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Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games

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  • Sam Ganzfried

Abstract

While fictitious play is guaranteed to converge to Nash equilibrium in certain game classes, such as two-player zero-sum games, it is not guaranteed to converge in non-zero-sum and multiplayer games. We show that fictitious play in fact leads to improved Nash equilibrium approximation over a variety of game classes and sizes than (counterfactual) regret minimization, which has recently produced superhuman play for multiplayer poker. We also show that when fictitious play is run several times using random initializations it is able to solve several known challenge problems in which the standard version is known to not converge, including Shapley's classic counterexample. These provide some of the first positive results for fictitious play in these settings, despite the fact that worst-case theoretical results are negative.

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  • Sam Ganzfried, 2020. "Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games," Papers 2001.11165, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2001.11165
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    References listed on IDEAS

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    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Sam Ganzfried & Austin Nowak & Joannier Pinales, 2018. "Successful Nash Equilibrium Agent for a 3-Player Imperfect-Information Game," Papers 1804.04789, arXiv.org.
    3. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, April.
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    Cited by:

    1. Sam Ganzfried, 2020. "Fast Complete Algorithm for Multiplayer Nash Equilibrium," Papers 2002.04734, arXiv.org, revised Jan 2023.
    2. Sam Ganzfried, 2021. "Algorithm for Computing Approximate Nash Equilibrium in Continuous Games with Application to Continuous Blotto," Games, MDPI, vol. 12(2), pages 1-11, June.
    3. Sam Ganzfried, 2020. "Algorithm for Computing Approximate Nash Equilibrium in Continuous Games with Application to Continuous Blotto," Papers 2006.07443, arXiv.org, revised Jun 2021.
    4. Sam Ganzfried, 2022. "Fictitious Play with Maximin Initialization," Papers 2203.10774, arXiv.org, revised Nov 2022.

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