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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. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 895, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-50, July.
  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.
  4. Yaw Nyarko, 1998. "Bayesian learning and convergence to Nash equilibria without common priors," Economic Theory, Springer, vol. 11(3), pages 643-655.
  5. Matthew Jackson & Ehud Kalai, 1995. "Social Learning in Recurring Games," Discussion Papers 1138, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
  7. 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.
  8. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-40, September.
  9. 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.
  10. Drew Fudenberg & David K. Levine, 1993. "Steady State Learning and Nash Equilibrium," Levine's Working Paper Archive 373, David K. Levine.
  11. Gilli, Mario, 1999. "On Non-Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 27(2), pages 184-203, May.
  12. 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.
  13. Alvaro Sandroni & Rann Smorodinsky, 1999. "The speed of rational learning," International Journal of Game Theory, Springer, vol. 28(2), pages 199-210.
  14. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
  15. Kalai, Ehud & Lehrer, Ehud, 1994. "Weak and strong merging of opinions," Journal of Mathematical Economics, Elsevier, vol. 23(1), pages 73-86, January.
  16. Fudenberg, Drew & Levine, David, 1986. "Limit Games and Limit Equilibria," Scholarly Articles 3350443, Harvard University Department of Economics.
  17. Aghion Philippe & Bolton, Patrick & Harris Christopher & Jullien Bruno, 1991. "Optimal learning by experimentation," CEPREMAP Working Papers (Couverture Orange) 9104, CEPREMAP.
  18. Fudenberg, Drew & Kreps, David M., 1995. "Learning in extensive-form games I. Self-confirming equilibria," Games and Economic Behavior, Elsevier, vol. 8(1), pages 20-55.
  19. Fudenberg, Drew & Levine, David K, 1993. "Self-Confirming Equilibrium," Econometrica, Econometric Society, vol. 61(3), pages 523-45, May.
  20. Aghion, Philippe, et al, 1991. "Optimal Learning by Experimentation," Review of Economic Studies, Wiley Blackwell, vol. 58(4), pages 621-54, July.
  21. Jordan J. S., 1995. "Bayesian Learning in Repeated Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 8-20, April.
  22. 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.
  23. 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.
  24. Jackson, Matthew O. & Kalai, Ehud, 1999. "Reputation versus Social Learning," Journal of Economic Theory, Elsevier, vol. 88(1), pages 40-59, September.
  25. Sandroni, Alvaro, 1998. "Does Rational Learning Lead to Nash Equilibrium in Finitely Repeated Games?," Journal of Economic Theory, Elsevier, vol. 78(1), pages 195-218, January.
  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. Jordan, J. S., 1991. "Bayesian learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 60-81, February.
  28. Eichberger Jurgen, 1995. "Bayesian Learning in Repeated Normal Form Games," Games and Economic Behavior, Elsevier, vol. 11(2), pages 254-278, November.
  29. Gilli, Mario, 2001. "A General Approach to Rational Learning in Games," Bulletin of Economic Research, Wiley Blackwell, vol. 53(4), pages 275-303, October.
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