Health provider networks with private contracts: Is there under-treatment in narrow networks?

Contracts between health insurers and providers are private. By modelling this explicitly, we find the following. Insurers with bigger provider networks, pay providers higher fee-for-service rates. This makes it more likely that a patient is treated and hence health care costs and utilization increase with provider network size. Although providers are homogeneous, the welfare maximizing provider network can consist of two or more providers. Provider profits are positive whereas they would be zero with public contracts. Increasing transparency of provider prices increases welfare only if consumers can "mentally process" the prices of all treatments involved in an insurance contract. If not, it tends to reduce welfare.