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On the Approximation Performance of Fictitious Play in Finite Games

  • Paul W. Goldberg
  • Rahul Savani
  • Troels Bjerre Sørensen
  • Carmine Ventre
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6942)

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).

Keywords

Nash Equilibrium Mixed Strategy Approximation Performance Pure Strategy Adjacent Block 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Paul W. Goldberg
    • 1
  • Rahul Savani
    • 1
  • Troels Bjerre Sørensen
    • 2
  • Carmine Ventre
    • 1
  1. 1.Department of Computer ScienceUniversity of LiverpoolUK
  2. 2.Department of Computer ScienceUniversity of WarwickUK

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