Abstract:
We analyze participating policies when policyholders choose a self-insurance measure, that is an action decreasing the size of any loss occurring. We consider both cooperative and noncooperative strategies in the action choice. We show that non-cooperative strategies lead to a Nash equilibrium with partial coverage where policyholders partially internalize the positive impact that self-insurance exerts on the premium. Cooperation, instead, leads to full internalization of the positive impact of the policyholders’ action and to full coverage. For an infinite size of the pool, the participating policy in the case of non-cooperation converges to the second-best non-participating policy; whereas, with cooperation, first-best efficiency is achieved. Finally, cooperation can be sustained as an equilibrium in a repeated interaction game for a sufficiently low size of pool.