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Complexity Results about Nash Equilibria

Vincent Conitzer

出版	School of Computer Science, Carnegie Mellon University, 2002
URL	http://books.google.com.hk/books?id=jX3OHAAACAAJ&hl=&source=gbs_api

註釋

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 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 PSP ACE-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."