(Neutrally) Optimal Mechanism under Adverse Selection: The canonical insurance problem

This paper revisits the problem of adverse selection in the insurance market of Rothschild and Stiglitz (1976). We extend the three-stage game in Hellwig (1987) by allowing firms to endogenously choose whether or not to pre-commit on their contractual offers (menus). We show how this mechanism can deliver the Miyazaki–Wilson–Spence allocation as the unique perfect-Bayesian equilibrium. This allocation is the unique incentive-efficient and individually-rational maximizer of the utility of the most profitable type. In fact, given that the informed player has only two types, it is the unique core allocation and thus the unique neutral optimum in the sense of Myerson (1983).