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/n 1-δ ) for arbitrarily small δ. We also show an essentially matching upper bound of 1/2-O(1/n). © 2011 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Goldberg, P. W., Savani, R., Sørensen, T. B., & Ventre, C. (2011). On the approximation performance of fictitious play in finite games. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6942 LNCS, pp. 93–105). https://doi.org/10.1007/978-3-642-23719-5_9
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