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Solving Large Games With Simulated Fictitious Play

Author

Listed:
  • DARRYL A. SEALE

    (Department of Management, University of Nevada Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154-6009, USA)

  • JOHN E. BURNETT

    (Department of Accounting and Finance, University of Alabama in Huntsville, Huntsville, AL 35899, USA)

Abstract

A computational procedure, Simulated Fictitious Play (SFP), is introduced to approximate equilibrium solutions forn-person, non-cooperative games with large strategy spaces. A variant of the iterative solution process fictitious play (FP), SFP is first demonstrated on several small n-person games with known solutions. In each case, SFP solutions are compared to those obtained through analytical methods. Sensitivity analyses are presented that examine the effects of iterations (repetitions of the stage game) and number of sample outcomes generated within each iteration on measures of convergence. The algorithm is then used to approximate the solution of a 20-player game, in which each player has 601 pure strategies. The resulting strategy space, 60120, or3.78 × 1055, has proved virtually unmanageable for existing solution methods and computer software packages that employ numerical methods. The paper discusses the origins and theoretical development of FP, as well as interest in FP as a model of learning. It concludes with a discussion of both the potential and limitations of SFP.

Suggested Citation

  • Darryl A. Seale & John E. Burnett, 2006. "Solving Large Games With Simulated Fictitious Play," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 437-467.
    • Handle: RePEc:wsi:igtrxx:v:08:y:2006:i:03:n:s0219198906001016
    DOI: 10.1142/S0219198906001016
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    References listed on IDEAS

    as
    1. van der Genugten, B.B., 1998. "A Weakend Form of Fictitious Play in Two-Person Zero-Sum Games," Discussion Paper 1998-88, Tilburg University, Center for Economic Research.
    2. Kreps, David M., 1990. "Game Theory and Economic Modelling," OUP Catalogue, Oxford University Press, number 9780198283812, Decembrie.
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    Cited by:

    1. Jiequn Han & Ruimeng Hu, 2019. "Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Games," Papers 1912.01809, arXiv.org, revised Jun 2020.

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    More about this item

    Keywords

    Cognitive decision models; strategic decision making; game theory; simulation;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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