The Dynamics of Rational Learning Processes with Asymmetric Information

This paper demonstrates that the dynamics of a rational learning process with private information differ substantially from those without such information. As has been shown by Jund and Vives (1996), the existence of private information has no effect upon the convergence of the learning process towards a limit equilibrium with correct expectations. Yet, as we show, the transitional dynamics of prices and the informativeness of public statistics are influenced by the presence of private information. Dependent upon the strength of the feed-back of price expectations on actual prices, it could be that the presence of private information enhances the informativeness of public statistics and thereby speeds up the learning process as well as the convergence of prices relative to a situation without such information. However, even the opposite might be true. Moreover, the existence of private information might give rise to an initially diverging learning process that nevertheless converges after some kind of learning-catastrophe occurs.