Insurance Under Moral Hazard and Adverse Selection: The Case of Pure Competition

We consider a model of pure competition between insurers a la RothschildStiglitz, where two types of agents privately choose an eort level, and where the eort costs and the resulting accident probabilities dier across agents. We characterize the set of possible separating equilibria, with a special emphasis on the case where the Spence-Mirrlees condition is not satisfied. We show, in particular, that several equilibria a la Rothschild-Stiglitz may coexist; that they are Pareto-ranked, only the best of them being an equilibrium in the sense of Hahn (1978); and that equilibria may take original forms (for instance, both revelation constraints may then be binding). Finally, we discuss the existence of an equilibrium in this context, and show that, though equilibria may fail to exist, conditions for existence may dier from those in the initial Rothschild-Stiglitz setting.