"Standard theories of insurance, dating from Rothschild and Stiglitz (1976), stress the role of adverse selection in explaining the decision to purchase insurance. In these models, higher risk people buy full or near-full insurance, while lower risk people buy less complete coverage, if they buy...

When health plans compete under adverse selection, the competitive equilibrium set of contracts is unique. However, the allocation of these contracts among health plans is undetermined. We show that three health plans suffice to sustain an equilibrium where each health plan offers a single...