The complexity of computing a Nash equilibrium

Authors:
Constantinos Daskalakis;Paul W. Goldberg;Christos H. Papadimitriou
Affiliations:
University of California, Berkeley;University of Warwick, U.K.;University of California, Berkeley
Venue:
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Year:
2006

Citing 14
Cited 136

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Abstract

We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recently-established equivalence between polynomial time solvability of normal form games and graphical games, establishing that these kinds of games can simulate a PPAD-complete class of Brouwer functions.