Priority and Externalities in Dynamic Matching

Abstract

Voucher programs in kidney exchange give priority to patients whose incompatible donors donate before the patient receives a kidney. Such pairs create a positive externality by initiating chains, but priority for these patients can limit this externality by terminating chains early. We study a dynamic matching market where each donor is compatible with each other pair's patient independently with probability p, and compare priority mechanisms that vary in how aggressively voucher patients are prioritized. We first analyze a Standard Priority rule, which extends a chain greedily until a voucher patient can be matched. Under this rule, a small fraction of voucher pairs q is enough (provided that q ≥ p) for both voucher and non-voucher patients to obtain near optimal waiting times; when voucher pairs are too scarce, non-voucher patients have long waiting times. We use simulations to compare Standard Priority with two alternatives. A Weak Priority rule, which extends the chain provided that the next pair can terminate with a voucher patient, substantially reduces waiting times for non-voucher patients with only a small increase in voucher patient waiting times. A Strict Priority rule, which searches for a shortest path to a voucher patient, benefits voucher patients but at a greater cost to other patients. We show that a similar separation arises in asymmetric markets, where voucher patients are easy-to-match.

Keywords: matching, priority, kidney exchange