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On the approximation performance of fictitious play in finite games

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Goldberg, Paul W., Savani, Rahul, Sørensen, Troels Bjerre and Ventre, Carmine (2012) On the approximation performance of fictitious play in finite games. International Journal of Game Theory . doi:10.1007/s00182-012-0362-6 ISSN 0020-7276.

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Official URL: http://dx.doi.org/10.1007/s00182-012-0362-6

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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×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/n1−δ) for arbitrarily small δ . We also show an essentially matching upper bound of 1/2−O(1/n) .

Item Type: Journal Article
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Journal or Publication Title: International Journal of Game Theory
Publisher: Springer-Verlag
ISSN: 0020-7276
Official Date: 2012
Dates:
DateEvent
2012Published
DOI: 10.1007/s00182-012-0362-6
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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