This study investigates hospitals' dynamic incentives to select patients when hospitals are remunerated according to a prospective payment system of the DRG type. Given that prices typically reflect past average costs, we use a discrete-time dynamic framework. Patients differ in severity within a DRG. Providers are to some extent altruistic. For low altruism, a downward spiral of prices is possible which induces hospitals to focus on low-severity cases. For high altruism, dynamic price adjustment depends on relation between patients' severity and benefit. In a steady state, DRG prices are unlikely to give optimal incentives to treat patients.