The complexity of computing a Nash equilibrium


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.

DOI: 10.1145/1132516.1132527

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@article{Daskalakis2005TheCO, title={The complexity of computing a Nash equilibrium}, author={Constantinos Daskalakis and Paul W. Goldberg and Christos H. Papadimitriou}, journal={SIAM J. Comput.}, year={2005}, volume={39}, pages={195-259} }