Bayesian Economist... Bayesian agents: An alternative approach to optimal learning

We generalize the results on Bayesian learning based on the martingale convergence theorem to the sequential framework. We show that the variability in the sequential framework is sufficient under mild conditions to circumvent the incomplete learning results that characterize the optimal learning literature. We then give an alternative approach whereby the economist is Bayesian with a prior on the space of agent priors. We illustrate the usefulness of our approach by applying it to two popular economic examples: a monopolist who does not know the demand curve he faces, and the stochastic single-sector growth model with an unknown production function.