Risk-sharing with self-insurance: the role of cooperation

We analyze mutual insurance arrangements (policies based on risk-sharing among a pool of policyholders) when consumers choose a self-insurance effort, that is an effort decreasing the size of any loss occurring. We consider both cooperative and non-cooperative strategies in the effort choice. Cooperation among policyholders leads to the full internalization of the positive impact the effort exerts on the premium. We show that, for an infinite size of pool, with cooperation first-best efficiency is achieved. Moreover, cooperation is sustained as an equilibrium in a repeated interaction game for a sufficiently low size of pool. An interesting implication of our results is that a cooperative mutual policy can dominate a stock insurance contract. Simulations show that mutual insurance with cooperation as an equilibrium dominates a second-best stock-type insurance policy even when pool size is low.