In an exchange economy with no aggregate uncertainty, and Bayesian agents, Pareto optimal allocations provide full insurance if and only if the agents have a common prior. It is hard to explain why there is relatively so little betting taking place. One is led to ask, when are full insurance allocations optimal for uncertainty averse agents? It turns out that commonality of beliefs, appropriately defined, is key again. Specifically, consider agents who are uncertainty averse and who maximize the minimal expected utility according to a set of possible priors. Pareto optimal allocations provide full insurance if and only if the agents share at least one prior. In the proof of this result, we develop a separation theorem among $n$ convex sets, that might be of independent interest.
Keywords. Betting, multiple prior, full insurance, Pareto optimality, separation theorem.
The paper is available in the following formats: