Nash and Correlated Equilibria: Some Complexity Considerations

Itzhak Gilboa (1) , Eitan Zemel (1)

1 Northwestern University [Evanston]

This paper deals with the complexity of computing Nash and correlated equilibria for a finite game in normal form. We examine the problems of checking the existence of equilibria satisfying a certain condition, such as "Given a game G and a number r, is there a Nash (correlated) equilibrium of G in which all players obtain an expected payoff of at least r?" or "Is there a unique Nash (correlated) equilibrium in G?" etc. We show that such problems are typically "hard" (NP-hard) for Nash equilibria but "easy" (polynomial) for correlated equilibria.

Keywords: Nash; Correlated Equilibria; Complexity Considerations

Domains: Economy and decision science

Itzhak Gilboa, Eitan Zemel. Nash and Correlated Equilibria: Some Complexity Considerations. Games and Economic Behavior, 1989, vol. 1, pp. 80-93. ⟨10.1016/0899-8256(89)90006-7⟩. ⟨hal-00753241⟩