Individual Rationality and Participation in Large Scale, Multi-Hospital Kidney Exchanges

by Itai Ashlagi & Alvin E. Roth

Overview — As kidney exchange moves from local networks to a national level, a new set of problems arises. One central issue, for example, is how individual hospitals can be motivated to participate. This paper by Itai Ashlagi (Sloan School of Management, MIT) and Alvin E. Roth (Harvard Business School) provides a theoretical framework to study and overcome the kinds of problems that can be anticipated. Key concepts include:

The paper addresses the growing problem of providing hospitals with incentives to participate fully in a national kidney exchange, in order to achieve the gains that exchange on a large scale makes possible.
Hospitals might be reluctant to enter a national exchange if it means they would have to give up kidneys to other institutions that could be used in their own patients.
In large markets it is possible to redesign the matching mechanisms to guarantee individually rational allocations to hospitals at very modest cost in terms of "lost transplants."
If care is taken in how kidney exchange mechanisms are organized, the problems of participation may be less troubling in large exchange programs than they are starting to be in multi-hospital exchanges as presently organized.

Author Abstract

As multi-hospital kidney exchange clearinghouses have grown, the set of players has grown from patients and surgeons to include hospitals. Hospitals have the option of enrolling only their hard-to-match patient-donor pairs, while conducting easily arranged exchanges internally. This behavior has already started to be observed. We show that the cost of making it individually rational for hospitals to participate fully is low in almost every large exchange pool (although the worst-case cost is very high), while the cost of failing to guarantee individually rational allocations could be large, in terms of lost transplants. We also identify an incentive compatible mechanism.