ASYMPTOTIC PROPERTIES OF EQUILIBRIUM FORECASTS IN BAYESIAN LEARNING-MODELS

In an earlier paper [Shah Journal of Mathematical Economics, 1995, 24( 5), 461-495], we studied Bayesian learning in an intertemporal, stocha stic 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 for ecast of the state, given their belief about the true kernel and the e quilibrium implemented by the players. Beliefs are updated by Bayes' r ule after observing the actual state. Our present results concern the dynamic behavior of the forecasts process. We show there is partial le arning in the sense of being able to (asymptotically) predict the futu re as well as an omniscient modeler who knows the true transition stru cture and understands the stochastic evolution of the state and player s' actions. Moreover, we characterize the limiting behavior of the for ecasts process in terms of the set of full information rational expect ations forecasts.