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Stochastic Approximation, Momentum, and Nash Play

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Abstract

Main objects here are normal-form games, featuring uncertainty and noncooperative players who entertain local visions, form local approximations, and hesitate in making large, swift adjustments. For the purpose of reaching Nash equilibrium, or learning such play, we advocate and illustrate an algorithm that combines stochastic gradient projection with the heavyball method. What emerges is a coupled, constrained, second-order stochastic process. Some friction feeds into and stabilizes myopic approximations. Convergence to Nash play obtains under seemingly weak and natural conditions, an important one being that accumulated marginal payoffs remains bounded above.

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  • Berglann, Helge & Flåm, Sjur Didrik, 2002. "Stochastic Approximation, Momentum, and Nash Play," Working Papers in Economics 09/02, University of Bergen, Department of Economics.
    • Handle: RePEc:hhs:bergec:2002_009
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    References listed on IDEAS

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    1. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    2. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    3. Flam, Sjur Didrik, 1996. "Approaches to economic equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1505-1522.
    4. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    5. S. D. Flåm & J. Morgan, 2004. "Newtonian Mechanics And Nash Play," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 181-194.
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    More about this item

    Keywords

    Noncooperative games; Nash equilibrium; stochastic programming and approximation; the heavy ball method.;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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