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Fictitious Play with Maximin Initialization

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  • Sam Ganzfried

Abstract

Fictitious play has recently emerged as the most accurate scalable algorithm for approximating Nash equilibrium strategies in multiplayer games. We show that the degree of equilibrium approximation error of fictitious play can be significantly reduced by carefully selecting the initial strategies. We present several new procedures for strategy initialization and compare them to the classic approach, which initializes all pure strategies to have equal probability. The best-performing approach, called maximin, solves a nonconvex quadratic program to compute initial strategies and results in a nearly 75% reduction in approximation error compared to the classic approach when 5 initializations are used.

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  • Sam Ganzfried, 2022. "Fictitious Play with Maximin Initialization," Papers 2203.10774, arXiv.org, revised Nov 2022.
    • Handle: RePEc:arx:papers:2203.10774
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    File URL: http://arxiv.org/pdf/2203.10774
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    References listed on IDEAS

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    1. Sam Ganzfried & Conner Laughlin & Charles Morefield, 2019. "Parallel Algorithm for Approximating Nash Equilibrium in Multiplayer Stochastic Games with Application to Naval Strategic Planning," Papers 1910.00193, arXiv.org, revised Mar 2020.
    2. Sam Ganzfried, 2020. "Empirical Analysis of Fictitious Play for Nash Equilibrium Computation in Multiplayer Games," Papers 2001.11165, arXiv.org, revised Jul 2024.
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