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On the approximation performance of fictitious play in finite games

Author

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  • Paul Goldberg
  • Rahul Savani
  • Troels Sørensen
  • Carmine Ventre

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

Suggested Citation

  • Paul Goldberg & Rahul Savani & Troels Sørensen & Carmine Ventre, 2013. "On the approximation performance of fictitious play in finite games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 1059-1083, November.
  • Handle: RePEc:spr:jogath:v:42:y:2013:i:4:p:1059-1083
    DOI: 10.1007/s00182-012-0362-6
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    References listed on IDEAS

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    4. Sergiu Hart & Andreu Mas-Colell, 2013. "Stochastic Uncoupled Dynamics And Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 8, pages 165-189, World Scientific Publishing Co. Pte. Ltd..
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    6. Sergiu Hart & Andreu Mas-Colell, 2013. "Uncoupled Dynamics Do Not Lead To Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 7, pages 153-163, World Scientific Publishing Co. Pte. Ltd..
    7. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
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    Cited by:

    1. Goldberg, Paul W. & Pastink, Arnoud, 2014. "On the communication complexity of approximate Nash equilibria," Games and Economic Behavior, Elsevier, vol. 85(C), pages 19-31.

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