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Social Learning in Recurring Games

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Author Info
Matthew Jackson
Ehud Kalai

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Abstract

In a recurring game, a stage game is played sequentially by different groups of players. Each group receives publicly available information about the play of earlier groups. Players begin with initial uncertainty about the distribution of types (representing the preferences and strategic behavior) of players in the population. Later groups of players are able to learn from the history of play of earlier groups. We first study the evolution of beliefs in this uncertain recurring setting and then study how the structure of uncertainty and information determine the eventual convergence of play. We show that beliefs converge over time and, moreover, that the limit beliefs are empirically correct: their forecast of future public information matches the true distribution of future public information. Next, we provide sufficient conditions to ensure that the play of any stage game is eventually close to that of a Bayesian equilibrium where players know the true type generating distribution. We go further to identify conditions under which play converges to the play of a trembling-hand perfect (Bayesian) equilibrium.

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File URL: http://www.kellogg.northwestern.edu/research/math/papers/1138.pdf
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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1138.

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Date of creation: Aug 1995
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Handle: RePEc:nwu:cmsems:1138

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  1. Schotter, A. & Sopher, B., 2000. "Social Learning and Coordination Conventions in Inter-Generational Games: An Experiment in Lamarckian Evolutionary Dynamics," Working Papers 00-01, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
    Other versions:
  2. Matthew O. Jackson & Ehud Kalai, 1997. "False Reputation in a Society of Players," Game Theory and Information 9711004, EconWPA. [Downloadable!]
    Other versions:
  3. Topi Miettinen, 2007. "Learning Foundations and Complexity of the Cursed Equilibrium," Discussion Papers on Strategic Interaction 2006-40, Max Planck Institute of Economics, Strategic Interaction Group. [Downloadable!]
  4. Philippe Jehiel & David Ettinger, 2007. "Towards a Theory of Deception," Levine's Bibliography 843644000000000126, UCLA Department of Economics. [Downloadable!]
    Other versions:
  5. Schotter, A. & Sopher, B., 2001. "Social Learning and Coordination Conventions in Inter-Generational Games: An Experimental Study," Working Papers 01-10, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
    Other versions:
  6. Dufwenberg, Martin & Gneezy, Uri, 1999. "Procurement and Information Feedback," Research Papers in Economics 2000:2, Stockholm University, Department of Economics. [Downloadable!]
  7. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1998. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Discussion Papers 1228, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
    Other versions:
  8. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1997. "Patterns, Types, and Bayesian Learning," Game Theory and Information 9711002, EconWPA. [Downloadable!]
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  9. Matthew Jackson & Ehud Kalai, 1995. "Recurring Bullies," Discussion Papers 1151, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  10. Goeree, Jacob & Palfrey, Thomas & Rogers, Brian, 2003. "Social learning with private and common values," Working Papers 1187, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
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  11. Roland G. Fryer & Matthew O. Jackson, 2002. "Categorical Cognition: A Psychological Model of Categories and Identification in Decision Making," Microeconomics 0211002, EconWPA. [Downloadable!]
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  12. John Duffy & Nick Feltovich, 1997. "Does Observation of Others Affect Learning in Strategic Environments? An Experimental Study," Levine's Working Paper Archive 592, UCLA Department of Economics. [Downloadable!]
    Other versions:
  13. Mario Gilli, 2002. "Rational Learning in Imperfect Monitoring Games," Working Papers 46, University of Milano-Bicocca, Department of Economics, revised Mar 2002. [Downloadable!]
  14. Philippe Jehiel, 2007. "Manipulative Auction Design," Levine's Bibliography 122247000000001547, UCLA Department of Economics. [Downloadable!]
  15. Francesco Squintani, 1999. "Games with Small Forgetfulness," Discussion Papers 1273, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  16. Roland Fryer & Matthew Jackson, 2008. "A Categorical Model of Cognition and Biased Decision Making," Contributions to Theoretical Economics, Berkeley Electronic Press, vol. 8(1), pages 1357-1357. [Downloadable!] (restricted)
  17. Jernej Copic & Andrea Galeotti, 2006. "Awareness as an Equilibrium Notion: Normal-Form Games," Economics Discussion Papers 614, University of Essex, Department of Economics. [Downloadable!]
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