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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.

Suggested Citation

  • Mario Gilli, 2002. "Rational Learning in Imperfect Monitoring Games," Working Papers 46, University of Milano-Bicocca, Department of Economics, revised Mar 2002.
  • Handle: RePEc:mib:wpaper:46
    as

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    File URL: http://dems.unimib.it/repec/pdf/mibwpaper46.pdf
    File Function: First version, 2002
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    rational learning; active and passive learning; stationarity; consistency; merging;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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