Learning by Trading in Infinite Horizon Strategic Market Games with Default.

We study the consequences of dropping the perfect competition assumption in an infinite horizon model with infinitely-lived traders and collateralized assets together with asymmetric information among players and incomplete monitoring. Trading assets is not only a way to hedge oneself against uncertainty and to smooth consumption across time: It also enables learning information. We focus on learning equilibria, at the end of which no player has incorrect beliefs because they have taken time to update their prior belief. We prove a partial Folk theorem à la Wiseman (2012) 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. When the number of traders grows to infinity, the resulting equilibrium set sharply contrasts with that of standard perfectly competitive equilibria.