Adverse Selection and Non-exclusive Contracts

This paper studies the Rothschild and Stiglitz (1976) insurance environment relaxing the assumption of exclusivity of insurance contracts. Agents can engage in multiple insurance contract simultaneously and the terms of these contracts are not observed by other firms. Insurance providers behave non-cooperativelly and compete offering menus of insurance contracts from an unrestricted contract space. We show that the Rothschild and Stiglitz equilibrium allocation is not an equilibrium in the presence of non-exclusive contracting, since firms will offer latent contracts to prevent deviation by other firms that prevent separation of the agents. This possibility also implies that latent menus can prevent cream-skimming strategies, however pooling equilibrium still fails to exists. We derive the conditions under which a separating equilibrium exists and fully characterize it. The equilibrium allocation consists of agents with a lower probability of accident purchasing no insurance and agents with higher accident probability buying the actuarilly fair competitive level of insurance. To sustain the equilibrium allocation firms must offer latent contracts. The equilibrium allocation also constitute a linear price schedule for insurance.