We evaluate the consequences of narrow hospital networks in commercial health care markets. We develop a bargaining solution, "Nash- in-Nash with Threat of Replacement," that captures insurers' incentives to exclude, and combine it with California data and estimates from Ho and Lee (2017) to simulate equilibrium outcomes under social, consumer, and insurer- optimal networks. Private incentives to exclude generally exceed social incentives, as the insurer benefits from substantially lower negotiated hospital rates. Regulation prohibiting exclusion increases prices and premiums and lowers consumer welfare without significantly affecting social surplus. However, regulation may prevent harm to consumers living close to excluded hospitals.

A “Nash equilibrium in Nash bargains” has become a workhorse bargaining model in applied analyses of bilateral oligopoly. This paper proposes a noncooperative foundation for “Nash-in-Nash” bargaining that extends Rubinstein’s alternating offers model to multiple upstream and downstream firms. We provide conditions on firms’ marginal contributions under which there exists, for sufficiently short time between offers, an equilibrium with agreement among all firms at prices arbitrarily close to Nash-in-Nash prices, that is, each pair’s Nash bargaining solution given agreement by all other pairs. Conditioning on equilibria without delayed agreement, limiting prices are unique. Unconditionally, they are unique under stronger assumptions.