Three Essays on the Design of Kidney Exchange and Doctor-Hospital Matching Mechanisms

The thesis addresses the problem of the significant shortage of kidneys from donors as well as that of the imbalanced distribution of doctors. In respect to the kidney exchange problem, we propose a general model in which there are a finite number of patient-donor pairs, patients on the waiting list, and single donors. In the first study, patients have general preferences. The kidney of each paired donor is regarded as a private property of the intended kidney recipient, while kidneys from single donors are publicly owned. We propose an appropriate modification of the classic solution of core
to the current model and develop a mechanism for finding a core matching that is Pareto optimal and stable
against any coalition deviation. The second study focuses on efficient exchange procedures with dichotomous preferences in which only one-way, two-way, three or four-way chains, or cycles of exchange, are used. We derive a tight upper bound of the possible number of feasible kidney transplants in each case of exchange and provide important simulation results. We find that two-way cycles and chains of exchange can substantially increase the number of feasible transplants, that three-way cycles and chains can have a visible effect, and, at most, four-way cycles and chains suffice to capture all the potential gains of exchange. Our results are not only theoretically interesting but also have meaningful policy implications. The third study moves to the doctor-hospital matching problem. This paper studies a general doctor-hospital model under distributional and hierarchical constraints. We find that a matching that satisfies the classic concept of stability does not always exist and hence introduce an appropriate modification of the concept of stability. We furthermore design a doctor-proposing deferred acceptance mechanism with appealing properties in that it is efficient, stable and strategy-proof for doctors.