Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
A note on approximate Nash equilibria
Theoretical Computer Science
The Complexity of Computing a Nash Equilibrium
SIAM Journal on Computing
New algorithms for approximate Nash equilibria in bimatrix games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Approximation guarantees for fictitious play
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
On the rate of convergence of fictitious play
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
On learning algorithms for nash equilibria
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
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We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a two-player game. We exhibit a class of two-player games having payoffs in the range [0, 1] that show that Fictitious Play fails to find a solution having an additive approximation guarantee significantly better than 1/2. Our construction shows that for n × n games, in the worst case both players may perpetually have mixed strategies whose payoffs fall short of the best response by an additive quantity 1/2-O(1/n1-δ) for arbitrarily small δ. We also show an essentially matching upper bound of 1/2 - O(1/n).