Efficient Bilateral Risk Sharing Without Commitment

This paper examines the properties of efficient sustainable allocations in an environment in which two agents want to share risk, have perfect information about each other, but cannot make commitments about future transfers. I describe as sustainable any allocation that can be supported as a subgame perfect equilibrium in a game in which individuals make simultaneous transfers. I consider the properties of efficient sustainable allocations. There are three main findings. First, if some first best allocation is sustainable, then any efficient allocation must converge with probability one to a first best allocation. In the long run, the lack of commitment is irrelevant. Second, if no first best allocation is sustainable, then the unconditional probability distribution of an agent's utility and consumption converge weakly over time to a nondegenerate distribution. Finally, under any conditions, the conditional contemporaneous covariance of individual income and