Complexity Results about Nash Equilibria
Abstract
Noncooperative game theory provides a normative framework for analyzing strategic interactions. However, for the toolbox to be operational, the solutions it defines will have to be computed. In this paper, we provide a single reduction that 1) demonstrates NPhardness of determining whether Nash equilibria with certain natural properties exist, and 2) demonstrates the #Phardness of counting Nash equilibria (or connected sets of Nash equilibria). We also show that 3) determining whether a purestrategy BayesNash equilibrium exists is NPhard, and that 4) determining whether a purestrategy Nash equilibrium exists in a stochastic (Markov) game is PSPACEhard even if the game is invisible (this remains NPhard if the game is finite). All of our hardness results hold even if there are only two players and the game is symmetric. Keywords: Nash equilibrium; game theory; computational complexity; noncooperative game theory; normal form game; stochastic game; Markov game; BayesNash equilibrium; multiagent systems.
 Publication:

arXiv eprints
 Pub Date:
 May 2002
 arXiv:
 arXiv:cs/0205074
 Bibcode:
 2002cs........5074C
 Keywords:

 Computer Science  Computer Science and Game Theory;
 Computer Science  Computational Complexity;
 Computer Science  Multiagent Systems;
 I.2.11
 EPrint:
 In Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI03), Acapulco, Mexico, 2003