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On the Approximation Performance of Fictitious Play in Finite Games
- Publication Year :
- 2011
-
Abstract
- We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-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 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).
- Subjects :
- Computer Science - Computer Science and Game Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1103.1040
- Document Type :
- Working Paper