Learning in Infinite Horizon Strategic Market Games with Collateral and Incomplete Information
We study a strategic market game with finitely many traders, infinite horizon and real assets. To this standard framework (see, e.g. Giraud and Weyers, 2004) we add two key ingredients: First, default is allowed at equilibrium by means of some collateral requirement for financial assets; second, information among players about the structure of uncertainty is incomplete. 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 then prove a partial Folk theorem a la Wiseman (2011) of the following form: For any function that maps each state of the world to a sequence of feasible and sequentially strictly 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.
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