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We study how to optimally match agents in a dynamic matching market with heterogeneous match cardinalities and values. A network topology determines the feasible matches in the market. In general, a fundamental tradeoff exists between short-term value—which calls for performing matches frequently—and long-term value—which calls, sometimes, for delaying match decisions in order to perform better matches. We find that in networks that satisfy a general position condition, the tension between short- and long-term value is limited, and a simple periodic clearing policy (nearly) maximizes the total match value simultaneously at all times. Central to our results is the general position gap ϵ; a proxy for capacity slack in the market. With the exception of trivial cases, no policy can achieve an all-time regret that is smaller, in terms of order, than [Formula: see text]. We achieve this lower bound with a policy, which periodically resolves a natural matching integer linear program, provided that the delay between resolving periods is of the order of [Formula: see text]. Examples illustrate the necessity of some delay to alleviate the tension between short- and long-term value. This paper was accepted by David Simchi-Levi, revenue management and market analytics. Funding: This work was supported by the National Science Foundation [Grant CMM-2010940] and the U.S. Department of Defense [Grant STTR A18B-T007]. 

Hindsight Optimality in Two-Way Matching Networks In “On the Optimality of Greedy Policies in Dynamic Matching”, Kerimov, Ashlagi, and Gurvich study centralized dynamic matching markets with finitely many agent types and heterogeneous match values. A matching policy is hindsight optimal if the policy can (nearly) maximize the total value simultaneously at all times. The article establishes that suitably designed greedy policies are hindsight optimal in two-way matching networks. This implies that there is essentially no positive externality from having agents waiting to form future matches. Proposed policies include the greedy longest-queue policy, with a minor variation, as well as a greedy static priority policy. The matching networks considered in this work satisfy a general position condition. General position is a weak (but necessary) condition that holds when the static-planning problem (a linear program that optimizes the first-order matching rates) has a unique and nondegenerate optimal solution. 

Waitlists are often used to ration scarce resources, but the trade‐offs in designing these mechanisms depend on agents' preferences. We study equilibrium allocations under alternative designs for the deceased donor kidney waitlist. We model the decision to accept an organ or wait for a preferable one as an optimal stopping problem and estimate preferences using administrative data from the New York City area. Our estimates show that while some kidney types are desirable for all patients, there is substantial match‐specific heterogeneity in values. We then develop methods to evaluate alternative mechanisms, comparing their effects on patient welfare to an equivalent change in donor supply. Past reforms to the kidney waitlist primarily resulted in redistribution, with similar welfare and organ discard rates to the benchmark first‐come, first‐served mechanism. These mechanisms and other commonly studied theoretical benchmarks remain far from optimal. We design a mechanism that increases patient welfare by the equivalent of an 18.2% increase in donor supply. 

We show that kidney exchange markets suffer from market failures whose remedy could increase transplants by 30 to 63 percent. First, we document that the market is fragmented and inefficient; most transplants are arranged by hospitals instead of national platforms. Second, we propose a model to show two sources of inefficiency: hospitals only partly internalize their patients’ benefits from exchange, and current platforms suboptimally reward hospitals for submitting patients and donors. Third, we calibrate a production function and show that individual hospitals operate below efficient scale. Eliminating this inefficiency requires either a mandate or a combination of new mechanisms and reimbursement reforms. (JEL D24, D47, I11) 

Many scarce public resources are allocated through wait lists that use priorities for individual agents. A new priority system for allocating deceased donor kidneys was adopted in 2014. This redesign was guided by simulations that held decision-rules fixed. We synthesize recent theoretical results to show that the welfare effects of a mechanism depend on the interaction between dynamic incentives and heterogeneity in preferences. We show evidence suggesting that patient decisions on the deceased donor kidney wait list respond to dynamic incentives. Therefore, an empirical approach to dynamic mechanism design is an essential complement to mechanism design theory in dynamic environments. 

Kidney exchange platforms serve patients who need a kidney transplant and who have a willing, but incompatible, donor. These platforms match patients and donors to produce transplants. This paper documents operational details of the three largest platforms in the United States. It then uses the framework developed in Agarwal et al. (2017) to examine how practical details influence platform productivity. The results show that reducing frictions in accepting proposed matches, frequent matching, and encouraging altruistic donors are important ways in which a platform can increase its productivity.