This paper provides an analysis of the asymptotic properties of consumption allocations in a stochastic general equilibrium model with heterogeneous consumers. In particular we investigate the market selection hypothesis, that markets favor traders with more accurate beliefs. We show that in any Pareto optimal allocation whether each consumer vanishes or survives is determined entirely by discount factors and beliefs. Since equilibrium allocations in economies with complete markets are Pareto optimal, our results characterize the limit behavior of these economies. We show that, all else equal, the market selects for consumers who use Bayesian learning with the truth in the support of their prior and selects among Bayesians according to the size of the their parameter space. Finally, we show that in economies with incomplete markets these conclusions may not hold. Payoff functions can matter for long run survival, and the market selection hypothesis fails.

We provide an axiomatic foundation for decision making in a complex environment. We do not assume that the decision maker has complete structural knowledge of the environment. Instead the agent knows the set of actions he can take, he formulates preferences directly on the actions, and chooses according to these preferences. On the basis of experience he modifies these preferences according to a systematic procedure. Our axioms are imposed on this procedure, rather than directly on the choice itself. The axioms consists of a group of natural structural restrictions and a group of independence axioms. Our main result is an axiomatic foundation for a set of simple adaptive learning procedures which include the replicator dynamic.

The problem of controlling a stochastic process, with unknown parameters over an infinite horizon, with discounting is considered. Agents express beliefs about unknown parameters in terms of distributions. Under general conditions, the sequence of beliefs converges to a limit distribution. The limit distribution may or may not be concentrated at the true parameter value. In some cases, complete learning is optimal; in others, the optimal strategy does not imply complete learning. The paper concludes with examination of some special cases and a discussion of a procedure for generating examples in which incomplete learning is optimal. Copyright 1988 by The Econometric Society.