Convergence in Economic Models with Bayesian Hierarchies of Beliefs

I study a model where hierarchies of beliefs (the beliefs about the beliefs of other agents, etc.) are important. I provide conditions under which optimal actions of agents will converge to the Nash equilibrium of the model characterized by the true, previously unknown ``fundamentals.'' The conditions are (i) a contraction property on the best-response mappings and (ii) a mutual absolute continuity condition on beliefs. Violation of (i) may result in an ``anything is possible'' result: any stochastic process of actions is consistent with maximizing behavior and Bayesian updating. Violation of (ii) may result in cyclical behavior of actions on each sample path. Journal of Economic Literature Classification Numbers: C70, C73, D81, D82, D83, D84. 1997 Academic Press