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A Weakened Form Of Fictitious Play In Two-Person Zero-Sum Games

Author

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  • BEN VAN DER GENUGTEN

    (Center for Economic Research, Tilburg University, The Netherlands)

Abstract

Fictitious play can be seen as a numerical iteration procedure for determining the value of a game and corresponding optimal strategies. Although convergence is slow, it needs only a modest computer storage. Therefore it seems to be a good way for analysing large games. In this paper we introduce a weakened form of fictitious play, where players at each stage do not have to make the best choice against the total of past choices of the other player but only an increasingly better one. Theoretical bounds for convergence are derived. Furthermore, it is shown that this new form can speed up convergence considerably in practice. It is seen that weakened fictitious play can be extended to models in which the game matrix itself becomes better known as the number of stages increases.

Suggested Citation

  • Ben Van Der Genugten, 2000. "A Weakened Form Of Fictitious Play In Two-Person Zero-Sum Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 307-328.
    • Handle: RePEc:wsi:igtrxx:v:02:y:2000:i:04:n:s0219198900000202
    DOI: 10.1142/S0219198900000202
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    Cited by:

    1. Leslie, David S. & Collins, E.J., 2006. "Generalised weakened fictitious play," Games and Economic Behavior, Elsevier, vol. 56(2), pages 285-298, August.

    More about this item

    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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