Computing Bayes-Nash Equilibria through Support Enumeration Methods in Bayesian Two-Player Strategic-Form Games

The computation of equilibria in games is a challenging task. The literature studies the problem of finding Nash equilibria with complete-information games in depth, but not enough attention is paid to searching for equilibria in Bayesian games. Customarily, these games are reduced to complete information games and standard algorithms for computing Nash equilibria are employed. However, no work studied how these algorithms perform with Bayesian games. In this paper we focus on two-player strategic-form games. We show that the most efficient algorithm for computing Nash equilibria with GAMUT data (i.e., Porter-Nudelman-Shoham) is inefficient with Bayesian games, we provide an extension, and we experimentally evaluate its performance.

[1]  Andrew McLennan,et al.  Asymptotic expected number of Nash equilibria of two-player normal form games , 2005, Games Econ. Behav..

[2]  Michael C. Ferris,et al.  Interfaces to PATH 3.0: Design, Implementation and Usage , 1999, Comput. Optim. Appl..

[3]  Jan Karel Lenstra,et al.  Sequencing by enumerative methods , 1977 .

[4]  John C. Harsanyi,et al.  Games with Incomplete Information Played by "Bayesian" Players, I-III: Part I. The Basic Model& , 2004, Manag. Sci..

[5]  C. E. Lemke Some pivot schemes for the linear complementarity problem , 1978 .

[6]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[7]  Nicola Gatti,et al.  Alternating-offers bargaining with one-sided uncertain deadlines: an efficient algorithm , 2008, Artif. Intell..

[8]  Vincent Conitzer,et al.  Mixed-Integer Programming Methods for Finding Nash Equilibria , 2005, AAAI.

[9]  M. Dufwenberg Game theory. , 2011, Wiley interdisciplinary reviews. Cognitive science.

[10]  Nicola Gatti,et al.  Game Theoretical Insights in Strategic Patrolling: Model and Algorithm in Normal-Form , 2008, ECAI.

[11]  Nicola Gatti,et al.  Alternating-Offers Bargaining Under One-Sided Uncertainty on Deadlines , 2006, ECAI.

[12]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[13]  Yoav Shoham,et al.  Simple search methods for finding a Nash equilibrium , 2004, Games Econ. Behav..

[14]  J. Szep,et al.  Games with incomplete information , 1985 .

[15]  Tim Roughgarden,et al.  Algorithmic Game Theory , 2007 .

[16]  Thomas Stützle,et al.  Stochastic Local Search: Foundations & Applications , 2004 .

[17]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[18]  Nicola Basilico,et al.  Leader-follower strategies for robotic patrolling in environments with arbitrary topologies , 2009, AAMAS.

[19]  C. E. Lemke,et al.  Equilibrium Points of Bimatrix Games , 1964 .

[20]  Vincent Conitzer,et al.  Complexity of (iterated) dominance , 2005, EC '05.

[21]  D. Koller,et al.  Efficient Computation of Equilibria for Extensive Two-Person Games , 1996 .

[22]  Yoav Shoham,et al.  Run the GAMUT: a comprehensive approach to evaluating game-theoretic algorithms , 2004, Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems, 2004. AAMAS 2004..

[23]  J. Harsanyi Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

[24]  Yoav Shoham,et al.  Multiagent Systems - Algorithmic, Game-Theoretic, and Logical Foundations , 2009 .