2011/03/05 by Goldberg, Paul W., Savani, Rahul, Sorensen, Troels Bjerre +1 · 1 citation
#Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1103.1040
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).