Abstract
We consider repeated games where at any period each player knows only his set of actions and the stream of payoffs that he has received in the past. He knows neither his own payoff function, nor the characteristics of the other players (how many there are, their strategies and payoffs). In this context, we present an adaptive procedure for play called “modified-regret-matching” — which is interpretable as a stimulus-response or reinforcement procedure, and which has the property that any limit point of the empirical distribution of play is a correlated equilibrium of the stage game.
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
Auer P., N. Cesa-Bianchi, Y. Freund and R. E. Schapire [ 1995 ], Gambling in a Rigged Casino: The Adversarial Multi-Armed Bandit Problem, Proceedings of the 36th Annual Symposium on Foundations of Computer Science, 322–331.
Aumann, R. J. [ 1974 ], Subjectivity and Correlation in Randomized Strategies, Journal of Mathematical Economics 1, 67–96.
Banos, A. [ 1968 ], On Pseudo-Games, The Annals of Mathematical Statistics 39, 1932–1945.
Blackwell, D. [ 1956 ], An Analog of the Minmax Theorem for Vector Payoffs, Pacific Journal of Mathematics 6, 1–8.
Borgers, T. and R. Sarin [ 1995 ], Naive Reinforcement Learning with Endogenous Aspirations, University College London (mimeo).
Bush, R. and F. Mosteller [1955], Stochastic Models for Learning,Wiley.
Erev, I. and A. E. Roth [ 1998 ], Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategies, American Economic Review 88, 848–881.
Foster, D. and R. V. Vohra [ 1993 ], A Randomized Rule for Selecting Forecasts, Operations Research 41, 704–709.
Foster, D. and R. V. Vohra [ 1997 ], Calibrated Learning and Correlated Equilibrium, Games and Economic Behavior 21, 40–55.
Foster, D. and R. V. Vohra [ 1998 ], Asymptotic Calibration, Biometrika 85, 379–390.
Fudenberg, D. and D. K. Levine [1998], Theory of Learning in Games,MIT Press.
Fudenberg, D. and D. K. Levine [ 1999 ], Conditional Universal Consistency, Games and Economic Behavior 29, 104–130.
Hannan, J. [ 1957 ], Approximation to Bayes Risk in Repeated Play, in Contributions to the Theory of Games, Vol. III (Annals of Mathematics Studies 39 ), M. Dresher, A. W. Tucker and P. Wolfe (eds.), Princeton University Press, 97–139.
Hart, S. and A. Mas-Colell [ 2000 ], A Simple Adaptive Procedure Leading to Correlated Equilibrium, Econometrica.
Hart, S. and A. Mas-Colell [ 2001 ], A General Class of Adaptive Strategies, Journal of Economic Theory.
Loève, M. [ 1978 ], Probability Theory, Vol. II, 4th Edition, Springer-Verlag.
Megiddo, N. [ 1980 ], On Repeated Games with Incomplete Information Played by Non-Bayesian Players, International Journal of Game Theory 9, 157–167.
Roth, A. E. and I. Erev [ 1995 ], Learning in Extensive-Form Games: Experimental Data and Simple Dynamic Models in the Intermediate Term, Games and Economic Behavior 8, 164–212.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Additional information
Dedicated with great admiration to Werner Hildenbrand on his 65th birthday. Previous versions of these results were included in the Center for Rationality Discussion Papers #126 (December 1996) and #166 (March 1998). We thank Dean Foster for suggesting the use of “modified regrets.” The research is partially supported by grants of the Israel Academy of Sciences and Humanities; the Spanish Ministry of Education; the Generalitat de Catalunya; CREI; and the EU-TMR Research Network.
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hart, S., Mas-Colell, A. (2001). A Reinforcement Procedure Leading to Correlated Equilibrium. In: Debreu, G., Neuefeind, W., Trockel, W. (eds) Economics Essays. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04623-4_12
Download citation
DOI: https://doi.org/10.1007/978-3-662-04623-4_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07539-1
Online ISBN: 978-3-662-04623-4
eBook Packages: Springer Book Archive