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Social Learning in Recurring Games

  • Jackson, Matthew O.
  • Kalai, Ehud

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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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 21 (1997)
Issue (Month): 1-2 (October)
Pages: 102-134

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Handle: RePEc:eee:gamebe:v:21:y:1997:i:1-2:p:102-134
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  1. Fudenberg, Drew & Levine, David K, 1993. "Steady State Learning and Nash Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 547-73, May.
  2. Fudenberg, D. & Levine, D.K., 1991. "Self-Confirming Equilibrium ," Working papers 581, Massachusetts Institute of Technology (MIT), Department of Economics.
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  10. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  11. Kalai, Ehud & Lehrer, Ehud, 1991. "Rational Learning Leads to Nash Equilibrium," Working Papers 91-18, C.V. Starr Center for Applied Economics, New York University.
  12. Sushil Bikhchandani & David Hirshleifer & Ivo Welch, 2010. "A theory of Fads, Fashion, Custom and cultural change as informational Cascades," Levine's Working Paper Archive 1193, David K. Levine.
  13. Lehrer, E, 1989. "Lower Equilibrium Payoffs in Two-Player Repeated Games with Non-observable Actions," International Journal of Game Theory, Springer, vol. 18(1), pages 57-89.
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