mechanism, this value is fixed through out the simulation.
A snow battle consists of 5 turns. The team that first wins 3 turns will be the winner of the battle. In a given turn, if the total performance of the current version of the player i’s robot and the rented clones added by si and a random value from 0 to ci is larger than that of the opponent team, the player i’s team will win that turn. If his team wins, player i will be rewarded with λ money units, and the rental fee of his robot be increased by βH . If player i additionally uses clones in the win battle, the programmer of each robot, from which its clone is reproduced, will be given the rental fee of the clone multiplied by γ; In addition, the rental fee of the rented version of each robot is increased by βL .
• The initial rental fee for each registered version of a robot is set to 10 money units. Rent related parameters τ , βH , βL , and γ are set to 3, 2.0, 0.5, and 0.1, respectively.
The number of simulation cycles required in this state is one cycle added by the number of cycles
• λ is set to 100 money units. Figure 2 shows the scatter plot of the normalized amount of money in hand versus the normalized robot performance of the players for (a) where the rental mechanism is not implemented, and (b) where the rental mechanism is implemented. As can be readily seen, trend of the power-law exponent is more pronounced in Fig. 2.a than in Fig. 2.b. Namely, without the proposed rental mechanism, players who have higher performance robots are richer. When the proposed rental mechanism is implemented, this trend is less evident.
without rental
1
1
0.8
0.8
money in hand
money in hand
without rental
0.6 0.4 0.2 0
0
0.2
0.4
0.6
0.8
0.6 0.4 0.2 0
1
robot performance
0
0.2
(a)
0.8
1
0.8
1
with rental
1
1
0.8 money in hand
money in hand
0.6
(a)
with rental
0.6 0.4 0.2 0
0.4
robot performance
0
0.2
0.4 0.6 robot performance
0.8
1
0.8 0.6 0.4 0.2 0
0
0.2
0.4
0.6
robot performance
(b) (b) Figure 2. Scatter plot of the normalized amount of money in hand versus the normalized robot performance of the players for (a) without rental and (b) with rental
To further investigate the above claim, we conducted nonlinear regression [9] of the data in Fig. 2 using the simplex algorithm for fitting function yi = axbi , where xi and yi are the robot performance and the amount of money in hand of player i, respectively, and a as well as b are initially set to 1. The resulting regression coefficients are shown in Table 2. The resulting regression curves overlayed on the scatter plots of Fig. 2 are depicted in Fig. 3. These results confirm our claim. Other statistics shown in Table 3 are the maximum, the mean, the median, and the standard deviation of both the robot performance and the amount of money in hand of the players. Note that a larger difference between the mean and the median indicates that the distribution of the data is more skewed, and this occurs in the case where the proposed rental mechanism is not implemented, especially for the amount of money in
Figure 3. Scatter plot of the normalized amount of money in hand versus the normalized robot performance of the players with the regression curve being overlayed for (a) without rental and (b) with rental
hand of the players. The standard deviation of both the robot performance and the amount of money in hand of the players are also much higher in the case where the proposed rental mechanism is not implemented. The results obtained so far conform to our expectation that the proposed robot rental mechanism can result in better game balance, in terms of the amount of money in hand versus the robot performance of the players. In addition, it should also be noted that the amount of money in hand of the players where the proposed rental mechanism is implemented is much lower. This means that the proposed rental mechanism well controls inflation in the system. Now we further analyze the data in the case where the proposed rental mechanism is implemented. We first consider as producers the players who register
Table 2. Regression coefficients for the case where the rental mechanism is not implemented, and the case where the rental mechanism is implemented coefficients a b
without rental 1.28 1.61
with rental 0.58 1.82
their robots for renting out more often than average players, and the rest of the players as consumers. Based on this, the players are divided into 1047 producers and 953 customers, where the average number of times the players register their robots is 29.04. The scatter plot for each type of players with the regression curve, obtained by the nonlinear regression discussed above, being overlayed is shown in Fig. 4.a and Fig. 4.b, respectively. The resulting regression coefficients for the producers and the consumers are given in Table 4. Table 5 shows for each type of players the maximum, the mean, the median, and the standard deviation of both the robot performance and the amount of money in hand of the players. These results reveal that the power-law relation between the robot performance and the amount of money in hand of the players is slightly higher for the producers. In addition, the producers have higher performance robots and are richer. The distribution of the amount of money in hand of the consumers is less skewed.
Table 3. Major statistics of both the robot performance and the amount of money in hand of the players for (a) without rental and (b) with rental
major statistics maximum mean median stdev
(a) without rental the robot the amount of performance money in hand 341 42700 105.74 9079.70 91 5500 57.34 9383.50
major statistics maximum mean median stdev
(b) with rental the robot the amount of performance money in hand 150 8822 83.53 1840.21 85 1767 19.60 1076.67
Table 4. Regression coefficients for the producers and the consumers coefficients a b
producers 0.61 1.95
consumers 0.53 1.65
6. Conclusions and future works In this paper, it has been shown that the artificial society approach can systematically examine effects of the proposed robot rental mechanism. Namely, the power-law relation between the robot performance and the amount of money in hand of the players is weakened by the proposed rental mechanism. Players can be divided into producers and consumers. The producers have relatively higher status, thus the motivation for being the players of this type should be preserved. At the same time, the players of the consumer type should enjoy playing the game because their status can be maintained by renting clones for snow battles and they do not differ much in terms of the robot performance and the amount of money in hand. In addition, inflation in the game is successfully controlled by the proposed rental mechanism. Consequently, it is expected that high player satisfaction can be achieved if the robot rental mechanism is actually implemented
in The ICE. Our future works include studying effects with more complex player behaviors, such as heterogeneous player agents with non-supervised learning ability, and comparing the results with those actually obtained from The ICE when in operation.
Acknowledgement
This work has been supported in part by the Ritsumeikan University’s Kyoto Art and Entertainment Innovation Research, a project of the 21st Century Center of Excellence Program funded by the Japan Society for Promotion of Science. Both authors are grateful to the other members of the Intelligent Computer Entertainment Laboratory for their fruitful discussions.
producers
Table 5. Major statistics of both the robot performance and the amount of money in hand of the players for (a) the producers and (b) the consumers
money in hand
1 0.8 0.6
0.2 0
0
0.2
0.4
0.6
0.8
1
robot performance
(a) consumers 1 money in hand
major statistics maximum mean median stdev
(a) producers the robot the amount of performance money in hand 150 8822 92.58 2175.16 92 2023 15.59 1083.72
major statistics maximum mean median stdev
(b) consumers the robot the amount of performance money in hand 122 5461 73.60 1472.23 75 1484 18.73 940.63
0.4
0.8 0.6 0.4 0.2 0
0
0.2
0.4
0.6
0.8
1
robot performance
(b) Figure 4. Scatter plot of the normalized amount of money in hand versus the normalized robot performance of the players with the regression curve being overlayed for (a) producers and (b) consumers
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