Market Design Working Group Meeting Fall 2020

Kidney failure is a worldwide scourge, made more lethal by the shortage of transplants. Akbarpour, Nikzad, Rees, and Roth propose a new way to organize kidney exchange chains internationally, between middle-income countries with financial barriers to transplantation and high income countries with many hard-to-match patients and patient-donor pairs facing lengthy dialysis. The proposal involves chains of exchange that begin in the middle income country and end in the high-income country. The researchers also propose a new way of financing such chains, using savings to U.S. healthcare payers.

Policymakers frequently use reserve categories to combine competing objectives in allocating scarce resources based on priority. For example, schools may prioritize students from underprivileged backgrounds for some of their seats while allocating the rest of them based solely on academic merit. The order in which different categories are processed has been shown to have an important, yet subtle impact on allocative outcomes--and has led to unintended consequences in practice. Delacretaz introduces a new, more transparent way of processing reserves, which handles all categories simultaneously. The researcher provides an axiomatic characterization of his solution, showing that it satisfies basic desiderata as well as category neutrality: if an agent qualifies for n categories, she takes 1/n units from each of them. A practical advantage of this approach is that the relative importance of categories is entirely captured by their quotas.

Moriguchi, Narita, and Tanaka study the short-run and long-run impacts of changing admissions systems in higher education. The researchers take advantage of the world’s first known implementation of nationally centralized admissions and its subsequent reversals in early twentieth-century Japan. This centralization was designed to make admissions more meritocratic, but their analysis shows that there was a sharp tradeoff between meritocracy and equal regional access to higher education and career advancement. Specifically, in the short run, the meritocratic centralization led students to make more inter-regional and ambitious applications. However, as high ability students were located disproportionately in urban areas, increased regional mobility caused urban applicants to crowd out rural applicants from higher education. Moreover, the impacts were persistent: Four decades later, compared to the decentralized admissions, the meritocratic centralization improved the quality of career elites, while increasing the number of urban-born elites (e.g., top income earners, top-ranking bureaucrats) relative to rural-born elites.

In 56 developing and developed countries, blood component donations by volunteer nonremunerated donors can only meet less than 50% of the demand. In these countries, blood banks heavily rely on donor replacement programs that provide blood to patients in return for donations made by their close relatives or friends. Such programs appear to be highly disorganized, non-transparent, and inefficient despite the scarcity of blood components. Han, Kesten, and Ünver introduce the design of donor replacement programs and blood allocation schemes as a new application of market design. The researchers formulate a general blood allocation and donation model including the blood bank, patients, volunteer non-remunerated and replacement donors. Within this framework, a class of blood allocation mechanisms is introduced, which sequentially accommodates various policy objectives of a blood bank while ensuring efficiency. Another novelty Han, Kesten, and Ünver introduce is a rich class of feasible allocation possibilities beyond the classical one-to-one exchange. This class accommodates endogenous exchange rates between donated and received blood units together with various fairness and efficiency objectives. Furthermore, they also ensure that our mechanisms provide correct incentives for the patients to bring forward as many replacement donors as possible. This framework and mechanisms also apply to exchange of general multi-unit indivisible goods.

Learning equilibria in multi-agent games is challenging because the players' rewards may change depending on the actions of other learning agents. While there has been progress in computing Nash equilibria in complete-information games, little is known about learning equilibria in Bayesian games. Such games are a research frontier with auctions as the best-known example. The key difference between complete-information games and auction games is that Bichler, Fichtl, Heidekrüger, Kohring, and Sutterer search an equilibrium bid function over a domain of infinitely many valuations, a problem for which no general solution theory is available. The researchers introduce a numerical technique to compute Bayes-Nash equilibria, which is based on neural networks and self-play. The method implements a gradient ascent scheme and approximates the expected utility via Monte Carlo sampling. Training neural networks in this environment is challenging as the payoff functions of individual auctions are discontinuous and nondifferentiable. Bichler, Fichtl, Heidekrüger, Kohring, and Sutterer solve this problem by leveraging an evolutionary strategy optimization technique that effectively smoothes the objective. This allows us to derive an estimate of the gradient of the smoothed game, and the individual agents adapt their policy by taking a step along their policy gradient. The researchers introduce conditions for which they can certify an e-Bayes-Nash equilibrium and provide extensive numerical experiments. The experimental results show that the method converges quickly to the analytical Bayes-Nash equilibrium in a wide range of auction games including auctions with asymmetric priors or risk aversion, or even in combinatorial auctions with correlation or multiple pure Bayes-Nash equilibria.

College admissions policies affect the educational experiences and labor market outcomes for millions of students each year. In China alone, 10 million high school seniors participate in the National College Entrance Examination to compete for 7 million seats at various universities each year, making this system the largest centralized matching market in the world. The last 20 y have witnessed radical reforms in the Chinese college admissions system, with many provinces moving from a sequential (immediate acceptance) mechanism to some version of the parallel college admissions mechanism, a hybrid between the immediate and deferred acceptance mechanisms. In this study, Chen, Jiang, and Kesten use a natural experiment to evaluate the effectiveness of the sequential and parallel mechanisms in motivating student college ranking strategies and providing stable matching outcomes. Using a unique dataset from a province that implemented a partial reform between 2008 and 2009, the researchers find that students list more colleges in their rank-ordered lists, and more prestigious colleges as their top choices, after the province adopts the parallel mechanism in its tier 1 college admissions process. These listing strategies in turn lead to greater stability in matching outcomes, consistent with their theoretical prediction that the parallel mechanism is less manipulable and more stable than the sequential mechanism.

COVID-19 has revealed several limitations of existing mechanisms for rationing scarce medical resources under emergency scenarios. Many argue that they abandon various ethical values such as equity by discriminating against disadvantaged communities. Illustrating that these limitations are aggravated by a restrictive choice of mechanism, Pathak, Sönmez, Ünver, and Yenmez formulate pandemic rationing of medical resources as a new application of market design and propose a reserve system as a resolution. The researchers develop a general theory of reserve design, introduce new concepts such as cutoff equilibria and smart reserves, extend previously-known ones such as sequential reserve matching, and relate these concepts to current debates.

Echenique, Miralles, and Zhang propose a market solution to the problem of resource allocation subject to constraints, such as considerations of diversity or geographical distribution. Constraints give rise to pecuniary externalities, which are internalized via prices. Agents pay to the extent that their purchases affect the value (at equilibrium prices) of the relevant constraints. The result is a constrained-efficient market equilibrium outcome. The outcome is fair whenever the constraints do not single out individual agents, which happens, for example with geographical distribution constraints. In economies with endowments, moreover, Echenique, Miralles, and Zhang can address participation constraints. Their equilibrium outcomes are then constrained efficient and approximately individually rational.

Most assets clear independently rather than jointly. This paper presents a model based on the uniform-price double auction which accommodates arbitrary restrictions on market clearing, including asset by asset market clearing (allowed when demand for each asset is contingent only on the price of that asset) and joint market clearing for all assets (required when demand for each asset is contingent on prices of all assets). Introducing additional trading protocols for traded assets -- neutral when the market clears jointly -- or linking existent trading protocols are generally not redundant innovations, even if all traders participate in all protocols. Multiple protocols that clear independently can always be designed to be at least as efficient as joint market clearing for all assets. Separation in market clearing can enhance diversification and risk sharing. When traders have price impact, regulation of innovation in trading technology should be guided by market characteristics.

Kapor, Karnani, and Neilson study the empirical relevance of the configuration of on- and off-platform options for students' welfare and for persistence and graduation in higher-education programs. The researchers document the importance of negative externalities generated by off-platform options and quantify a measure of aftermarket frictions that contribute to generating them in practice. Their empirical application uses data from the centralized assignment system for higher education in Chile and leverages a recent policy change that significantly increased the number of on-platform slots by approximately 50%. Kapor, Karnani, and Neilson first present an event study analysis which shows that when more relevant options are included on the centralized platform, students start college sooner, are less likely to drop out, and are more likely to graduate within six years. Importantly, these effects were larger for students from lower SES backgrounds, suggesting the design of platforms can have effects on both efficiency and equity. To quantify welfare impacts and decompose channels, Kapor, Karnani, and Neilson develop an empirical model of college applications, aftermarket waitlists, and matriculation choices. They find that welfare increases substantially, especially for less advantaged students and for women, following the policy change. These externalities are driven by students who receive and decline on-platform offers, and are amplified by substantial frictions in waitlists. Their results indicate that expanding the scope of a higher education platform can have real impacts on welfare and human capital. The researchers' findings suggest policymakers need to consider the implications of off-platform options and their characteristics when designing regulation surrounding centralized assignment systems.

In a Vickrey auction, if one bidder can invest to increase his value, the combined mechanism including investments is still fully optimal. By contrast, there exist monotone allocation rules that are arbitrarily close to the the allocative optimum, but such that the associated mechanism with investments by one bidder cannot guarantee any positive fraction of the full optimum. Akbarpour, Kominers, Li, and Milgrom show that if a monotone allocation rule that guarantees some fraction of the allocative optimum also "excludes bossy negative externalities," then the same guarantee applies to the combined mechanism with investments. The researchers show moreover that a mild weakening of this property is necessary and sufficient for the result.