Competitive pooling: Rothschild-Stiglitz reconsidered

We build a model of competitive pooling, which incorporates adverse selection and signaling into general equilibrium. Pools are characterized by their quantity limits on contributions. Households signal their reliability by choosing which pool to join. In equilibrium, pools with lower quantity limits sell for a higher price, even though each household's deliveries are the same at all pools. The Rothschild-Stiglitz model of insurance is included as a special case. We show that by recasting their hybrid oligopolistic-competitive story in our perfectly competitive framework, their separating equilibrium always exists (even when they say it does not) and is unique.