Publications

In environments without transfers, market designers usually restrict attention to ordinal mechanisms. Ordinal mechanisms are simpler but miss potentially welfare‐relevant information. Under what conditions is it without loss to focus on ordinal mechanisms? We show that all group strategy‐proof mechanisms are ordinal. While not all Pareto efficient mechanisms are ordinal, all mechanisms maximizing an Arrovian social welfare function must be. These results accommodate feasibility constraints and allow for simple or complex demand. As applications, we characterize important classes of mechanisms in public choice and in the allocation of private goods under unit and multiunit demand.

A priority system has traditionally been the protocol of choice for the allocation of scarce life-saving resources during public health emergencies. COVID-19 revealed the limitations of this allocation rule. Many argue that priority systems abandon ethical values, such as equity, by discriminating against disadvantaged communities. We show that a restrictive feature of the traditional priority system largely drives these limitations. Following minimalist market design, an institution design paradigm that integrates research and policy efforts, we formulate pandemic allocation of scarce life-saving resources as a new application of market design. Interfering only with the restrictive feature of the priority system to address its shortcomings, we formulate a reserve system as an alternative allocation rule. Our theoretical analysis develops a general theory of reserve design. We relate our analysis to debates during COVID-19 and describe the impact of our paper on policy and practice.

Economists have long recognized that the effect of move order on outcomes is non-negligible in sequential contests. We study tiebreak mechanisms used in team sports and known as penalty shootouts through a dynamic model. We characterize all order-independent mechanisms where two balanced teams have equal chances to win the shootout whenever they are tied after equal numbers of attempts; thus, move order has no relevance for winning chances. In most sports, such as football and hockey, teams take penalties in a fixed order, known as ABAB, while some tournaments adopted the alternating-order variant, ABBA. We find that these and all other exogenous-order mechanisms – with one exception – are order-dependent in regular rounds. Although ABBA is order independent in sudden-death rounds, ABAB is not. Our theory supports empirical studies linking ABAB to unfair outcomes and multiple equilibria in terms of winning chances of the first- vs. second-kicking teams in different football traditions.

Over the last 15 years, kidney exchange has become a mainstream paradigm to increase transplants. However, compatible pairs do not participate, and full benefits from exchange can be realized only if they do. We propose incentivizing compatible pairs to participate in exchange by insuring their patients against future renal failure via increased priority in deceased-donor queue. We analyze equity and welfare benefits of this scheme through a new dynamic continuum model. We calibrate the model with US data and quantify substantial gains from adopting incentivized exchange, both in terms of access to living-donor transplants and reduced competition for deceased-donor transplants. (JEL D47, I11, I12, I18)

Liver exchange has been practiced in small numbers, mainly to overcome blood‐type incompatibility between patients and their living donors. A donor can donate either his smaller left lobe or the larger right lobe, although the former option is safer. Despite its elevated risk, right‐lobe transplantation is often utilized due to size‐compatibility requirement with the patient. We model liver exchange as a market‐design problem, focusing on logistically simpler two‐way exchanges, and introduce an individually rational, Pareto‐efficient, and incentive‐compatible mechanism. Construction of this mechanism requires novel technical tools regarding bilateral exchanges under partial‐order‐induced preferences. Through simulations we show that not only can liver exchange increase the number of transplants by more than 30%, it can also increase the share of the safer left‐lobe transplants.

We introduce a new matching model to mimic two-sided exchange programs such as tuition and worker exchanges, in which export-import balances are required for longevity of programs. These exchanges use decentralized markets, making it difficult to achieve this goal. We introduce the two-sided top trading cycles, the unique mechanism that is balanced-efficient, worker-strategy-proof, acceptable, individually rational, and respecting priority bylaws regarding worker eligibility. Moreover, it encourages exchange, because full participation induces a dominant-strategy equilibrium for firms. We extend it to dynamic settings permitting tolerable yearly imbalances and demonstrate that its regular and tolerable versions perform considerably better than models of current practice.

Even though kidney exchange became an important source of kidney transplants over the last decade with the introduction of market design techniques to organ transplantation, the shortage of kidneys for transplantation is greater than ever. Due to biological disadvantages, patient populations of blood types B/O are disproportionately hurt by this increasing shortage. The disadvantaged blood types are overrepresented among minorities in the US. In order to mitigate the disproportionate harm to these biologically disadvantaged groups, the UNOS reformed in 2014 the US deceased-donor kidney-allocation system, utilizing a technological advance in blood typing. The improved technology allows a certain fraction of blood type A kidneys, referred to as subtype A2 kidneys, to be transplanted to medically qualified patients of blood types B/O. The recent reform prioritizes subtype A2 deceased-donor kidneys for blood type B patients only. When restricted to the deceased-donor allocation system, this is merely a distributional reform with no adverse impact on the overall welfare of the patient population. In this paper we show that the current implementation of the reform has an unintended consequence, and it de facto extends the preferential allocation to kidney exchange as well. Ironically this “spillover” not only reduces the number of living-donor transplants for the overall patient population, but also for the biologically disadvantaged groups who are the intended beneficiaries of the reform. We show that minor variations of the current policy do not suffer from this unintended consequence, and we make two easy-to-implement, welfare-increasing policy recommendations.

Within the last decade, the use of living-donor kidney exchanges for transplants has emerged as a cross-disciplinary success for medical doctors and ethicists, market design economists, and computer scientists. This paper describes the fronts on which these efforts have been successful and what needs to be done further to increase their impact. This paradigm is also partially being applied to liver exchanges. There are other organs for which living donation is possible and gains from exchange can be much bigger than for kidneys. Recent academic work on single-graft liver and dual-donor organ exchanges for lobar lung, dual-graft liver, and simultaneous liver–kidney transplantation are also discussed.

Owing to the worldwide shortage of deceased‐donor organs for transplantation, living donations have become a significant source of transplant organs. However, not all willing donors can donate to their intended recipients because of medical incompatibilities. These incompatibilities can be overcome by an exchange of donors between patients. For kidneys, such exchanges have become widespread in the last decade with the introduction of optimization and market design techniques to kidney exchange. A small but growing number of liver exchanges have also been conducted. Over the last two decades, a number of transplantation procedures emerged where organs from two living donors are transplanted to a single patient. Prominent examples include dual‐graft liver transplantation, lobar lung transplantation, and simultaneous liver‐kidney transplantation. Exchange, however, has been neither practiced nor introduced in this context. We introduce dual‐donor organ exchange as a novel transplantation modality, and through simulations show that living‐donor transplants can be significantly increased through such exchanges. We also provide a simple theoretical model for dual‐donor organ exchange and introduce optimal exchange mechanisms under various logistical constraints.

The allocation and exchange of discrete resources, such as transplant organs, public housing, dormitory rooms, and many other resources for which agents have single-unit demand, is often conducted via direct mechanisms without monetary transfers. Incentive compatibility and efficiency are primary concerns when designing such mechanisms. We construct the full class of group strategy-proof and Pareto efficient mechanisms and show that each of them can be implemented by endowing agents with control rights over resources. This new class, which we call trading cycles, contains new mechanisms as well as known mechanisms such as top trading cycles, serial dictatorships, and hierarchical exchange. We illustrate how one can use our construction to show what can and what cannot be achieved in a variety of allocation and exchange problems, and we provide an example in which the new trading-cycles mechanisms are more Lorenz equitable than all previously known mechanisms.

The Pennsylvania Adoption Exchange (PAE) helps caseworkers who represent children in Pennsylvania’s child welfare system by recommending prospective families for adoption. We describe PAE’s operational challenges using caseworker surveys, and analyze child outcomes through a regression analysis of data collected over multiple years. A match recommendation spreadsheet tool implemented by PAE incorporates insights from this analysis and allows PAE managers to better utilize available information. Using a discrete-event simulation of PAE, we justify the value of a statewide adoption network, and demonstrate the importance of generating better information about family preferences for increasing the percentage of children who are successfully adopted. Finally, we detail a series of simple improvements that PAE achieved by collecting more valuable information and aligning incentives for families to provide useful preference information.

Random mechanisms have been used in real-life situations for reasons such as fairness. Voting and matching are two examples of such situations. We investigate whether the desirable properties of a random mechanism survive decomposition of the mechanism as a lottery over deterministic mechanisms that also hold such properties. To this end, we represent properties of mechanisms–such as ordinal strategy-proofness or individual rationality–using linear constraints. Using the theory of totally unimodular matrices from combinatorial integer programming, we show that total unimodularity is a sufficient condition for the decomposability of linear constraints on random mechanisms. As two illustrative examples we show that individual rationality is totally unimodular in general, and that strategy-proofness is totally unimodular in some individual choice models. We also introduce a second, more constructive approach to decomposition problems, and prove that feasibility, strategy-proofness, and unanimity, with and without anonymity, are decomposable in non-dictatorial single-peaked voting domains. Just importantly, we establish that strategy-proofness is not decomposable in some natural problems.

A new mechanism was introduced in New York City and Boston to assign students to public schools. This mechanism was advocated for its superior fairness property, besides others. We introduce a new framework for school-choice problems and two notions of fairness in lottery design based on ex-ante stability. This framework unifies known many-to-one and one-sided matching models. We show that the NYC/Boston mechanism fails to satisfy these fairness properties. We then propose two new mechanisms, one that is ordinally Pareto-dominant within the class of strongly ex-ante stable mechanisms and one that satisfies ex-ante stability, equal treatment, and constrained ordinal-Pareto-efficiency.

Many end-stage renal disease sufferers who require a kidney transplant to prolong their lives have a relative or friend who has volunteered to donate a kidney to them, but whose kidney is incompatible with the intended recipient. This incompatibility can sometimes be overcome by exchanging a kidney with another incompatible patient-donor pair. Such kidney exchanges have emerged as a standard mode of kidney transplantation in the United States. The Alliance for Paired Donation (APD) developed and implemented nonsimultaneous extended altruistic donor (NEAD) chains, an innovative technique that allows a previously binding constraint (of simultaneity) to be relaxed; thus, it permits longer chains and better-optimized matching of potential donors to patients, greatly increasing the number of possible transplants. Since 2006, the APD has saved more than 220 lives through its kidney exchange program, with more than 75 percent of these achieved through nonsimultaneous chains. Other kidney exchange programs have adopted the technology and methods pioneered by APD, resulting in more than 1,000 lives already saved, with the promise of increasing impact in coming years. In 2013, the percentage of transplants from nonsimultaneous chains reached more than six percent of the number of transplants from living donors. In this paper, we describe the long-term optimization and market design research that supports this innovation. We also describe how a team of physicians and operations researchers worked to overcome the skepticism and resistance of the medical community to the NEAD innovation.

The Boston mechanism is a popular student-placement mechanism in school-choice programs around the world. We provide two characterizations of the Boston mechanism. We introduce two new axioms; favoring higher ranks and rank-respecting invariance. A mechanism is the Boston mechanism for some priority if and only if it favors higher ranks and satisfies consistency, resource monotonicity, and rank-respecting invariance. In environments where each type of object has exactly one unit, as in house allocation, a characterization is given by favoring higher ranks, individual rationality, population monotonicity, and rank-respecting invariance.

This paper studies the problem of assigning a set of indivisible objects to a set of agents when monetary transfers are not allowed and agents reveal only ordinal preferences, but random assignments are possible. We offer two characterizations of the probabilistic serial mechanism, which assigns lotteries over objects. We show that it is the only mechanism satisfying non-wastefulness and ordinal fairness and the only mechanism satisfying sd-efficiency, sd-envy-freeness, and weak invariance or weak truncation robustness (where "sd" stands for first-order stochastic dominance).

We analyze mechanisms that are used to allocate dormitory rooms to students at college campuses. Students consist of newcoming freshmen, who do not currently occupy any rooms, and more senior students each of whom occupies a room from the previous year. In addition to the rooms already occupied by the existing tenants, there are vacated rooms by the graduating class. Students have strict preferences over dormitory rooms. Each student shall be assigned a dormitory room in an environment where monetary transfers are not allowed. An existing tenant can move to another room as a result of the assignment. We show that you request my house-I get your turn mechanisms are the only mechanisms that are Pareto-efficient, individually rational, strategy-proof, weakly neutral, and consistent.

When aggregating individual preferences through the majority rule in an n-dimensional spatial voting model, the ‘worst-case’ scenario is a social choice configuration where no political equilibrium exists unless a super-majority rate as high as 1 — 1/(n+1) is adopted. In this paper we assume that a lower d-dimensional (d < n) linear map spans the possible candidates’ platforms. These d ‘ideological’ dimensions imply some linkages between the n political issues. We randomize over these linkages and show that there almost surely exists a 50%-majority equilibria in the above worst-case scenario, when n grows to infinity. Moreover, the equilibrium is the mean voter.

Mechanisms that rely on course bidding are widely used at business schools in order to allocate seats at oversubscribed courses. Bids play two key roles under these mechanisms: to infer student preferences and to determine who have bigger claims on course seats. We show that these two roles may easily conflict, and preferences induced from bids may significantly differ from the true preferences. Therefore, these mechanisms, which are promoted as market mechanisms, do not necessarily yield market outcomes. We introduce a Pareto‐dominant market mechanism that can be implemented by asking students for their preferences in addition to their bids over courses.

We study how barter exchanges should be conducted through a centralized mechanism in a dynamically evolving agent pool with time- and compatibility-based preferences. We derive the dynamically efficient two-way and multi-way exchange mechanisms that maximize total discounted exchange surplus. Recently several live-donor kidney exchange programmes were established to swap incompatible donors of end-stage kidney disease patients. Since kidney exchange can be modelled as a special instance of our more general model, dynamically efficient kidney exchange mechanisms are derived as corollaries. We make policy recommendations using simulations.

We develop a model of internet auctions with the aim of understanding how rules for ending such auctions (a "hard"- or "soft"-close) affect bidding behavior. We model bidding strategies using finite automata and report results from simulations involving populations of artificial bidders who update their strategies using a genetic algorithm. Our model is shown to deliver late or early bidding behavior, depending on whether the auction has a hard- or soft-close rule in accordance with the empirical evidence. We report on other interesting properties of our model and offer some conclusions from a market design point of view.

This paper considers a decentralized process in many-to-many matching problems. We show that if agents on one side of the market have substitutable preferences and those on the other side have responsive preferences, then, from an arbitrary matching, there exists a finite path of matchings such that each matching on the path is formed by satisfying a blocking individual or a blocking pair for the previous matching, and the final matching is pairwise-stable. This implies that an associated stochastic process converges to a pairwise-stable matching in finite time with probability one, if each blocking individual or pair is satisfied with a positive probability at each period along the process.

Many markets have “unraveled” and experienced transactions at dispersed and apparently inefficiently early times. Often these markets develop institutions to coordinate and delay the timing of transactions. However it has proved difficult to gather data that allows the efficiency gains to be identified and measured. The present paper considers a market for which such data can be gathered. Prior to 1992, college football teams were matched for post-season play, in “bowl” games, up to several weeks before the end of the regular football season. Since 1992, the market has undergone a series of reorganizations that postpone this matching until the end of the regular season. We show that this has promoted more efficient matching of teams, as measured by the resulting television viewership. The chief driver has been the increased ability of later matching to produce “championship” games.

Patients needing kidney transplants may have donors who cannot donate to them because of blood or tissue incompatibility. Incompatible patient-donor pairs can exchange donor kidneys with other pairs only when there is a “double coincidence of wants.” Developing infrastructure to perform three-way as well as two-way exchanges will have a substantial effect on the number of transplants that can be arranged. Larger than three-way exchanges have less impact on efficiency. In a general model of type-compatible exchanges, the size of the largest exchanges required to achieve efficiency equals the number of types. (JEL C78, I12)

We examine a repeated one-to-one two-sided decentralized matching environment. Using an experimental strategic framework, we seek to characterize the convergence outcome of this process and its sensitivity to environmental factors such as the information structure.

In this paper, we analyze capacity manipulation games in hospital-intern markets inspired by the real-life entry-level labor markets for young physicians who seek residencies at hospitals. In a hospital-intern market, the matching is determined by a centralized clearinghouse using the preferences revealed by interns and hospitals and the number of vacant positions revealed by hospitals. We consider a model in which preferences of hospitals and interns are common knowledge. Hospitals play a capacity-reporting game. We analyze the equilibria of the game-form under the two most widely used matching rules: hospital-optimal and intern-optimal stable rules. We show that (i) there may not be a pure strategy equilibrium in general; and (ii) when a pure strategy equilibrium exists, every hospital weakly prefers this equilibrium outcome to the outcome of any larger capacity profile. Finally, we present conditions on preferences to guarantee the existence of pure strategy equilibria.

It is known that in two-sided many-to-many matching problems, pairwise-stable matchings may not be immune to group deviations, unlike in many-to-one matching problems (Blair, 1988). In this paper, we show that pairwise stability is equivalent to credible group stability when one side has responsive preferences and the other side has categorywise-responsive preferences. A credibly group-stable matching is immune to any “executable” group deviations with an appropriate definition of executability. Under the same preference restriction, we also show the equivalence between the set of pairwise-stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic-form game.

We examine whether a simple agent-based model can generate asset price bubbles and crashes of the type observed in a series of laboratory asset market experiments beginning with the work of Smith, Suchanek and Williams (1988). We follow the methodology of Gode and Sunder (1993, 1997) and examine the outcomes that obtain when populations of zero-intelligence (ZI) budget constrained, artificial agents are placed in the various laboratory market environments that have given rise to price bubbles. We have to put more structure on the behavior of the ZI-agents in order to address features of the laboratory asset bubble environment. We show that our model of “near-zero-intelligence” traders, operating in the same double auction environments used in several different laboratory studies, generates asset price bubbles and crashes comparable to those observed in laboratory experiments and can also match other, more subtle features of the experimental data.

In September of 1998, the Judicial Conference of the United States abandoned as unsuccessful the attempt—the sixth since 1978—to regulate the dates at which law students are hired as clerks by Federal appellate judges. The market promptly resumed the unraveling of appointment dates that had been temporarily slowed by these efforts. In the academic year 1999–2000 many judges hired clerks in the fall of the second year of law school, almost two years before employment would begin, and before hardly any information about candidates other than first year grades was available. Hiring dates moved still earlier in the Fall of 2000 and 2001. The present paper explores proposed reforms of the market, experimentally in the laboratory, and computationally using genetic algorithms. Our results suggest that some of the special features of the judge/law-clerk market—in particular the feeling among many students and judges that students must accept offers when they are made–present obstacles to the success of the proposed reforms, including the latest reforms proposed by the judges, in 2002 and 2003. Unlike markets in which the inability to make binding contracts contributes to market failure, in the law clerk market it is the ease with which binding contracts are forged that harms efficiency.

The literature on exchange of indivisible goods finds natural application in the exchange of live donor kidneys for transplant. However, in kidney exchange, there are constraints on the size of exchanges. Initially, kidney exchanges are likely to be between just two patient–donor pairs. We show that, although this constraint eliminates some potential exchanges, there is a wide class of constrained-efficient mechanisms that are strategy-proof when patient–donor pairs and surgeons have 0–1 preferences. This includes deterministic mechanisms that accommodate the priority setting that organ banks currently use to allocate cadaver organs, and stochastic mechanisms that allow distributive justice issues to be addressed.

A group of friends consider renting a house but they shall first agree on how to allocate its rooms and share the rent. We propose an auction mechanism for room assignment-rent division problems which mimics the market mechanism. Our auction mechanism is efficient, envy-free, individually-rational and it yields a non-negative price to each room whenever that is possible with envy-freeness.

Most transplanted kidneys are from cadavers, but there are also many transplants from live donors. Recently, there have started to be kidney exchanges involving two donor-patient pairs such that each donor cannot give a kidney to the intended recipient because of immunological incompatibility, but each patient can receive a kidney from the other donor. Exchanges are also made in which a donor-patient pair makes a donation to someone waiting for a cadaver kidney, in return for the patient in the pair receiving high priority for a compatible cadaver kidney when one becomes available. There are stringent legal/ethical constraints on how exchanges can be conducted. We explore how larger scale exchanges of these kinds can be arranged efficiently and incentive compatibly, within existing constraints. The problem resembles some of the "housing" problems studied in the mechanism design literature for indivisible goods, with the novel feature that while live donor kidneys can be assigned simultaneously, cadaver kidneys cannot. In addition to studying the theoretical properties of the proposed kidney exchange, we present simulation results suggesting that the welfare gains from larger scale exchange would be substantial, both in increased number of feasible live donation transplants, and in improved match quality of transplanted kidneys.

This paper studies an evolutionary programming technique, namely a genetic algorithm, to analyze how a population of decision-makers learn to coordinate the selection of an equilibrium or a social convention in a two-sided matching game with incomplete information. In the contexts of centralized and decentralized entry-level labor markets, evolution and adjustment paths of unraveling are explored using this technique in an environment inspired by the Kagel and Roth (2000. Quarterly Journal of Economics 115(1), 201–235) experimental study. As an interesting result, it is demonstrated that stability need not be required for the success of a matching mechanism under incomplete information in the long run.

A significant portion of liver transplantations in many countries is conducted via living-donor liver transplantation (LDLT). However, numerous potential donors are unable to donate to their intended recipients due to factors such as blood type incompatibility or size incompatibility. Despite this, an incompatible donor for one recipient may still be a viable donor for another patient. In recent decades, several transplant centers have introduced liver paired exchange (LPE) programs, facilitating donor exchanges between patients and their incompatible donors, thereby enabling compatible transplants. Initially, LPE programs in Asia primarily involved ABO-i pairs, resulting in 2-way exchanges mainly between blood type A and B recipients and donors. This practice has led to a modest 1% to 2% increase in LDLTs at some centers. Incorporating size incompatibility alongside blood type incompatibility further enhances the efficacy and significance of multiple-pair LPEs. Launched in July 2022, a single-center LPE program established at Inonu University Liver Transplant Institute in Malatya, Türkiye, has conducted thirteen 2-way, nine 3-way, four 4-way, two 5-way, and one 6-way LPEs until February 2024. In 2023 alone, this program facilitated 64 LDLTs, constituting 27.7% of the total 231 LDLTs performed. This paper presents the world's first two 5-way LPEs and the first 6-way LPE.

We report initial results of a liver paired exchange (LPE) program established at the Liver Transplant Institute at Inonu University through collaboration with design economists. Since June 2022, the program has been using a matching procedure that maximizes the number of living donor liver transplants (LDLTs) to the patients in the pool subject to the ethical framework and the logistical constraints of the program. In 1 4-way and 4 2-way exchanges, 12 LDLTs have been performed via LPE in 2022. The 4-way exchange, generated in the same match run with a 2-way exchange, is a first worldwide. This match run generated LDLTs for 6 patients, revealing the value of the capacity to carry out larger than 2-way exchanges. With only 2-way exchanges, only 4 of these patients would receive a LDLT. The number of LDLTs from LPE can be increased by developing the capacity to perform larger than 2-way exchanges in either high-volume centers or multicenter programs.

Importance. Equitable allocation of scarce medications is an important health policy goal. There are few data about attempts to achieve equitable allocation in the community setting.

Objective. To describe the development and use of a weighted lottery to allocate a scarce supply of tixagevimab with cilgavimab as preexposure prophylaxis to COVID-19 for immunocompromised individuals and examine whether this promoted equitable allocation to disadvantaged populations.

Design, setting, and participants. This quality improvement study analyzed a weighted lottery process from December 8, 2021, to February 23, 2022, that assigned twice the odds of drug allocation of 450 tixagevimab with cilgavimab doses to individuals residing in highly disadvantaged neighborhoods according to the US Area Deprivation Index (ADI) in a 35-hospital system in Pennsylvania, New York, and Maryland. In all, 10 834 individuals were eligible for the lottery. Weighted lottery results were compared with 10 000 simulated unweighted lotteries in the same cohort performed after drug allocation occurred.

Main outcomes. Proportion of individuals from disadvantaged neighborhoods and Black individuals who were allocated and received tixagevimab with cilgavimab.

Results. Of the 10 834 eligible individuals, 1800 (16.6%) were from disadvantaged neighborhoods and 767 (7.1%) were Black. Mean (SD) age was 62.9 (18.8) years, and 5471 (50.5%) were women. A higher proportion of individuals from disadvantaged neighborhoods was allocated the drug in the ADI-weighted lottery compared with the unweighted lottery (29.1% vs 16.6%; P < .001). The proportion of Black individuals allocated the drug was greater in the weighted lottery (9.1% vs 7.1%; P < .001). Among the 450 individuals allocated tixagevimab with cilgavimab in the ADI-weighted lottery, similar proportions of individuals from disadvantaged neighborhoods accepted the allocation and received the drug compared with those from other neighborhoods (27.5% vs 27.9%; P = .93). However, Black individuals allocated the drug were less likely to receive it compared with White individuals (3 of 41 [7.3%] vs 118 of 402 [29.4%]; P = .003).

Conclusions and relevance. The findings of this quality improvement study suggest an ADI-weighted lottery process to allocate scarce resources is feasible in a large health system and resulted in more drug allocation to and receipt of drug by individuals who reside in disadvantaged neighborhoods. Although the ADI-weighted lottery also resulted in more drug allocation to Black individuals compared with an unweighted process, they were less likely to accept allocation and receive it compared with White individuals. Further strategies are needed to ensure that Black individuals receive scarce medications allocated.

Background. In fall 2020, the Food and Drug Administration issued emergency use authorization for monoclonal antibody (mAb) therapies for outpatients with COVID-19. The Commonwealth of Massachusetts issued guidance outlining the use of a reserve system with a lottery for allocation of mAbs in the event of scarcity that would prioritize socially vulnerable patients for 20% of the infusion slots. The Mass General Brigham health system subsequently implemented such a reserve system.

Research question. Can a reserve system be deployed successfully in a large health system in a way that promotes equitable access to mAb therapy among socially vulnerable patients with COVID-19?

Study design and methods. We conducted a retrospective review of the operation of the reserve system for allocation of mAb therapies to identify how referrals moved through the allocation process and what proportion of patients who were offered and received mAb therapies were socially vulnerable.

Results. Notwithstanding multiple operational challenges, the reserve system for allocation of mAb therapy worked as intended to enhance the number of socially vulnerable patients who were offered and received mAb therapy. A significantly higher proportion of patients offered mAb therapy were socially vulnerable (27.0%) than would have been the case if the infusion appointments had been allocated using a pure lottery system without a vulnerable reserve (19.8%), and a significantly higher proportion of patient who received infusions were socially vulnerable (25.3%) than would have been the case if the infusion appointments had been allocated using a pure lottery system (17.6%) INTERPRETATION: Our health system experience demonstrates that a reserve system with a lottery for tiebreaking is a viable way to distribute scarce therapeutics when enhancing access for certain groups is desirable.

We report a chain of 10 kidney transplantations, initiated in July 2007 by a single altruistic donor (i.e., a donor without a designated recipient) and coordinated over a period of 8 months by two large paired-donation registries. These transplantations involved six transplantation centers in five states. In the case of five of the transplantations, the donors and their coregistered recipients underwent surgery simultaneously. In the other five cases, "bridge donors" continued the chain as many as 5 months after the coregistered recipients in their own pairs had received transplants. This report of a chain of paired kidney donations, in which the transplantations were not necessarily performed simultaneously, illustrates the potential of this strategy.

In a list exchange (LE), the intended recipient in an incompatible pair receives priority on the deceased donor waitlist (DD-waitlist) after the paired incompatible donor donates a kidney to a DD-waitlist candidate. A nondirected donor's (ND-D) kidney is usually transplanted directly to a DD-waitlist candidate. These two established practices would help even more transplant candidates if they were integrated with kidney paired donation (KPD). We consider a scenario in which the donor of an LE intended recipient (LE-IR) donates to a compatible KPD intended recipient (KPD-IR), and the KPD donor (KPD-D) donates to the waitlist (an LE-chain). We consider a similar scenario in which an ND-D donates to a KPD-IR and the KPD-D donates to the DD-waitlist (an ND-chain). Using data derived from the New England Program for Kidney Exchange (NEPKE) and from OPTN/SRTR recipient-donor distributions, simulations are presented to evaluate the potential impact of chain exchanges coordinated with KPD. LE donors (LE-D) and ND-D who are ABO-O result in the highest number of additional transplants, while results for ABO-A and B donors are similar to each other. We recommend that both LE and ND donations be utilized through chain exchanges.

Background. To expand the opportunity for paired live donor kidney transplantation, computerized matching algorithms have been designed to identify maximal sets of compatible donor/recipient pairs from a registry of incompatible pairs submitted as candidates for transplantation.

Methods. Demographic data of patients who had been evaluated for live donor kidney transplantation but found to be incompatible with their potential donor (because of ABO blood group or positive crossmatch) were submitted for computer analysis and matching. Data included ABO and HLA types of donor and recipient, %PRA and specificity of recipient alloantibody, donor/recipient relationship, and the reason the donor was incompatible. The data set used for the initial simulation included 29 patients with one donor each and 16 patients with multiple donors for a total of 45 patients and 68 donor/patient pairs. In addition, a simulation based on OPTN/SRTR data was used to further assess the practical importance of multiple exchange combinations.

Results. If only exchanges involving two patient-donor pairs were allowed, a maximum of 8 patient-donor pairs in the data set could exchange kidneys. If three-way exchanges were also allowed, a maximum of 11 pairs could exchange kidneys. Simulations with OPTN/SRTR data demonstrate that the increase in the number of potential transplants if three-way exchanges are allowed is robust, and does not depend on the particular patients in our sample.

Conclusions. A computerized matching protocol can be used to identify donor/recipient pairs from a registry of incompatible pairs who can potentially enter into donor exchanges that otherwise would not readily occur.

Kidney exchange emerges as a pioneering application in the early stages of market design. In contrast to most other successful applications in the field, where design economists primarily serve as consultants to decision-makers, in the context of kidney exchange, they assumed the role of outsider critics, ultimately succeeding in shaping real-life practices and institutions. This paper delves into the strategies that facilitated this influential role. Drawing on our two-decade involvement in shaping kidney and liver exchange clearinghouses in the United States and Turkey, we provide insights into factors pivotal for the effectiveness of market design research in shaping policy. Building upon these experiences and incorporating lessons from school choice reforms in the 2000s, Sönmez (2023) introduces a novel institutional design paradigm termed "minimalist market design." Recent years have witnessed tangible outcomes resulting from integrated research and policy efforts employing this framework, notably contributing to the 2021 reform of the US Army's cadet branching system and the establishment of reserve systems during the Covid-19 pandemic for vaccine and therapy allocation across multiple states.

We survey the literature on matching theory under non-transferable utility using a classification based on property rights (i) with private ownership, (ii) with common and mixed ownership, and (iii) under priority-based entitlements.

We survey the literature on applications of matching theory under non-transferable utility. We cover the following six applications in detail: living-donor kidney exchange, living-donor liver exchange, cadet-branch matching in the US Army, affirmative action in India, matching market for entry-level physicians in the US, and course allocation at universities. We also survey other notable applications.

Federal, state, local, and nonprofit agencies in the United States spend over $40 billion each year to serve vulnerable children. Interactions with the child welfare system can profoundly alter children’s lives, ideally protecting children from harm and helping families thrive. This chapter describes key challenges for managing processes at three salient stages of the child welfare system: investigations and pre-removal services, foster care, and adoption. We highlight relevant operations-focused insights from child welfare researchers and the limited research on child welfare by economists and operations researchers. We also identify important issues to consider in future research and connect them to the operations management literature from related domains.

This paper investigates a case study in designing auctions with optimal reserve prices when an analytical solution for the equilibrium bid functions does not exist. The Runge-Kutta integration method nested in a backward-shooting algorithm is used to solve the equilibrium bid functions for a first-price auction with bidders whose value ranking is common knowledge. The optimal reserve price is determined after a numerical search for the seller’s maximum average revenue using simulated auction markets at equilibrium. We observe that setting the optimal reserve price can continue to raise, on average, more revenue for the seller in the first-price auction than in the second-price auction.