Rational Learning in Imperfect Monitoring Games

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.