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Stochastic Game Theory: Adjustment to Equilibrium Under Noisy Directional Learning

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  • Simon P. Anderson
  • Jacob K. Goeree
  • Charles A. Holt

Abstract

This paper presents a dynamic model in which agents adjust their decisions in the direction of higher payoffs, subject to random error. This process produces a probability distribution of players' decisions whose evolution over time is determined by the Fokker-Planck equation. The dynamic process is stable for all potential games, a class of payoff structures that includes several widely studied games. In equilibrium, the distributions that determine expected payoffs correspond to the distributions that arise from the logit function applied to those expected payoffs. This "logit equilibrium" forms a stochastic generalization of the Nash equilibrium and provides a possible explanation of anomalous laboratory data.

Suggested Citation

  • Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 1999. "Stochastic Game Theory: Adjustment to Equilibrium Under Noisy Directional Learning," Virginia Economics Online Papers 327, University of Virginia, Department of Economics.
    • Handle: RePEc:vir:virpap:327
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    References listed on IDEAS

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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Article Summary: Noisy Directional Learning and the Logit Equilibrium
      by John Barrdear in John Barrdear on 2009-08-24 18:38:19

    Citations

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    Cited by:

    1. JIMENEZ Edward, 2002. "Unified Game Theory," Computing in Economics and Finance 2002 25, Society for Computational Economics.
    2. Philip A. Haile & Ali Hortaçsu & Grigory Kosenok, 2008. "On the Empirical Content of Quantal Response Equilibrium," American Economic Review, American Economic Association, vol. 98(1), pages 180-200, March.
    3. C. Monica Capra & Susana Cabrera & Rosario Gómez, 2003. "The Effects of Common Advice on One-shot Traveler’s Dilemma Games: Explaining Behavior through an Introspective Model with Errors," Economic Working Papers at Centro de Estudios Andaluces E2003/17, Centro de Estudios Andaluces.
    4. C. Monica Capra & Jacob K Goeree & Rosario Gomez & Charles A Holt, 2002. "Learning and Noisy Equilibrium Behavior in an Experimental Study of Imperfect Price Competition," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(3), pages 613-636, August.
    5. Veronika Grimm & Jaromir Kovarik & Giovanni Ponti, 2008. "Fixed price plus rationing: an experiment," Experimental Economics, Springer;Economic Science Association, vol. 11(4), pages 402-422, December.
    6. Basov, S., 2001. "An Evolutionary Model of Reciprocity," Department of Economics - Working Papers Series 812, The University of Melbourne.
    7. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2002. "The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies," Southern Economic Journal, John Wiley & Sons, vol. 69(1), pages 21-47, July.
    8. Goeree, Jacob K. & Holt, Charles A., 2005. "An experimental study of costly coordination," Games and Economic Behavior, Elsevier, vol. 51(2), pages 349-364, May.
    9. Hofbauer,J. & Sandholm,W.H., 2001. "Evolution and learning in games with randomly disturbed payoffs," Working papers 5, Wisconsin Madison - Social Systems.
    10. Jiabin Wu, 2021. "Stochastic Value Formation," Dynamic Games and Applications, Springer, vol. 11(3), pages 597-611, September.
    11. Suren Basov, 2005. "Bounded rationality: static versus dynamic approaches," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(4), pages 871-885, June.
    12. Charles A. Holt & Jacob K. Goeree, 1999. "Stochastic Game Theory: For Playing Games, Not Just for Doing Theory," Virginia Economics Online Papers 306, University of Virginia, Department of Economics.
    13. Michihiro Kandori, 2003. "The Erosion and Sustainability of Norms and Morale," The Japanese Economic Review, Japanese Economic Association, vol. 54(1), pages 29-48, March.
    14. Hofbauer,J. & Sandholm,W.H., 2001. "Evolution and learning in games with randomly disturbed payoffs," Working papers 5, Wisconsin Madison - Social Systems.
    15. Armantier, Olivier, 2004. "Does observation influence learning?," Games and Economic Behavior, Elsevier, vol. 46(2), pages 221-239, February.
    16. Simon P Anderson & Jacob K Goeree & Charles A Holt, 2001. "A Thoeretical Anlysis of Altruism and Decision Error in Public Goods Games," Levine's Working Paper Archive 563824000000000075, David K. Levine.
    17. Stegeman, Mark & Rhode, Paul, 2004. "Stochastic Darwinian equilibria in small and large populations," Games and Economic Behavior, Elsevier, vol. 49(1), pages 171-214, October.
    18. Basov, S., 2001. "A Noisy Model of Individual Behaviour," Department of Economics - Working Papers Series 791, The University of Melbourne.

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    More about this item

    Keywords

    bounded rationality; noisy directional learning; Fokker- Planck equation; potential games; logit equilibrium; stochastic potential.;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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