This paper provides a complete characterization of equilibria in a game-theoretic version of Rothschild and Stiglitz (1976)’s 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.