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.
The authors thank the California Institute of Technology and the Sherman Fairchild Foundation for their generous hospitality while doing this research. They also thank Eric van Damme for comments on an early draft and the National Science Foundation for financial support under grants SBR-9223156 and SBR-9223338.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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.
Aumann, R. J. and M. Maschler (1967), “Repeated Games with Incomplete Information: A Survey of Recent Results,” Mathematica, ST - 116, Ch. III, 287–403.
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.
Fudenberg, D. and E. Maskin (1986), “The Folk Theorem in Repeated Games with Discounting and Incomplete Information,” Econometrica, 54, 533–554.
Fudenberg, D. and D. Kreps (1988), “A Theory of Learning, Experimentation and Equilibrium in Games,” mimeo: Stanford University.
Fudenberg, D. and D. Kreps (1995), “Learning in Extensive Form Games: Self Confirming Equilibrium,” Games and Economic Behavior, 8, 20–55.
Fudenberg, D. and D. Levine (1993), “Steady State Learning and Nash Equilibrium,” Econometrica, 61, 547–573.
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.
Jackson, M. and E. Kalai (1995a), “Social Learning in Recurring Games”, mimeo, California Institute of Technology.
Jackson, M. and E. Kalai (1995b), “Learning to Play Perfectly in Recurring Extensive Form Games”, mimeo, California Institute of Technology.
Jordan, J. (1991), “Bayesian Learning in Normal Form Games,” Games and Economic Behavior, 3, 60–81.
Kalai, E. and E. Lehrer (1993), “Rational Learning Leads to Nash Equilibrium”, Econometrica, 61, 1019–1045.
Kreps, D. and R. Wilson (1982), “Reputation and Imperfect Information”, Journal of Economic Theory, 27, 253–279.
Lehrer, E. and R. Smorodinsky (1994), “Repeated Large Games with Incomplete Information”, Tel-Aviv University.
Milgrom, P. and J. Roberts (1982), “Predation, Reputation, and Entry Deterrence”, Journal of Economic Theory, 27, 280–312.
Nash, J. (1950), “Non-Cooperative Games”, PhD Thesis, Mathematics Department, Princeton University.
Selten, R. (1975), “Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games”, International Journal of Game Theory, 4, 25–55.
Selten, R. (1978), “The Chain-Store Paradox”, Theory and Decision, 9, 127–159.
Selten, R. (1983), “Evolutionary Stability in Extensive 2-Person Games,” Mathematical Social Sciences, 5, 269–363.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin — Heidelberg
About this chapter
Cite this chapter
Jackson, M., Kalai, E. (1997). Recurring Bullies, Trembling and Learning. In: Albers, W., Güth, W., Hammerstein, P., Moldovanu, B., van Damme, E. (eds) Understanding Strategic Interaction. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60495-9_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-60495-9_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64430-6
Online ISBN: 978-3-642-60495-9
eBook Packages: Springer Book Archive