Publications [#303207] of Vincent Conitzer

Journal articles or Book chapters PUBLISHED

1. Conitzer, V; Sandholm, T, Complexity results about Nash equilibria, IJCAI International Joint Conference on Artificial Intelligence, vol. cs.GT/0205074 (December, 2003), pp. 765-771 [0205074v1]
   (last updated on 2024/04/24)

   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.