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Rational Learning in Imperfect Monitoring Games

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  • Mario Gilli

    ()
    (Department of Economics, University of Milan-Bicocca)

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
File Function: First version, 2002
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Bibliographic 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;

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References

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  1. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-45, September.
  2. Yaw Nyarko, 1998. "Bayesian learning and convergence to Nash equilibria without common priors," Economic Theory, Springer, vol. 11(3), pages 643-655.
  3. Aghion, P. & Bolton, P. & Harris, C. & Jullien, B., 1990. "Optimal Learning By Experimentation," DELTA Working Papers 90-10, DELTA (Ecole normale supérieure).
  4. 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.
  5. Miller, Ronald I. & Sanchirico, Chris William, 1999. "The Role of Absolute Continuity in "Merging of Opinions" and "Rational Learning"," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 170-190, October.
  6. Eichberger Jurgen, 1995. "Bayesian Learning in Repeated Normal Form Games," Games and Economic Behavior, Elsevier, vol. 11(2), pages 254-278, November.
  7. Ehud Kalai & Ehud Lehrer, 1992. "Weak and Strong Merging of Opinions," Discussion Papers 983, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Mario Gilli, 1999. "On Non-Nash Equilibria," Levine's Working Paper Archive 2084, David K. Levine.
  9. Aghion, Philippe, et al, 1991. "Optimal Learning by Experimentation," Review of Economic Studies, Wiley Blackwell, vol. 58(4), pages 621-54, July.
  10. Alvaro Sandroni & Rann Smorodinsky, 1999. "The speed of rational learning," International Journal of Game Theory, Springer, vol. 28(2), pages 199-210.
  11. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  12. Drew Fudenberg & David K. Levine, 1993. "Steady State Learning and Nash Equilibrium," Levine's Working Paper Archive 373, David K. Levine.
  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.
  14. Fudenberg, D. & Levine, D.K., 1991. "Self-Confirming Equilibrium ," Working papers 581, Massachusetts Institute of Technology (MIT), Department of Economics.
  15. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
  16. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
  17. 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.
  18. 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.
  19. Fudenberg, Drew & Levine, David, 1986. "Limit games and limit equilibria," Journal of Economic Theory, Elsevier, vol. 38(2), pages 261-279, April.
  20. 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.
  21. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Econometrica, Econometric Society, vol. 67(4), pages 875-894, July.
  22. Ehud Kalai & Ehud Lehrer, 1991. "Subjective Equilibrium in Repeated Games," Discussion Papers 981, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  23. Nyarko, Yaw, 1994. "Bayesian Learning Leads to Correlated Equilibria in Normal Form Games," Economic Theory, Springer, vol. 4(6), pages 821-41, October.
  24. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
  25. Gilli, Mario, 2001. "A General Approach to Rational Learning in Games," Bulletin of Economic Research, Wiley Blackwell, vol. 53(4), pages 275-303, October.
  26. Jackson, Matthew O. & Kalai, Ehud, 1999. "Reputation versus Social Learning," Journal of Economic Theory, Elsevier, vol. 88(1), pages 40-59, September.
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