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Games with Small Forgetfulness

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  • Francesco Squintani

Abstract

While it is known how players may learn to play in a game they know, the issue of how their model of the game evolves over time is largely unexplored. This paper introduces small forgetfulness and shows that it may destabilize standard full-memory solutions. Players are repeatedly matched to play a game. After any match, they forget with infinitesimal probability the feasibility of any opponents' unobserved action, and they are reminded of all actions that they observe. During each period, they play an equilibrium consistent with their perception of the game. We show that the unique backward induction path drifts into a non-Nash, self-confirming equilibrium, in a class of extensive-form games that are fully characterized. Such a long-run prediction is always Pareto-undominated, and may Pareto dominate the original backward induction path. In one-shot simultaneous-move games, forgetfulness yields a refinement stronger than trembling hand perfection. Our results imply that there are games that players may never fully learn.

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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1273.

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Date of creation: Aug 1999
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Handle: RePEc:nwu:cmsems:1273

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Web page: http://www.kellogg.northwestern.edu/research/math/
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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. Levine, David & Kreps, David & Fudenberg, Drew, 1988. "On the Robustness of Equilibrium Refinements," Scholarly Articles 3350444, Harvard University Department of Economics.
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  9. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May.
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  14. Aumann, Robert & Brandenburger, Adam, 1995. "Epistemic Conditions for Nash Equilibrium," Econometrica, Econometric Society, vol. 63(5), pages 1161-80, September.
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  18. Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B 361, University of Bonn, Germany, revised Mar 1996.
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