Highly Influenced

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- Published 2005 in Commun. ACM

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.

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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}
}