Understanding Strategic Interaction pp 171-184 | Cite as
Recurring Bullies, Trembling and Learning
Abstract
In a recurring game, a stage game is played consecutively by different groups of players, with each group receiving information about the play of earlier groups. Starting with uncertainty about the distribution of types in the population, late groups may learn to play a correct Bayesian equilibrium, as if they know the type distribution.
This paper concentrates on Selten’s Chain Store game and the Kreps, Milgrom, Roberts, Wilson phenomenon, where a small perceived inaccuracy about the type distribution can drastically alter the equilibrium behavior. It presents sufficient conditions that prevent this phenomenon from persisting in a recurring setting.
Keywords
Recurring Game Social Learning Chain Store ParadoxPreview
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References
- Aumann, R. J. (1992), “Irrationality in Game Theory,” in Economic Analysis of Markets and Games: Essays in Honor of Frank Halm, edited by P. Dasgupta, D. Gale, O. Hart, and E. Maskin, MIT Press, Cambridge MA, 214–227.Google Scholar
- Aumann, R. J. and M. Maschler (1967), “Repeated Games with Incomplete Information: A Survey of Recent Results,” Mathematica, ST - 116, Ch. III, 287–403.Google Scholar
- Battigalli, P., M. Gilli, and M.C. Molinari (1992) “Learning and Convergence to Equilibrium in Repeated Strategic Interactions: An Introductory Survey,” Richerche Economiche, 96, 335–378.Google Scholar
- Fudenberg, D. and E. Maskin (1986), “The Folk Theorem in Repeated Games with Discounting and Incomplete Information,” Econometrica, 54, 533–554.CrossRefGoogle Scholar
- Fudenberg, D. and D. Kreps (1988), “A Theory of Learning, Experimentation and Equilibrium in Games,” mimeo: Stanford University.Google Scholar
- Fudenberg, D. and D. Kreps (1995), “Learning in Extensive Form Games: Self Confirming Equilibrium,” Games and Economic Behavior, 8, 20–55.CrossRefGoogle Scholar
- Fudenberg, D. and D. Levine (1993), “Steady State Learning and Nash Equilibrium,” Econometrica, 61, 547–573.CrossRefGoogle Scholar
- Harsanyi, J. (1967–68), “Games of Incomplete Information Played by Bayesian Players (Parts I, II, and III)”, Management Science, 14, 159–182; 320–334; 486–503.CrossRefGoogle Scholar
- Jackson, M. and E. Kalai (1995a), “Social Learning in Recurring Games”, mimeo, California Institute of Technology.Google Scholar
- Jackson, M. and E. Kalai (1995b), “Learning to Play Perfectly in Recurring Extensive Form Games”, mimeo, California Institute of Technology.Google Scholar
- Jordan, J. (1991), “Bayesian Learning in Normal Form Games,” Games and Economic Behavior, 3, 60–81.CrossRefGoogle Scholar
- Kalai, E. and E. Lehrer (1993), “Rational Learning Leads to Nash Equilibrium”, Econometrica, 61, 1019–1045.CrossRefGoogle Scholar
- Kreps, D. and R. Wilson (1982), “Reputation and Imperfect Information”, Journal of Economic Theory, 27, 253–279.CrossRefGoogle Scholar
- Lehrer, E. and R. Smorodinsky (1994), “Repeated Large Games with Incomplete Information”, Tel-Aviv University.Google Scholar
- Milgrom, P. and J. Roberts (1982), “Predation, Reputation, and Entry Deterrence”, Journal of Economic Theory, 27, 280–312.CrossRefGoogle Scholar
- Nash, J. (1950), “Non-Cooperative Games”, PhD Thesis, Mathematics Department, Princeton University.Google Scholar
- Selten, R. (1975), “Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games”, International Journal of Game Theory, 4, 25–55.CrossRefGoogle Scholar
- Selten, R. (1978), “The Chain-Store Paradox”, Theory and Decision, 9, 127–159.CrossRefGoogle Scholar
- Selten, R. (1983), “Evolutionary Stability in Extensive 2-Person Games,” Mathematical Social Sciences, 5, 269–363.CrossRefGoogle Scholar