Competitive Insurance Markets with Asymmetric Information: A Cournot-Arrow-Debreu Approach*

Douglas Gale () and Martin F. Hellwig

No 02-19, Sonderforschungsbereich 504 Publications from Sonderforschungsbereich 504, Universität Mannheim

Abstract: The paper studies insurance with asymmetric information in a system of contingent-claims markets with a finite number of risk averse agents. If the informed trader is a price taker, equilibrium prices disclose his information and, conditional on this information, equilibrium outcomes are efficient, as in Grossman (1981). With many agents to share risks, the informed trader gets close to full insurance at conditionally fair odds, which is not incentive compatible. If the informed trader behaves as a Cournot monopolist, equilibrium outcomes are always incentive compatible. Learning from prices generates the same outcomes as learning directly from the informed agent's behaviour in a 'signalling' version of the Cournot model. As in Spence (1973), these outcomes may be separating or pooling. With many agents to share risks, equilibrium outcomes approximate the sequential-equilibrium outcomes of a signalling game in which the insurance buyer names the premium he wants to pay, and risk neutral insurers respond with competing indemnity offers.

Date: 2002-03-13
Note: * This paper owes its existence to Laurenz Kohlleppel's asking the question: What is the relation between Rothschild-Stiglitz (1976) and Grossman (1981)? We are grateful to him as well as Tilman Börgers and Piero Gottardi for helpful discussions about the ideas in this paper. Financial support from the Deutsche Forschungsgemeinschaft, SFB 504, at the University of Mannheim, is gratefully acknowledged.
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