Working Papers

To find families for the more than 70,000 children in need of adoptive placements, most United States child welfare agencies have employed a family-driven search approach in which prospective families respond to announcements made by the agency. However, some agencies have switched to a caseworker-driven search approach in which the caseworker directly contacts families recommended for a child. We introduce a novel search-and-matching model that captures the key features of the adoption process and compare family-driven with caseworker-driven search in a game-theoretical framework. Under either approach, the equilibria are generated by threshold strategies and form a lattice structure. Our main theoretical finding then shows that no family-driven equilibrium can Pareto dominate any caseworker-driven outcome, whereas it is possible that each caseworker-driven equilibrium Pareto dominates every equilibrium attainable under family-driven search. We also find that, within our model, when families are sufficiently impatient, caseworker-driven search is better for all children. We numerically illustrate that most agents are better off under caseworker-driven search across a wide range of parameter values. Finally, we present an empirical study of an agency that switched to caseworker-driven search, finding a three-year adoption probability that outperformed a statewide benchmark by 44.9%, along with a statistically significant 54% higher adoption hazard rate.

In 55 countries, volunteer, non-remunerated donations meet less than 22% of blood demand, necessitating replacement donor programs that exchange patients’ donors for transfusions. Current first-come, first-served practices are inefficient, as they preclude beneficial exchanges among patients. We introduce feasible schedule menus — a novel concept that enables flexible exchange rates — and propose weighted utilitarian mechanisms that accommodate efficiency and fairness objectives when patients value transfusions monotonically and incur donor-provision costs. Under suitable menus, these mechanisms are incentive compatible for donor revelation; priority mechanisms — a subclass that includes maximal mechanisms — also ensure incentive compatibility for utility function revelation.

Children with disabilities age out of the U.S. child welfare system at disproportionately high rates. Understaffed agencies struggle with the higher effort required to successfully place such children with families. This is further compounded by the need to rely on family self-reports to identify high-capability families for these children, which may lead families to under- or overstate their capabilities. These challenges can waste caseworkers’ limited time and, more importantly, risk creating unsuitable adoptions. Given that each family’s true capability to care for a high-needs child is unobservable, we model the dynamic placement process under three objectives: maximizing overall adoptions, maximizing adoptions for the most disadvantaged children, and equalizing placement attempts per child across child types. Under full information, each objective entails distinct trade-offs. Under incomplete information, when families act strategically, adoption rates may deteriorate, especially when low-capability families are overrepresented. In that case, misreporting leads to many adoptions of high-needs children by unsuitable families in equilibrium when using naive mechanisms. On the other hand, incentive-compatible mechanisms also prove inadequate, as they may preclude the placement of any high-needs child. We propose incentive-aware mechanisms that strategically lead to some misreporting by low-capability families and a tolerable risk of unsuitable adoptions of high-needs children. These mechanisms improve the ability to suitably place high-needs children and always (weakly) outperform the respective incentive-compatible mechanism in achieving their desired objective. We lastly derive managerial insights on workload allocation.

Labor contracts typically do not limit worker mobility. Interesting exceptions exist in foreign worker reemployment, sports transfers and sometimes through non-compete clauses. We develop a model to address contractual designs for such markets. Although legally, a firm can contest its worker’s recruitment by a competitor, it may be more lenient if he can be replaced immediately. We develop a theory of stability suitable for such markets and propose stable-uncontested mechanisms. As our application, we consider transfers in collegiate sports governed by the NCAA, where before 2021, a student-athlete had to sit out a year after a transfer. Beginning in 2021, free mobility was allowed. Anecdotal evidence suggests while pre-2021 regulations were detrimental to student and college welfare, post-2020 regulations led to colleges struggling to keep rosters and withholding new scholarship slots to use in transfers. Our model also captures the NCAA’s pre-2021 and post-2020 regulations as well as our new proposed efficiency-enhancing criterion. Then, using data from men’s collegiate basketball, we estimate college and student-athlete preferences. Using the preferences we estimate from transfer data, we run counterfactual analyses of pre-2021 and post-2020 environments and our proposed regulations. Our proposal achieves closer student-athlete welfare to post-2020 than pre-2021 and increases college welfare with respect to post-2020 and pre-2021.

In the past two decades, the design and implementation of living donor kidney exchange clearinghouses have been a major success story in market design. Instead of batching and optimizing exchanges over a fixed pool of incompatible patient-donor pairs, the busiest programs now operate dynamically, matching pairs as they arrive. This feature has also sparked interest in dynamic matching mechanisms. Yet for general matching problems with high-dimensional state spaces, a full characterization of optimal dynamic mechanisms remains elusive, and only approximate solutions are known. We develop a new methodology to characterize and compute dynamically optimal mechanisms for bilateral matching over arbitrary state spaces, provided that compatibility between agent types follows a linear spatial structure. This technique applies to optimal dynamic kidney exchange and extends to other spatial matching problems. Our approach leverages second-order properties of the value function, extending recent advances in Markov Decision Processes and queueing systems, which traditionally focus only on substitutable components.

Centralized (re)assignment of workers to jobs is increasingly common in public and private sectors. However, these markets often suffer from distributional problems. We propose a new strategy-proof mechanism that efficiently improves individual and distributional welfare over the status quo. We justify our constructive and practical approach by micro-founding it through the theory of inequality measures in welfare economics. To evaluate the performance of our mechanism, we focus on teacher (re)assignment, where the unequal distribution of experienced teachers across schools is a well-documented concern. Using French data, we demonstrate that our mechanism reduces the teacher experience gap across regions more effectively than benchmarks, including the current mechanism, while providing higher average welfare for teachers.

In a 3-2 split verdict, the Supreme Court approved the exclusion of India’s socially and economically backward classes from its affirmative action measures to address economic deprivation. Dissenting justices, including the Chief Justice of India, protested the Majority Opinion for sanctioning “an avowedly exclusionary and discriminatory principle.” To justify their controversial decision, the majority justices relied on technical arguments that are categorically false. The confusion of the justices is due to a subtle technical aspect of the affirmative action system in India: the significance of overlaps between members of protected groups. Conventionally, protected classes were determined by the caste system, which meant they did not overlap. The addition of a new protected class defined by economic criteria alters this structure, unless it is artificially enforced. The majority justices failed to appreciate the significance of this critical change and inaccurately argued that the controversial exclusion is a technical necessity to provide benefits to previously unprotected members of a new class. We show that this case could have been resolved with three competing policies that each avoid the controversial exclusion. One of these policies aligns with the core arguments in the Majority Opinion, whereas a second aligns with those in the Dissenting Opinion.

Calls for eliminating prioritization for SARS-CoV-2 vaccines are growing amid concerns that prioritization reduces vaccination speed. We use an SEIR model to study the effects of vaccination distribution on public health, comparing prioritization policy and speed under mitigation measures that are either eased during the vaccine rollout or sustained through the end of the pandemic period. NASEM’s recommended prioritization results in fewer deaths than no prioritization, but does not minimize total deaths. If mitigation measures are eased, abandoning NASEM will result in about 134,000 more deaths at 30 million vaccinations per month. Vaccination speed must be at least 53% higher under no prioritization to avoid increasing deaths. With sustained mitigation, discarding NASEM prioritization will result in 42,000 more deaths, requiring only a 26% increase in speed to hold deaths constant. Therefore, abandoning NASEM’s prioritization to increase vaccination speed without substantially increasing deaths may require sustained mitigation.

Convalescent plasma is a blood product produced by recovered patients with several valuable uses, especially during public health emergencies. We develop a model of plasma donation and distribution and consider two incentive schemes to increase plasma supply based on “paying it backward” and “paying it forward” principles. Under the former, donors obtain credits that can be transferred to patients of their choosing. Under the latter, patients obtain priority for plasma-derived products in exchange for a future donation pledge. We show that both incentives generally increase overall treatment rates for all patients—not just those with credits or who have pledged. Finally, we examine the implications of pooling blood types on the efficiency and equity of plasma distribution. Our formal results are of independent interest for egalitarian divisible goods rationing programs with compatibility constraints.

In Europe, every year more than 200,000 college students study in different countries thanks to the Erasmus Student Exchange program. The program aims to improve the integration all around Europe. Although this exchange program is successful in many dimensions, it has two major drawbacks. First of all, the number of exchange students imported and exported by countries are not balanced. Unbalanced exchange causes a financial burden for countries that are importing more exchange students than their exports. Secondly, we do not observe diversity among the exchange students. That is, certain countries are exchanging students mainly with each other. To solve these two problems observed in the current practice, we propose a version of the Top Trading Cycles and Chains (TTCC) mechanism. We show that our mechanism solves these observed problems while satisfying constrained efficiency, strategy-proofness, and fairness. Moreover, TTCC may increase the number of students benefiting from the Erasmus program. To our knowledge, this is the first application of the TTCC mechanism to the many to one market, and this is the first paper solving distributional constraints via the Top Trading Cycles type mechanism.

End-stage renal disease (ESRD) is the ninth-leading cause of death in the U.S. Transplantation is the most viable renal replacement therapy for ESRD patients, but there is a severe disparity between the demand for kidneys for transplantation and the supply. This shortage is further complicated by incompatibilities in blood-type and antigen matching between patient-donor pairs. Paired kidney exchange (PKE), a cross-exchange of kidneys among incompatible patient-donor pairs, overcomes many difficulties in matching patients with incompatible donors. In a typical PKE, transplantation surgeries take place simultaneously so that no donor may renege after her intended recipient receives the kidney. Therefore, in a PKE, the occurrence of a transplantation requires compatibility among the pairs’ willingnesses to exchange. We consider an arbitrary number of autonomous patients with probabilistically evolving health statuses in a prearranged PKE, and model their transplant timing decisions as a discrete-time non-zero-sum noncooperative stochastic game. We explore necessary and sufficient conditions for patients’ decisions to be a stationary-perfect equilibrium, and formulate a mixed-integer linear programming representation of equilibrium constraints, which provides a characterization of the socially optimal stationary-perfect equilibria. We carefully calibrate our model using a large scale nationally representative clinical data, and empirically confirm that randomized strategies, which are less consistent with clinical practice and rationality of the patients, do not yield a significant social welfare gain over pure strategies. We also quantify the social welfare loss due to patient autonomy and demonstrate that maximizing the number of transplants may be undesirable. Our results highlight the importance of the timing of an exchange and the disease severity on matching patient-donor pairs.

In this note we study the allocation and exchange of discrete resources in environments in which monetary transfers are not allowed. We allow each discrete resource to be represented by several copies, extend onto this environment the trading cycles mechanisms of Pycia and Ünver [2009], and show that the extended mechanisms are Pareto efficient and strategy-proof. In particular, we construct the counterpart of Pápai [2000] hierarchical exchange mechanisms for environments with copies.

This paper studies the problem of fair allocation of indivisible objects and money among agents with quasi-linear preferences. A mechanism determines an allocation for each problem. We introduce a class of mechanisms, namely market mechanisms, which use tâtonnement process. We prove that adjustment process converges to an envy-free, efficient, and individually rational allocation. Some interesting examples of mechanisms in this class are presented.