{"type":"ScholarlyArticle","title":"Complexity Results about Nash Equilibria","authors":[{"name":"Vincent Conitzer","slug":"vincent-conitzer","given":"Vincent","family":"Conitzer","affiliation":""},{"name":"Tuomas Sandholm","slug":"tuomas-sandholm","given":"Tuomas","family":"Sandholm","affiliation":""}],"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 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 purestrategy Bayes-Nash equilibrium exists is NPhard, and that 4) determining whether a purestrategy Nash equilibrium exists in a stochastic (Markov) game is PSPAC£-hard even ifthe 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.","doi":null,"url":"https://ijcai.org/proceedings/2003/111","pdf":"https://ijcai.org/proceedings/2003/0111.pdf","markdown":"https://ijcai.org/proceedings/2003/111.md","bibtex":"https://ijcai.org/proceedings/2003/bibtex/111","volume":{"slug":"2003","title":"Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2003","url":"https://ijcai.org/proceedings/2003/","year":2003,"location":"Acapulco, Mexico","dates":"","editors":"Georg Gottlob","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":111,"pages":{"first":765,"last":770},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}