Impact of management models on revenue sharing for signaling medical equipment reliability

Abstract

This paper examines the contracting problem between a medical equipment vendor and a hospital in the healthcare industry. Many medical treatments depend heavily on the reliability of newly developed equipment, which typically encompasses private information on the part of the vendor. We built a game-theoretic model to examine the optimal contract a vendor can offer to prevent hospitals from underpaying for a reliable machine. First, the contract format including revenue sharing may serve as a signaling device of reliability. Second, the management model of a hospital has a strong impact on contract design. In particular, the vendor is better able to signal its reliability through revenue sharing to a non-profit hospital than to a for-profit hospital. Lastly, revenue sharing becomes more attractive to vendors as hospitals are more concerned about social welfare.

Keywords:

• Healthcare management
• revenue sharing
• signaling
• information asymmetry

Acknowledgments

The authors thank the Editor in Chief, the Associate Editor, and two anonymous referees for their many helpful comments and suggestions. They also thank seminar participants at National Taiwan University, Academia Sinica, and Ministry of Science and Technology, and participants at 2017 POMS Hong Kong Conference, 2018 Marketing Science Conference, 2018 INFORMS International Conference, and 2018 POMS Annual Conference, for comments on earlier versions of this study. Lastly, they thank Yi-Syuan Tzeng for editing and proofreading. This work was supported by MOST 106-2410-H-002-050-MY2 in Taiwan.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 A radiation oncologist in a hospital and a procurement officer in another hospital, both of whom are also authors of this study.

2 Please refer to Online Appendix B. The attributes for each hospital are described in Online Appendix Table 1, and the complete dataset is shown in Online Appendix Table 2.

3 Revenue-sharing ratios for machine R were 51.8% for public hospitals and 42.3% for private hospitals (though there were no statistically significant differences between these ratios). Three of the public hospitals in our study acquired all machines through revenue-sharing plans and only one public hospital acquired its machines through a fixed-fee contract. By contrast, more private hospitals paid fixed fees for all their machines (five fixed-fee contracts and two revenue-sharing contracts).

4 Note that vendor preference for these two types of contracts is of critical importance even though it seems like the hospitals are the parties choosing which contract they wish to sign. For example, if a vendor prefers revenue sharing, it can offer a fixed-fee contract with very high fixed fees to motivate the hospital to select the revenue-sharing contract with fair per-treatment payments.

5 Our radiation oncologist mentioned that linear accelerators with the lowest reliability in his hospital broke down once per fortnight on average.

6 The linear demand function is the most general functional form, and this is adequate for capturing the price-demand trade-off. With the linear demand function, we can focus on the impact of information and contracting without being distracted by unnecessarily complicated derivations.

7 We use the following numerical example to illustrate why the average treatment volume per day is $\min \{D(p),rK\}.$ Suppose that the daily capacity of a hospital is K = 30 (i.e., 30 time slots to serve patients per day) and the daily demand D(p) = 20 (as 20 treatments are scheduled each day). If the machine is perfectly reliable, all 20 treatments will be completed. If the reliability is imperfect, for instance, if r = 0.8, indicating that the machine shuts down every day out of five on average, the 20 unlucky treatments scheduled on the day the machine breaks down will be rescheduled to later days. As the hospital completes an average of 120 treatments over five days, there are enough time slots for the 20 unlucky treatments. The hospital can still complete all 100 treatments in 5 days, or equivalently, $\min \{20,24\}=20$ per day. However, if r = 0.6, such that the machine is broken every two out of five days, only 90 treatments can be completed. Since there is no excess capacity to serve so many patients, the average treatment volume becomes $\min \{20,18\}=18$ per day. In short, $\min \{D(p),rK\}$ correctly reflects the long-run average treatment volume per unit of time.

8 More precisely, we select the equilibrium that the reliable vendor yields the highest expected profit among all possible outcomes. It is intuitively appealing that the reliable vendor designs the contract since the unreliable vendor is the one having an incentive to pool with the reliable vendor but not vice versa.

9 We thank an anonymous referee for this note.