Complexity results about Nash equilibria


Journal Article

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.

Duke Authors

Cited Authors

  • Conitzer, V; Sandholm, T

Published Date

  • December 1, 2003

Published In

Start / End Page

  • 765 - 771

International Standard Serial Number (ISSN)

  • 1045-0823

Citation Source

  • Scopus