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)


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).


Nash Equilibrium Mixed Strategy Approximation Performance Pure Strategy Adjacent Block 
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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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