No Crowding Out despite Kickbacks: Competition between Gatekeeping GPs

In health service markets, patients often rely on the advice of their general practitioner (GP) to decide which treatment best fits their needs. Hospitals, in turn, influence GPs referral decisions through kickbacks. We formulate a model with competitive heterogeneous GPs who differ in the degree to which they internalize the disutility that their patients suffer from inappropriate treatments. We prove that a separable equilibrium with referring and not referring GPs exist.