Complexity Results about Nash Equilibria

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dc.creatorConitzer, Vincent
dc.creatorSandholm, Tuomas
dc.date2002-05-28
dc.date.accessioned2026-07-07T03:18:28Z
dc.date.available2026-07-07T03:18:28Z
dc.descriptionNoncooperative 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 NP-hardness of determining whether Nash equilibria with certain natural properties exist, and 2) demonstrates the #P-hardness of counting Nash equilibria (or connected sets of Nash equilibria). We also show that 3) determining whether a pure-strategy Bayes-Nash equilibrium exists is NP-hard, and that 4) determining whether a pure-strategy Nash equilibrium exists in a stochastic (Markov) game is PSPACE-hard even if the game is invisible (this remains NP-hard 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; Bayes-Nash equilibrium; multiagent systems.
dc.identifierhttps://arxiv.org/abs/cs/0205074
dc.identifierhttp://arxiv.org/abs/cs/0205074
dc.identifierIn Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI-03), Acapulco, Mexico, 2003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/31124
dc.subjectComputer Science and Game Theory
dc.subjectComputational Complexity
dc.subjectMultiagent Systems
dc.subjectI.2.11
dc.titleComplexity Results about Nash Equilibria
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