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Improving Behavior of Computer Game Bots Using fictitious play

International Journal of Automation and computing 2012年第2期9卷 122-134页

作者： Ushma Kesha Patel Purvag Patel Henry Hexmoor Norman Carver Department of Computer Science Southern Illinois University

In modern computer games, ＂bots＂ - intelligent realistic agents play a prominent role in the popularity of a game in the market. Typically, bots are modeled using finite-state machine and then programmed via simple conditional statements which are hard-coded in bots logic. Since these bots have become quite predictable to an experienced games＇ player, a player might lose interest in the game. We propose the use of a game theoretic based learning rule called fictitious play for improving behavior of these computer game bots which will make them less predictable and hence, more a enjoyable game.

关键词： Agents computer game bots fictitious play game theory learning Nash equilibrium.

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Nash Equilibrium Solving for General Non-Zero-Sum Games from Non-Convergent Dynamics of fictitious play

Nash Equilibrium Solving for General Non-Zero-Sum Games from...

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第43届中国控制会议

作者： Zhouming Wu Yifen Mu Xiaoguang Yang Ge Chen Key Lab of Systems and Control ISSAcademy of Mathematics and Systems ScienceCAS School of Mathematical Sciences University of Chinese Academy of Sciences Key Lab of Management Decision and Information SystemISSAcademy of Mathematics and Systems ScienceCAS School of Economies and Management University of Chinese Academy of Sciences

Solving Nash equilibrium(NE) is a fundamental problem in game ***,for general non-zero-sum games,computing NE remains challenging(in fact,it is PPAD-hard),and there are no known efficient algorithms so *** from classical combinatorial methods,learning-based approaches offer an alternative for approximating ***,for general non-zero-sum games,the dynamics of learning algorithms turns out to be intricate,and often fail to *** this paper,we give a novel method to solve NE from the trajectory of fictitious play(FP),a classical learning algorithm in repeated *** leveraging the equalization principle of NE,we demonstrate that hidden NE can be unveiled via the trajectory ***,we focus on two *** the 3 × 3 game with interior equilibrium when FP exhibits non-convergent behavior,such as cyclic or erratic trajectories,we can obtain an approximate NE by estimating the indifferent lines and solving their intersection *** the games without an interior equilibrium,by identifying the intersection points between the indifferent lines and the edges of the players' strategy simplexes,and proposing a label-matching principle,we can still find the approximate *** via this method,we can solve all 3 × 3 games from finite trajectory date of FP no matter how complicated the dynamics *** experiments show that the method can be extended to more general normal form games and special kind of stochastic *** paper reveals that there is more information hidden in the behavior of learning dynamics,and thus indicating a promising way to utilize trajectory data.

关键词： NE Solving Non-Zero-Sum Games fictitious play Repeated Games Dynamical Systems Equalization Principle

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Prospect Theoretic Analysis on Weighted Vertex Cover of Networks

Prospect Theoretic Analysis on Weighted Vertex Cover of Netw...

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第40届中国控制会议

作者： Yuanyuan Hu Jie Chen Changbing Tang College of Physics and Electronic Engineering Zhejiang Normal University Adaptive Networks and Control Lab Department of Electronic EngineeringFudan University

Weighted vertex cover（WVC） is a classical combinatorial optimization problem, which has rich practice ***, the existing WVC studies based on game theory has introduced the traditional expected utility theory（EUT）, where each vertex is treated as a rational player. However, the uncertainty caused by the weight factor is neglected. So how does this uncertainty affect players’ behaviour? In this paper, the complete theoretical analysis is shown. Specifically, we model the WVC problem as an non-cooperative game on weighted networks and respectively establish EUT-based and prospect theory-based utility functions. Then, we prove the existence of mixed NE on this weighted game. Further, by designing a state function,we find that the vertices’ state under mixed NE satisfies weighted vertex cover state of the network. Finally, a fictitious play algorithm is proposed to get a NE of the game. Our findings will pave the way for the future numerical simulation, which can demonstrate the impact of the prospect theory on weighted vertex cover.

关键词： Weighted vertex cover(WVC) Game theory Prospect theory Nash equilibrium fictitious play

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