Abstract
In an earlier paper [Shah Journal of Mathematical Economics, 1995, 24(5), 461–495], we studied Bayesian learning in an intertemporal, stochastic setting. The results stated in the present paper are significant generalizations and simplifications of the earlier results. We study a sequence of games in which the stochastic kernel that links the state variable is unknown. Successive stage games are played by successive generations of identical players. Each generation makes a rational forecast of the state, given their belief about the true kernel and the equilibrium implemented by the players. Beliefs are updated by Bayes' rule after observing the actual state. Our present results concern the dynamic behavior of the forecasts process. We show there is partial learning in the sense of being able to (asymptotically) predict the future as well as an omniscient modeler who knows the true transition structure and understands the stochastic evolution of the state and players' actions. Moreover, we characterize the limiting behavior of the forecasts process in terms of the set of full information rational expectations forecasts.
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