Competition Between Hospitals Under Bundled Payments and Fee-for-Service: An Equilibrium Analysis of Insurer’s Choice

Abstract

Problem definition: We consider the quality competition between two hospitals under the plan of one insurer. The insurer aims to maximize the overall achievable quality in the system by selecting either the fee-for-service (FFS) or the bundled payment (BP) scheme to compensate each hospital. The demand, the costs, and the probability of successfully treating patients depend on a hospital’s chosen quality. Under such a setting, we use game theoretic models to study the choice of insurer and the impact of payment schemes on the equilibrium qualities of hospitals. Our models seek answers to the following questions. Is BP (FFS) payment scheme always associated with high (low) equilibrium quality? What factors affect the equilibrium qualities of competing hospitals and the choice of the insurer and how? Academic/practical relevance: Competing hospitals under same or different payment models from an insurer is rather common for healthcare delivery in the United States. However, there is a lack of understanding about the impact of payment schemes on quality outcomes from both the hospital’s and the insurer’s perspective. To the best of our knowledge, ours is the first paper to incorporate competition and the insurer’s perspective to study the impact of different payment models on quality. Methodology: Game theory, equilibrium analysis. Results: We show that BP (FFS) is not always associated with high (low) equilibrium quality and that the equilibrium qualities of the two hospitals are strategic complements. We characterize when the insurer might assign the BP to both hospitals, the FFS to both hospitals, or the BP to one and the FFS to the other hospital. Managerial implications: Our findings provide prescriptive guidelines to an insurer choosing payment models. We also show that a specific quality outcome is achievable not by choosing any payment model but by a careful design of its parameters. Our numerical studies show that hospital readmission reduction initiatives are most effective when run in conjunction with cost reduction initiatives.