Adverse Selection and Non-Exclusive Contracts

This paper studies the Rothschild and Stiglitz (1976) adverse selection environment, relaxing the assumption of exclusivity of insurance contracts. There are three types of agents that differ in their risk level, their riskiness is private information and known before any contract is signed. Agents can engage in multiple insurance contracts simultaneously, and the terms of these contracts are not observed by other firms. Insurance providers behave non-cooperatively and compete offering menus of insurance contracts from an unrestricted contract space. We derive conditions under which a separating equilibrium exists and fully characterize it. The unique equilibrium allocation consists of agents with a lower probability of accident purchasing no insurance and agents with higher accident probability buying the actuarially-fair level of insurance. The equilibrium allocation also constitutes a linear price schedule for insurance. To sustain the equilibrium allocation,firms must offer latent contracts. These contracts are necessary to prevent deviations by other firms; in particular they can prevent cream-skimming strategies. As in Rothschild and Stiglitz (1976), pooling equilibrium still fails to exists.