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Stochastic Game Theory: Adjustment to Equilibrium Under Noisy Directional Learning

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Author Info
Simon P. Anderson ()
Jacob K. Goeree ()
Charles A. Holt ()

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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.

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File URL: http://www.virginia.edu/economics/RePEc/vir/virpap/papers/virpap327.pdf
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Publisher Info
Paper provided by University of Virginia, Department of Economics in its series Virginia Economics Online Papers with number 327.

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Length: 30 pages
Date of creation: Jul 1999
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Handle: RePEc:vir:virpap:327

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Web page: http://www.virginia.edu/economics/home.html

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Related research
Keywords: bounded rationality noisy directional learning Fokker- Planck equation potential games logit equilibrium stochastic potential.

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

References listed on IDEAS
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  1. Slade, Margaret E, 1994. "What Does an Oligopoly Maximize?," Journal of Industrial Economics, Blackwell Publishing, vol. 42(1), pages 45-61, March. [Downloadable!] (restricted)
    Other versions:
  2. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June. [Downloadable!] (restricted)
  3. Ochs Jack, 1995. "Games with Unique, Mixed Strategy Equilibria: An Experimental Study," Games and Economic Behavior, Elsevier, vol. 10(1), pages 202-217, July. [Downloadable!] (restricted)
  4. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August. [Downloadable!] (restricted)
    Other versions:
  5. Rosenthal, Robert W, 1989. "A Bounded-Rationality Approach to the Study of Noncooperative Games," International Journal of Game Theory, Springer, vol. 18(3), pages 273-91.
  6. Smith, Vernon L & Walker, James M, 1993. "Monetary Rewards and Decision Cost in Experimental Economics," Economic Inquiry, Oxford University Press, vol. 31(2), pages 245-61, April.
  7. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January. [Downloadable!] (restricted)
    Other versions:
  8. Anderson, Simon P. & Goeree, Jacob K. & Holt, Charles A., 1998. "A theoretical analysis of altruism and decision error in public goods games," Journal of Public Economics, Elsevier, vol. 70(2), pages 297-323, November. [Downloadable!] (restricted)
  9. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
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  10. Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Blackwell Publishing, vol. 66(2), pages 363-93, April. [Downloadable!] (restricted)
  11. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September. [Downloadable!] (restricted)
  12. Binmore, Ken, and Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Discussion Paper Serie B 275, University of Bonn, Germany.
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  13. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July. [Downloadable!] (restricted)
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  15. C. Monica Capra et al., 1999. "Anomalous Behavior in a Traveler's Dilemma?," American Economic Review, American Economic Association, vol. 89(3), pages 678-690, June. [Downloadable!] (restricted)
  16. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  17. Binmore Kenneth G. & Samuelson Larry & Vaughan Richard, 1995. "Musical Chairs: Modeling Noisy Evolution," Games and Economic Behavior, Elsevier, vol. 11(1), pages 1-35, October. [Downloadable!] (restricted)
  18. Chen, Hsiao-Chi & Friedman, James W. & Thisse, Jacques-Francois, 1997. "Boundedly Rational Nash Equilibrium: A Probabilistic Choice Approach," Games and Economic Behavior, Elsevier, vol. 18(1), pages 32-54, January. [Downloadable!] (restricted)
    Other versions:
  19. Selten, Reinhard, and Joachim Buchta, 1994. "Experimental Sealed Bid First Price Auctions with Directly Observed Bid Functions," Discussion Paper Serie B 270, University of Bonn, Germany.
  20. Bryant, John, 1983. "A Simple Rational Expectations Keynes-Type Model," The Quarterly Journal of Economics, MIT Press, vol. 98(3), pages 525-28, August. [Downloadable!] (restricted)
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  22. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May. [Downloadable!] (restricted)
  23. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 1998. "Rent Seeking with Bounded Rationality: An Analysis of the All-Pay Auction," Journal of Political Economy, University of Chicago Press, vol. 106(4), pages 828-853, August. [Downloadable!] (restricted)
  24. 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. [Downloadable!] (restricted)
    Other versions:
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. JIMENEZ Edward, 2002. "Unified Game Theory," Computing in Economics and Finance 2002 25, Society for Computational Economics. [Downloadable!]
  2. Basov, S., 2001. "An Evolutionary Model of Reciprocity," Department of Economics - Working Papers Series 812, The University of Melbourne. [Downloadable!]
  3. Suren Basov, 2002. "Bounded Rationality: Static versus Dynamic Approach," Department of Economics - Working Papers Series 864, The University of Melbourne. [Downloadable!]
  4. Michihiro Kandori, 2002. "The Erosion and Sustainability of Norms and Morale," CIRJE F-Series CIRJE-F-169, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  5. Veronika Grimm & Giovanni Ponti & Jaromir Kovarik, 2006. "Fixed Price Plus Rationing: An Experiment," Working Papers. Serie AD 2006-26, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  6. 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. [Downloadable!]
  7. Philip A. Haile & Ali Hortacsu & Grigory Kosenok, 2003. "On the Empirical Content of Quantal Response Equilibrium," Cowles Foundation Discussion Papers 1432, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  8. Michihiro Kandori, 2002. "The Erosion and Sustainability of Norms and Morale," Levine's Bibliography 506439000000000030, UCLA Department of Economics. [Downloadable!]
  9. 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, UCLA Department of Economics. [Downloadable!]
  10. Suren Basov, 2003. "Bounded Rationality:Static Versus Dynamic Approaches," Department of Economics - Working Papers Series 874, The University of Melbourne. [Downloadable!]
  11. Josef Hofbauer & William H. Sandholm, 2001. "Evolution and Learning in Games with Randomly Disturbed Payoffs," Vienna Economics Papers 0205, University of Vienna, Department of Economics. [Downloadable!]
  12. repec:att:wimass:192015 is not listed on IDEAS
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