On the Approximation Performance of Fictitious Play in Finite Games

Details On the Approximation Performance of Fictitious Play in Finite Games On the Approximation Performance of Fictitious Play in Finite Games

2011-03-05

arxiv.org/abs/1103.1040v2

Computer Science

Computer Science and Game Theory

Scientific paper

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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