Nash Equilibria in Symmetric Games with Partial Observation

We investigate a model for representing large multiplayer games, which satisfy strong symmetry properties. This model is made of multiple copies of an arena; each player plays in his own arena, and can partially observe what the other players do. Therefore, this game has partial information and symmetry constraints, which make the computation of Nash equilibria difficult. We show several undecidability results, and for bounded-memory strategies, we precisely characterize the complexity of computing pure Nash equilibria (for qualitative objectives) in this game model.

[1]  A. Prasad Sistla,et al.  Reasoning about systems with many processes , 1992, JACM.

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

[3]  Christel Baier,et al.  Principles of model checking , 2008 .

[4]  Kevin Leyton-Brown,et al.  Symmetric games with piecewise linear utilities , 2010, BQGT.

[5]  Felix A. Fischer,et al.  Symmetries and the complexity of pure Nash equilibrium , 2007, J. Comput. Syst. Sci..

[6]  E. Maskin,et al.  The Existence of Equilibrium in Discontinuous Economic Games, II: Applications , 1986 .

[7]  J. Nash.  Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Patricia Bouyer,et al.  Concurrent Games with Ordered Objectives , 2012, FoSSaCS.

[9]  Daniel M. Reeves,et al.  Notes on Equilibria in Symmetric Games , 2004 .

[10]  Johan van Benthem,et al.  Reasoning about Strategies , 2013, Computation, Logic, Games, and Quantum Foundations.

[11]  Nicolas Markey,et al.  ATL with Strategy Contexts: Expressiveness and Model Checking , 2010, FSTTCS.

[12]  Eric van Damme,et al.  Non-Cooperative Games , 2000 .

[13]  Dominik Wojtczak,et al.  The Complexity of Nash Equilibria in Stochastic Multiplayer Games , 2011, Log. Methods Comput. Sci..

[14]  E. Maskin,et al.  The Existence of Equilibrium in Discontinuous Economic Games, I: Theory , 1986 .

[15]  Amir Pnueli,et al.  Distributed reactive systems are hard to synthesize , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[16]  Krishnendu Chatterjee,et al.  On Nash Equilibria in Stochastic Games , 2004, CSL.

[17]  A. Prasad Sistla,et al.  Symmetry and model checking , 1993, Formal Methods Syst. Des..

[18]  Parosh Aziz Abdulla,et al.  On the Existence of Network Invariants for Verifying Parameterized Systems , 1999, Correct System Design.

[19]  C. Papadimitriou.  Algorithmic Game Theory: The Complexity of Finding Nash Equilibria , 2007 .

[20]  Thomas A. Henzinger,et al.  Games in system design and verification , 2005, TARK.

[21]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .