Market Design

Members of the NBER's Market Design Working Group met at Stanford University on October 19-20. Research Associates Michael Ostrovsky of Stanford University and Parag A. Pathak of MIT organized the meeting. These researchers' papers were presented and discussed:

Mohammad Akbarpour and Negar Matoorian, Stanford University, and Farshad Fatemi, Sharif University of Technology

A Monetary Market for Kidneys

Alvin E. Roth, Stanford University and NBER

Recent Developments in Kidney Exchange: Market Design in a Large World

Piotr Dworczak, Northwestern University; Scott Duke Kominers, Harvard University; and Mohammad Akbarpour, Stanford University

Redistribution through Markets

When macroeconomic tools fail to respond to wealth inequality optimally, regulators can still seek to mitigate inequality within individual markets. A social planner with distributional preferences might distort allocative efficiency to achieve a more desirable split of surplus, for example, by setting higher prices when sellers are poor--effectively, using the market as a redistributive tool.
In this paper, Dworczak, Kominers, and Akbarpour seek to understand how to design goods markets optimally in the presence of inequality. Using a mechanism design approach, they uncover the constrained Pareto frontier by identifying the optimal trade-off between allocative efficiency and redistribution in a setting where the second welfare theorem fails because of private information and participation constraints. The researchers find that competitive equilibrium allocation is not always optimal. Instead, when there is substantial inequality across sides of the market, the optimal design uses a tax-like mechanism, introducing a wedge between the buyer and seller prices, and redistributing the resulting surplus to the poorer side of the market via lump-sum payments. When there is significant within-side inequality, meanwhile, it may be optimal to impose price controls even though doing so induces rationing.

Yeon-Koo Che, Columbia University, and Olivier Tercieux, Paris School of Economics

Top Trading Cycles in Prioritized Matching: An Irrelevance of Priorities in Large Markets

Top trading cycles (TTC) provides a method for assigning resources efficiently while taking agents' priorities into account. Although TTC favors agents with high priorities in the assignment, Che and Tercieux show in a canonical random preference/priority model that the effect of priorities in TTC disappears as the market grows large, leading in the limit to an assignment that entails virtually the same amount of justified envy as does Random Serial Dictatorship, which completely ignores priorities.

Atila Abdulkadiroglu, Duke University and NBER; Yeon-Koo Che, Columbia University; Parag A. Pathak; Alvin E. Roth; and Olivier Tercieux, Paris School of Economics

Minimizing Justified Envy in School Choice: The Design of New Orleans' OneApp (NBER Working Paper No. 23265)

In 2012, New Orleans Recovery School District (RSD) became the first U.S. district to unify charter and traditional public school admissions in a single-offer assignment mechanism known as OneApp. The RSD also became the first district to use a mechanism based on Top Trading Cycles (TTC) in a real-life allocation problem. Since TTC was originally devised for settings in which agents have endowments, there is no formal rationale for TTC in school choice. In particular, TTC is a Pareto efficient and strategy-proof mechanism, but so are other mechanisms. Abdulkadiroglu, Che, Pathak, Roth, and Tercieux show that TTC is constrained-optimal in the following sense: TTC minimizes justified envy among all Pareto efficient and strategy-proof mechanisms when each school has one seat. When schools have more than one seat, there are multiple possible implementations of TTC. Data from New Orleans and Boston indicate that there is little difference across these versions of TTC, but significantly less justified envy compared to a serial dictatorship.

Hongyao Ma and David Parkes, Harvard University, and Fei Fang, Carnegie Mellon University

Spatio-Temporal Pricing for Ridesharing Platforms

Ridesharing platforms match drivers and riders to trips, using dynamic prices to balance supply and demand. A challenge is to set prices that are appropriately smooth in space and time, so that drivers will choose to accept their dispatched trips, rather than drive to another area or wait for higher prices or a better trip. Ma, Fang, and Parkes work in a complete information, discrete time, multi-period, multi-location model, and introduce the Spatio-Temporal Pricing (STP) mechanism. The mechanism is incentive-aligned, in that it is a subgame-perfect equilibrium for drivers to accept their dispatches, and the mechanism is also welfare-optimal, envy-free, individually rational and budget balanced, and core-selecting from any history onward. The proof of incentive alignment makes use of the natural concavity of min-cost flow objectives. The researchers also give an impossibility result, that there can be no dominant-strategy mechanism with the same economic properties. An empirical analysis conducted in simulation suggests that the STP mechanism can achieve significantly higher social welfare than a myopic pricing mechanism.

Atila Abdulkadiroglu; Joshua Angrist, MIT and NBER; Yusuke Narita, Yale University; and Parag A. Pathak

Impact Evaluation in Matching Markets with General Tie-Breaking (NBER Working Paper No. 24172)

Many centralized matching schemes incorporate a mix of random lottery and non-lottery tiebreaking. A leading example is the New York City public school district, which uses criteria like test scores and interviews to generate applicant rankings for some schools, combined with lottery tie-breaking at other schools. Abdulkadiroglu, Angrist, Narita, and Pathak develop methods that identify causal effects of assignment in such settings. Their approach generalizes the standard regression discontinuity design to allow for many running variables and treatments, some of which are randomly assigned. The researchers show that lottery variation generates assignment risk at non-lottery programs for applicants away from nonlottery cutoffs, while non-lottery variation randomizes applicants near cutoffs regardless of lottery risk. These methods are applied to evaluate New York City's school progress assessments, which give schools letter grades as a summary measure of quality. The researchers' estimates reveal that although Grade A schools boost achievement, these gains emerge only for students who attend lottery schools. Attendance at a coveted Grade A screened school, including some of the highest performing in the district, generates no measurable effects. Evaluation methods that fail to take advantage of both lottery and non-lottery variation miss this difference in impact.

Surender Baswana, India Institute of Technology (IIT) Kanpur; Partha Pratim Chakrabarti, IIT Kharagpur; Sharat Chandran, IIT Bombay; and Yash Kanoria and Utkarsh Patange, Columbia University

Centralized Admissions for Engineering Colleges in India

Baswana, Chakrabarti, Chandran, Kanoria, and Patange designed and implemented a new joint seat allocation process for undergraduate admissions to over 500 programs spread across 80 technical universities in India, including the prestigious Indian Institutes of Technology (IITs). Their process is based on the well known Deferred Acceptance algorithm, but complex affirmative action seat reservations led them to make a number of algorithmic innovations, including (i) a carefully constructed heuristic for incorporating non-nested common quotas that span multiple programs, (ii) a method to utilize unfilled reserved seats with no modifications to the core software, and (iii) a robust approach to reduce variability in the number of reserved category candidates admitted, while retaining fairness. The researchers' new seat allocation process went live in 2015, and based on its success, including significant and provable reduction in vacancies, it has remained in successful use since, with continuing improvements.

Dirk Bergemann, Yale University; Benjamin A. Brooks, University of Chicago; and Stephen Morris, Princeton University

Revenue Guarantee Equivalence

Bergemann, Brooks, and Morris revisit the revenue comparison of standard auction formats, including first-price, second-price, and English auctions. They rank auctions according to their revenue guarantees, i.e., the greatest lower bound of revenue across all informational environments, where they hold fixed the distribution of bidders' values. The researchers conclude that if they restrict attention to the symmetric affiliated models of Milgrom and Weber (1982) and monotonic pure-strategy equilibria, first-price, second-price, and English auctions all have the same revenue guarantee, which is equal to that of the first-price auction as characterized by Bergemann, Brooks, and Morris (2017a). If the researchers consider all equilibria or if they allow more general models of information, then first-price auctions have a greater revenue guarantee than all other auctions considered.

Onur Kesten, Carnegie Mellon University, and Selcuk Ozyurt, Sabanci University

Efficient and Incentive Compatible Mediation: An Ordinal Market Design Approach

Mediation is an alternative dispute resolution method, which has gained increasing popularity over the last few decades and become a multi-billion dollar industry. When two or more parties are in a disagreement, they can take the case to a court and let the judge make a binding final decision. Alternatively, the disputing parties can get assistance from an experienced, neutral third party, i.e., a mediator, who facilitates the negotiation and help them voluntarily reach an agreement short of litigation. The emphasis in mediation is not upon who is right or wrong, but rather on exploring mutually satisfactory solutions. Employment disputes, patent/copyright violations, construction disputes, and family disputes are some of the most common mediated disputes. The rising popularity of mediation is often attributed to the increasing workload of courts, its cost effectiveness and speed relative to litigation, and disputants' desire to have control over the final decision. Many traditional "cardinal" settings of bargaining and mechanism design, starting with the seminal work of Myerson and Satterhwaite (1983), have shown the incompatibility between efficiency and incentives, even in Bayesian sense. Kesten and Ozyurt use an "ordinal" market/mechanism design approach, where the mediator seeks a resolution over (at least) two issues in which negotiators have diametrically opposed rankings over the alternatives. Each negotiator has private information about her own ranking of the outside option, e.g., the point beyond which the negotiator would rather take the case to the court. The researchers construct a simple theoretical framework that is rich and practical enough allowing for optimal mechanisms that the mediators can use for efficient resolution of disputes. They propose and characterize the class of strategy-proof, efficient, and individually rational mediation mechanisms. A central member of this class, the "constrained shortlisting" mechanism stands out as the unique strategy-proof, efficient, and individually rational mechanism that minimizes rank variance. The researchers also provide analogous mechanisms when the issues consist of a continuum of alternatives.

Yuichiro Kamada, Harvard University, and Fuhito Kojima, Stanford University

Fair Matching under Constraints: Theory and Applications

Kamada and Kojima study a general model of matching with constraints. Observing that a stable matching typically does not exist, they focus on feasible, individually rational, and fair matchings. The researchers characterize such matchings by fixed points of a certain function. Building on this result, they characterize the class of constraints on individual schools under which there exists a student-optimal fair matching (SOFM), the matching that is the most preferred by every student among those satisfying the three desirable properties. The researchers study the numerical relevance of the theory using data on government organized daycare allocation.

Tamas Fleiner, Budapest University of Technology and Economics; Ravi Jagadeesan, Harvard University; Zsuzsanna Jankó, Corvinus University; and Alexander Teytelboym, University of Oxford

Trading Networks with Frictions

Fleiner, Jagadeesan, Jankó, and Teytelboym show how frictions and continuous transfers jointly affect equilibria in a model of matching in trading networks. Their model incorporates distortionary frictions such as transaction taxes, bargaining costs, and incomplete markets When contracts are fully substitutable for firms, competitive equilibria exist and coincide with outcomes that satisfy a cooperative stability property called trail stability. In the presence of frictions, competitive equilibria might be neither stable nor (constrained) Pareto-efficient. In the absence of frictions, on the other hand, competitive equilibria are stable and in the core, even if utility is imperfectly transferable.

Xiao Liu, Tsinghua University; Zhixi Wan, Didi Chuxing Technology Co.; and Chenyu Yang, University of Rochester

The Efficiency of A Dynamic Decentralized Two-Sided Matching Market

Liu, Wan, and Yang empirically study a decentralized dynamic matching market. They use data from a leading ride-sharing platform in China to estimate a continuous time dynamic model of search and match between drivers and passengers. In counterfactual simulations, the researchers assess the efficiency of the decentralized market and examine how centralized algorithms may improve welfare. They find that the strategic waiting incentive in the decentralized market increases market thickness and average match quality but decreases the number of matches. Compared with the equilibrium in the decentralized market, centralized algorithms can increase both the match quality and the number of matches by making matches less frequently and matching agents more assortatively.

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