Two types of agents have diverse beliefs about the law of motion for an exogenous endowment. One knows the true process, and the other learns about it via Bayes' theorem. Financial market structure affects the dynamics of the wealth distribution. When markets are complete, the learning agent loses wealth, as in Blume and Easley (2006). The absence of markets for some Arrow securities alters the direction in which wealth is transferred. When the only traded asset is a risk-free bond, the learning agent accumulates wealth, both agents survive and the more knowledgeable agent is driven to his debt limit.