The growth of kidney exchange presents new challenges for the design of kidney exchange clearinghouses. The players now include directors of transplant centers, who see sets of patient-donor pairs, and can choose to reveal only difficult-to-match pairs to the clearinghouse, while withholding easy-to-match pairs to transplant locally. This reduces the number of transplants. We discuss how the incentives for hospitals to enroll all pairs in kidney exchange can be achieved, and how the concentration of hard to match pairs increases the importance of long, non-simultaneous nondirected donor chains.

Consider an environment with a finite number of alternatives, and agents with private values and quasilinear utility functions. A domain of valuation functions for an agent is a monotonicity domain if every finite-valued monotone randomized allocation rule defined on it is implementable in dominant strategies. We fully characterize the set of all monotonicity domains.

We study competition in matching markets with random heterogeneous preferences and an unequal number of agents on either side. First, we show that even the slightest imbalance yields an essentially unique stable matching. Second, we give a tight description of stable outcomes, showing that matching markets are extremely competitive. Each agent on the short side of the market is matched with one of his top choices, and each agent on the long side either is unmatched or does almost no better than being matched with a random partner. Our results suggest that any matching market is likely to have a small core, explaining why small cores are empirically ubiquitous.

We study non-monetary markets where objects that arrive over time are allocated to unit-demand agents with private types, such as in the allocation of public housing or deceased-donor organs. An agent’s value for an object is supermodular in her type and the object quality, and her payoff is her value minus her waiting cost. The social planner’s objective is a weighted sum of allocative efficiency (i.e. the sum of values) and welfare (i.e. the sum of payoffs). We identify optimal mechanisms in the class of direct-revelation mechanisms. When the social planner can design the information disclosed to the agents about the objects, the optimal mechanism has a simple implementation: a first-come first-served waitlist with deferrals. In this implementation, the object qualities are partitioned into intervals; only the interval containing the object quality is disclosed to agents. When the planner places a higher weight on welfare, optimal disclosure policies become coarser.

We study dynamic matching in exchange markets with easy- and hard-to-match agents. A greedy policy, which attempts to match agents upon arrival, ignores the positive externality that waiting agents provide by facilitating future matchings. We prove that the trade-off between a “thicker” market and faster matching vanishes in large markets; the greedy policy leads to shorter waiting times and more agents matched than any other policy. We empirically confirm these findings in data from the National Kidney Registry. Greedy matching achieves as many transplants as commonly used policies (1.8% more than monthly batching) and shorter waiting times (16 days faster than monthly batching).

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.

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 percent increase in donor supply.