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.
Asymmetric and private information mechanism design oligopoly economics of contracts insurance