On the approximation performance of fictitious play in finite games

Paul Goldberg (), Rahul Savani (), Troels Sørensen () and Carmine Ventre ()

International Journal of Game Theory, 2013, vol. 42, issue 4, 1059-1083

Abstract: We study the performance of Fictitious Play (FP), 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 FP 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 $$1/2 - O(1/n)$$ . Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Fictitious play; Approximate Nash equilibria; Decentralized dynamics (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s00182-012-0362-6

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