Rational Expectations and Rational Learning

We provide an overview of the methods of analysis and results obtained, and, most important, an assessment of the success of rational learning dynamics in tying down limit beliefs and limit behavior. We illustrate the features common to rational or Bayesian learning in single agent, game theoretic and equilibrium frameworks. We show that rational learing is possible in each of these environments. The issue is not in whether rational learning can occur, but in what results it produces. If we assume a natural complex parameterization of the choice environment all we know is the rational learner believes that his posteriors will converge somewhere with prior probability one. Alternatively, if we, the modelers, assume the simple parameterization of the choice environment that is necessary to obtain positive results we are closing our models in the ad hoc fashion that rational learning was inroduced to avoid. We believe that a partial resolution of this conundrum is to pay more attention to how learning interacts with other dynamic forces. We show that in a simple economy, the forces of market selection can yield convergence to rational expectations equilibria even without every agent behaving as a rational learner.