Optimal Risk-Sharing under Dual Asymmetry of both Information and Market Power: A Unifying Approach∗

The impact of information distribution on optimal risk-sharing between different parties has been an important field of research over the past 30 years. In the literature of insurance, however, the focus has remained essentially on one configuration: insurers (the principal) propose a contract to insured (the agent), but are unable to observe perfectly the risk of their insured who can. This asymmetry of information is the source of the well-known adverse selection effect that leads higher risk individuals to buy full or near-full insurance, while lower risk buy less complete coverage, if they buy at all. While the prediction seems to hold in some markets, there is growing empirical evidence it does not in a number of others (advantageous selection or no selection at all). This paper proposes a model of risk-sharing between two risk-averse agents that expands the traditional approach by studying 4 different cases. It comprises two possible allocations of information (the insured knows the risk better, or the insurer knows the risk better) and of market power (the principal is the insurer, or the insured). We show that when the insurer is the principal and is less informed, we have the traditional adverse selection effect: high risks are optimally covered, low risks are not. When the insurer is the principal but knows more about the risk than the insured (reversed asymmetric information), the result is reversed: high risks are not optimally covered, but low risks are. These results are mirrored when the market power is reversed (i.e., the insured is the principal, not the insurer). Many economic situations are specific cases of our setting. JEL Classification: G22; D81; D82 ∗We wish to thank Francis Bloch, Claude Henry, Howard Kunreuther, Pierre Picard, Jean-Charles Rochet and Bernard Sinclair-Desgagne for their suggestions on earlier versions of this paper. †IDEP-GREQAM, Université de la Méditerranée (Marseille, France). Email: [email protected]. ‡The Wharton School, University of Pennsylvania (USA) Email: [email protected]