Optimal risk-sharing under mutually singular beliefs

We focus on the situation in which agents might have mutually singular beliefs in a maxmin expected utility framework. We show the existence of an equilibrium under fairly general conditions. We further demonstrate that the characterization of Pareto optimal allocation is significantly different from the classical situation, where all beliefs are mutually equivalent for each agent. Absent aggregate uncertainty, we prove that with common beliefs among agents, any Pareto optimal allocation is a full insurance under the upper capacities for all agents. But the full insurance feature of all Pareto optimal allocations, if true, does not necessarily ensure common beliefs. Moreover, despite agents have sharing beliefs, a full insurance Pareto optimal allocation could be associated with intricate allocation form.