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arXiv · 1103.1040

On the Approximation Performance of Fictitious Play in Finite Games

Paul W. Goldberg·Rahul Savani·Troels Bjerre Sorensen·Carmine Ventre
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Abstract

We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-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 times 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/n^(1-delta)) for arbitrarily small delta. We also show an essentially matching upper bound of 1/2 - O(1/n).

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Paul W. Goldberg, Rahul Savani, Troels Bjerre Sorensen, Carmine Ventre. 2011-03-19. On the Approximation Performance of Fictitious Play in Finite Games. https://arxiv.org/abs/1103.1040

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