On the Approximation Performance of Fictitious Play in Finite Games
Computer Science and Game Theory
2011-03-22 v2
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).
Keywords
Cite
@article{arxiv.1103.1040,
title = {On the Approximation Performance of Fictitious Play in Finite Games},
author = {Paul W. Goldberg and Rahul Savani and Troels Bjerre Sorensen and Carmine Ventre},
journal= {arXiv preprint arXiv:1103.1040},
year = {2011}
}