Learning by Trading in Infinite Horizon Strategic Market Games with Default

We study the consequences of dropping the perfect competition assumption in a standard infinite horizon model with infinitely-lived traders and real collateralized assets, together with one additional ingredient: information among players is asymmetric and monitoring is incomplete. The key insight is that trading assets is not only a way to hedge oneself against uncertainty and to smooth consumption across time: It also enables learning information. Conversely, defaulting now becomes strategic: Certain players may manipulate prices so as to provoke a default in order to prevent their opponents from learning. We focus on learning equilibria, at the end of which no player has incorrect beliefs — not because those players with heterogeneous beliefs were eliminated from the market (although default is possible at equilibrium) but because they have taken time to update their prior belief. We prove a partial Folk theorem à la Wiseman (2011) of the following form: For any function that maps each state of the world to a sequence of feasible and strongly individually rational allocations, and for any degree of precision, there is a perfect Bayesian equilibrium in which patient players learn the realized state with this degree of precision and achieve a payoff close to the one specified for each state.