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Random Initialization Solves Shapley's Fictitious Play Counterexample

Sam Ganzfried
Sep 2022
摘要
In 1964 Shapley devised a family of games for which fictitious play fails toconverge to Nash equilibrium. The games are two-player non-zero-sum with 3 purestrategies per player. Shapley assumed that each player played a specific purestrategy in the first round. We show that if we use random (mixed) strategyprofile initializations we are able to converge to Nash equilibriumapproximately 1/3 of the time for a representative game in this class.
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