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This paper provides a complete characterization of equilibria in a game‐theoretic version of Rothschild and Stiglitz's (1976) model of competitive insurance. I allow for stochastic contract offers by insurance firms and show that a unique symmetric equilibrium always exists. Exact conditions under which the equilibrium involves mixed strategies are provided. The mixed equilibrium features (i) cross‐subsidization across risk levels, (ii) dependence of offers on the risk distribution, and (iii) price dispersion generated by firm randomization over offers.

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractThis note considers the problem of a principal (she) who faces a privately informed agent (he) and only knows one moment of the distribution from which his types are drawn.Payoffs are non-linear in the allocation and the principal maximizes her worst-case expected profits. We recast the robust design problem as a zero-sum game played by the principal and an adversarial nature who seeks to minimize her expected payoffs. The robust mechanism and the worst case distribution are, then, the Nash equilibrium of such game. A robustness property of the optimal mechanism imposes restrictions on the principal's ex-post profit function. These restrictions then lead to the optimal mechanism. The robust mechanism entails exclusion of low types and distortions at the intensive margin that (in a precise sense)are larger than what those that prevail in standard Bayesian mechanism design problems. D86 (Economics of Contract Theory) * This note is being extended to incorporate two sets of analysis: (i) a dynamic version of the main model in which the agent's information evolves over time and all is known by the principal is that types satisfy a martingale condition, and (ii) a multidimensional version of the model. We are also working on the full derivation of examples (e.g., regulation and taxation) that use the results this work derives. A paper incorporating (i), (ii) and the examples will subsume this note.† We have benefited from conversations with Gabriel Carroll, Nicolás Figueroa, Stephen Morris, Leonardo Rezende and Yuliy Sannikov. Moreira gratefully acknowledges financial support from CNPq.