In many countries, insurers build preferred provider networks to reduce costs. In this paper, we address the issue of the optimal size of such networks. Considering the case of medical services whose price is not regulated, we assume that the insurer sets a number of in-network providers and organizes price competition to select the preferred providers among suppliers. Policyholders benefit from a higher reimbursement when they choose an in-network provider. We show that both in-network and off-network prices decrease with the number of in-network providers, that the largest possible network is optimal for the representative policyholder and for a not-for-profit insurer while a network with only one provider is preferred by a for-profit insurer.
