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.
Shapley, Lloyd S., On the Nonconvergence of Fictitious Play. Santa Monica, CA: RAND Corporation, 1962. https://www.rand.org/pubs/research_memoranda/RM3026.html. Also available in print form.
Shapley, Lloyd S., On the Nonconvergence of Fictitious Play, Santa Monica, Calif.: RAND Corporation, RM-3026-PR, 1962. As of September 09, 2021: https://www.rand.org/pubs/research_memoranda/RM3026.html