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Random Initialization Solves Shapley's Fictitious Play Counterexample

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  • Sam Ganzfried

Abstract

In 1964 Shapley devised a family of games for which fictitious play fails to converge to Nash equilibrium. The games are two-player non-zero-sum with 3 pure strategies per player. Shapley assumed that each player played a specific pure strategy in the first round. We show that if we use random (mixed) strategy profile initializations we are able to converge to Nash equilibrium approximately 1/3 of the time for a representative game in this class.

Suggested Citation

  • Sam Ganzfried, 2022. "Random Initialization Solves Shapley's Fictitious Play Counterexample," Papers 2209.02154, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2209.02154
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    File URL: http://arxiv.org/pdf/2209.02154
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