Abstract
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).
Supported by EPSRC grants EP/G069239/1 and EP/G069034/1 “Efficient Decentralised Approaches in Algorithmic Game Theory.”
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Goldberg, P.W., Savani, R., Sørensen, T.B., Ventre, C. (2011). On the Approximation Performance of Fictitious Play in Finite Games. In: Demetrescu, C., Halldórsson, M.M. (eds) Algorithms – ESA 2011. ESA 2011. Lecture Notes in Computer Science, vol 6942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23719-5_9
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DOI: https://doi.org/10.1007/978-3-642-23719-5_9
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