On the Nonconvergence of Fictitious Play

by Lloyd S. Shapley

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An examination of the "method of fictitious play," generally considered a useful tool in game-theoretic analysis. This method, which can be applied to any finite game, imitates a multistage learning process. A counterexample is given to disprove the long-standing conjecture that the method will solve any noncooperative game. It is concluded that the method is of limited reliability in analyzing nonzero-sum games.

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