The paper studies insurance with moral hazard in a system of contingent-claims markets. Insurance buyers are modelled as Cournot monopolists or oligopolists. The other agents condition their expectations on market prices, as in models of rational-expectations equilibrium with asymmetric information. Thereby they correctly anticipate accident probabilities corresponding to effort incentives induced by insurance buyers? net trades. When there are many agents to share the insurance buyer?s risk, Cournot equilibrium outcomes are close to being second-best. In contrast, if insurance buyers are price takers, equilibria fail to exist or are bounded away from being second-best.