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Noisy Directional Learning and the Logit Equilibrium

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

Abstract

We specify a dynamic model in which agents adjust their decisions toward higher payoffs, subject to normal error. This process generates a probability distribution of players' decisions that evolves over time according to 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. Copyright The editors of the "Scandinavian Journal of Economics", 2004 .

Suggested Citation

  • Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2004. "Noisy Directional Learning and the Logit Equilibrium," Scandinavian Journal of Economics, Wiley Blackwell, vol. 106(3), pages 581-602, October.
  • Handle: RePEc:bla:scandj:v:106:y:2004:i:3:p:581-602
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    1. Article Summary: Noisy Directional Learning and the Logit Equilibrium
      by John Barrdear in John Barrdear on 2009-08-24 18:38:19

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    2. Jasmina Arifovic & John Ledyard, 2012. "Individual Evolutionary Learning, Other-regarding Preferences, and the Voluntary Contributions Mechanism," Discussion Papers wp12-01, Department of Economics, Simon Fraser University.
    3. Jean-François Laslier & Bernard Walliser, 2015. "Stubborn learning," Theory and Decision, Springer, vol. 79(1), pages 51-93, July.
    4. Friedman, Daniel & Ostrov, Daniel N., 2010. "Gradient dynamics in population games: Some basic results," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 691-707, September.
    5. Ockenfels, Axel & Selten, Reinhard, 2014. "Impulse balance in the newsvendor game," Games and Economic Behavior, Elsevier, vol. 86(C), pages 237-247.
    6. Charles Figuières & David Masclet & Marc Willinger, 2013. "Weak Moral Motivation Leads to the Decline of Voluntary Contributions," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 15(5), pages 745-772, October.
    7. Lahkar, Ratul & Riedel, Frank, 2015. "The logit dynamic for games with continuous strategy sets," Games and Economic Behavior, Elsevier, vol. 91(C), pages 268-282.
    8. Rachel Hess & Charles Holt & Angela Smith, 2007. "Coordination of strategic responses to security threats: Laboratory evidence," Experimental Economics, Springer;Economic Science Association, vol. 10(3), pages 235-250, September.
    9. 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.
    10. Zhang, Boyu & Hofbauer, Josef, 2016. "Quantal response methods for equilibrium selection in 2×2 coordination games," Games and Economic Behavior, Elsevier, vol. 97(C), pages 19-31.
    11. Golman, Russell, 2012. "Homogeneity bias in models of discrete choice with bounded rationality," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 1-11.
    12. Zhang, Boyu, 2016. "Quantal response methods for equilibrium selection in normal form games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 113-123.
    13. Daniele Cassese & Paolo Pin, 2018. "Edgeworth trading on networks," Papers 1803.08836, arXiv.org.
    14. Xuanming Su, 2008. "Bounded Rationality in Newsvendor Models," Manufacturing & Service Operations Management, INFORMS, vol. 10(4), pages 566-589, May.
    15. Wilfred Amaldoss & Teck-Hua Ho & Aradhna Krishna & Kay-Yut Chen & Preyas Desai & Ganesh Iyer & Sanjay Jain & Noah Lim & John Morgan & Ryan Oprea & Joydeep Srivasatava, 2008. "Experiments on strategic choices and markets," Marketing Letters, Springer, vol. 19(3), pages 417-429, December.
    16. Suren Basov & Svetlana Danilkina & David Prentice, 2008. "When does Variety increase with Quality?," Working Papers 2008.04, School of Economics, La Trobe University.
    17. Arifovic, Jasmina & Ledyard, John, 2012. "Individual evolutionary learning, other-regarding preferences, and the voluntary contributions mechanism," Journal of Public Economics, Elsevier, vol. 96(9-10), pages 808-823.
    18. Friedman, Daniel & Ostrov, Daniel N., 2013. "Evolutionary dynamics over continuous action spaces for population games that arise from symmetric two-player games," Journal of Economic Theory, Elsevier, vol. 148(2), pages 743-777.
    19. Russell, Golman, 2011. "Quantal response equilibria with heterogeneous agents," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2013-2028, September.
    20. Smith, Angela M., 2011. "An experimental study of exclusive contracts," International Journal of Industrial Organization, Elsevier, vol. 29(1), pages 4-13, January.
    21. S. Cerreia-Vioglio & F. Maccheroni & M. Marinacci & A. Rustichini, 2017. "Multinomial logit processes and preference discovery: inside and outside the black box," Working Papers 615, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

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