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Rational Learning in Imperfect Monitoring Games

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Author Info
Mario Gilli () (Department of Economics, University of Milan-Bicocca)

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Abstract

This paper provides a genera1 framework to analyze rational learning in strategic situations where the players have private information and update their private priors collecting data through optimal experimentation. The theory of statistica1 inference for stochastic processes and of Markovian dynamic programming is applied to study players asymptotic behavior in the context of repeated and recurring games, proving convergence towards Conjectural equilibria, an oyporturie generalization of Nash equilibria for this kind of strategic situations. Since the main bulk of the literature on rational learning regards convergence towards equilibria of repeated games, the main contribution of this paper is to argue for rational learning in recurring games, providing dynamic foundations for equilibria of the one-shot game. The analysis focuses on the problem of non stationary environment and on the problem of the correct specification of the stochastic law which regulates players' observations. In this way the paper shows both the limitations and the possibilities of rational learning models in game theory, in particular explaining when and why consistency rather than merging is the correct notion of learning in games.

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File URL: http://dipeco.economia.unimib.it/repec/pdf/mibwpaper46.pdf
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File Function: First version, 2002
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Publisher Info
Paper provided by University of Milano-Bicocca, Department of Economics in its series Working Papers with number 46.

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Length: 34 pages
Date of creation: Mar 2002
Date of revision: Mar 2002
Handle: RePEc:mib:wpaper:46

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Related research
Keywords: rational learning; active and passive learning; stationarity; consistency; merging;

Other versions of this item:

Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information

References listed on IDEAS
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  1. R. I. Miller & C. W. Sanchirico, 1996. "The Role of Absolute Continuity in "Merging of Opinions" and "Rational Learning"," Game Theory and Information 9612001, EconWPA, revised 04 Dec 1996. [Downloadable!]
    Other versions:
  2. Nyarko, Y., 1992. "Bayesian Learning without Common Priors and Convergence to Nash Equilibria," Working Papers 92-25, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  3. Eddie Dekel & Drew Fudenberg & David K. Levine, 2000. "Learning to Play Bayesian Games," Discussion Papers 1322, Northwestern University, Center for Mathematical Studies in Economics and Management Science, revised Jul 2001. [Downloadable!]
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  4. Michihiro Kandori, 2001. "Introduction to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-114, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  5. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March. [Downloadable!] (restricted)
  6. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-45, September. [Downloadable!] (restricted)
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  7. Mario Gilli, 1999. "Adaptive Learning in Imperfect Monitoring Games," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 2(2), pages 472-485, April. [Downloadable!] (restricted)
  8. Fudenberg, Drew & Levine, David, 1986. "Limit games and limit equilibria," Journal of Economic Theory, Elsevier, vol. 38(2), pages 261-279, April. [Downloadable!] (restricted)
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  9. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May. [Downloadable!] (restricted)
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  10. Drew Fudenberg & David K. Levine, 1993. "Steady State Learning and Nash Equilibrium," Levine's Working Paper Archive 373, David K. Levine. [Downloadable!]
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  11. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1998. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Discussion Papers 1228, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
    Other versions:
  12. Koutsougeras, Leonidas C & Yannelis, Nicholas C, 1994. "Convergence and Approximation Results for Non-cooperative Bayesian Games: Learning Theorems," Economic Theory, Springer, vol. 4(6), pages 843-57, October.
  13. Jackson, Matthew O. & Kalai, Ehud, 1997. "Social Learning in Recurring Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 102-134, October. [Downloadable!] (restricted)
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  14. Gilli, Mario, 2001. "A General Approach to Rational Learning in Games," Bulletin of Economic Research, Blackwell Publishing, vol. 53(4), pages 275-303, October.
  15. Chakrabarti, Subir K, 1992. "Equilibrium in Behavior Strategies in Infinite Extensive Form Games with Imperfect Information," Economic Theory, Springer, vol. 2(4), pages 481-94, October.
  16. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January. [Downloadable!] (restricted)
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  17. Nyarko, Yaw, 1991. "The Convergence of Bayesian Belief Hierarchies," Working Papers 91-50, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  18. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-40, September. [Downloadable!] (restricted)
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  19. Aghion Philippe & Bolton, Patrick & Harris Christopher & Jullien Bruno, 1991. "Optimal learning by experimentation," CEPREMAP Working Papers (Couverture Orange) 9104, CEPREMAP.
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  20. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July. [Downloadable!] (restricted)
  21. Eichberger Jurgen, 1995. "Bayesian Learning in Repeated Normal Form Games," Games and Economic Behavior, Elsevier, vol. 11(2), pages 254-278, November. [Downloadable!] (restricted)
  22. Jackson, Matthew O. & Kalai, Ehud, 1999. "Reputation versus Social Learning," Journal of Economic Theory, Elsevier, vol. 88(1), pages 40-59, September. [Downloadable!] (restricted)
  23. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April. [Downloadable!] (restricted)
  24. Nyarko, Y., 1998. "The Truth is in the Eye of the Beholder: or Equilibrium in Beliefs and Rational Learning in Games," Working Papers 98-12, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
  25. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February. [Downloadable!] (restricted)
  26. Nyarko, Yaw, 1994. "Bayesian Learning Leads to Correlated Equilibria in Normal Form Games," Economic Theory, Springer, vol. 4(6), pages 821-41, October.
  27. Alvaro Sandroni & Rann Smorodinsky, 1999. "The speed of rational learning," International Journal of Game Theory, Springer, vol. 28(2), pages 199-210. [Downloadable!] (restricted)
  28. Aghion, Philippe, et al, 1991. "Optimal Learning by Experimentation," Review of Economic Studies, Blackwell Publishing, vol. 58(4), pages 621-54, July. [Downloadable!] (restricted)
  29. Mario Gilli, 1999. "On Non-Nash Equilibria," Levine's Working Paper Archive 2084, David K. Levine. [Downloadable!]
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