The Complexity of Computing a Nash Equilibrium

Constantinos Daskalakis, Paul W. Goldberg, Christos H. Papadimitriou
2009 SIAM journal on computing (Print)  
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 polynomialtime solvability of normal-form games and graphical games, and shows that these kinds of games can implement arbitrary members of a PPAD-complete class of Brouwer functions.
doi:10.1137/070699652 fatcat:e47s5caowzecrj7fe24dkuwh2i