NATIONAL BUREAU OF ECONOMIC RESEARCH

# Market Design

October 23-24, 2015
Michael Ostrovsky of Stanford University and Parag Pathak of MIT, Organizers

Tayfun Sonmez and Utku Ünver, Boston College, and Ozgur Yilmaz, Koç University

How (not) to Integrate Blood Subtyping Technology to Kidney Exchange

Following a series of collaborations between members of the transplantation community and researchers in market design, kidney exchange became an important source of transplant kidneys over the last decade. Given the persistent shortage of kidneys for transplantation throughout the world, analysis of policies and procedures that could increase the contribution of kidney exchange to the number of kidney transplants became an active area of research not only in the transplantation community, but also among the researchers in market design. Sonmez, Ünver, and Yilmaz analyze the potential spillovers of a recent policy change in allocation of deceased donor kidneys in the US on the number of transplants from living donors including those from kidney exchanges. The policy involves preferential allocation of subtype A2 kidneys (a subset of blood type A kidneys that generate milder antibody reaction when transplanted to blood type B or O patients) to blood type B patients to mitigate the biological disadvantages these patients face in kidney transplantation. Authors show that, if care is not taken, extension of this policy to kidney exchange can result in a reduction of the number of transplants from living donors (due to a reduction of transplants via exchanges) even though a number of its variants have great potential to increase this number.

Mehmet Ekmekci, Boston College, and M. Bumin Yenmez, Carnegie Mellon University

As school districts integrate charter schools for centralized admissions in Denver, New Orleans, Newark and Washington D.C., some schools have stayed out. Ekmekci and Yenmez provide a new framework to study the incentives of a school to join a clearinghouse and show that each school prefers to remain out of the system when others join it. Therefore, the researchers' analysis provides an explanation of why some charter schools have evaded the clearinghouse. To overcome this issue, the authors propose two schemes that can be used by policymakers to incentivize schools to join the system, which achieves the desired integration of schools.

Atila Abdulkadiroğlu, Duke University; Joshua Angrist, MIT and NBER; Yusuke Narita, MIT; and Parag Pathak

Research Design meets Market Design: Using Centralized Assignment for Impact Evaluation

A growing number of school districts use centralized assignment mechanisms to allocate school seats in a manner that reflects student preferences and school priorities. Many of these assignment schemes use lotteries to ration seats when schools are oversubscribed. The resulting random assignment opens the door to credible quasi-experimental research designs for the evaluation of school effectiveness. Yet the question of how best to separate the lottery-generated variation integral to such designs from non-random preferences and priorities remains open. This paper develops easily-implemented empirical strategies that fully exploit the random assignment embedded in the widely-used deferred acceptance mechanism and its variants. Abdulkadiroğlu, Angrist, Narita, and Pathak use these new methods to evaluate charter schools in Denver, one of a growing number of districts that integrate charter and traditional public schools in a unified assignment system. The resulting estimates show large achievement gains from charter school attendance. The researchers' approach generates substantial efficiency gains over ad hoc methods that fail to exploit the full richness of the lotteries generated by centralized assignment with random tie-breaking.

Shuchi Chawla, University of Wisconsin; Jason Hartline, Northwestern University; and Denis Nekipelov, University of Virginia

Mechanism Design for Data Science

John Hatfield, University of Texas, Austin; Scott Duke Kominers, Harvard University; Alexandru Nichifor, University of St Andrews; Michael Ostrovsky; and Alexander Westkamp, University of Bonn

Full Substitutability

Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. Hatfield, Kominers, Nichifor, Ostrovsky, and Westkamp extend earlier models' canonical definitions of substitutability to settings in which an agent can be both a buyer in some transactions and a seller in others, and show that all these definitions are equivalent. The researchers introduce a new class of substitutable preferences that allows them to model intermediaries with production capacity. They then prove that substitutability is preserved under economically important transformations such as trade endowments, mergers, and limited liability. They also show that substitutability corresponds to submodularity of the indirect utility function, the single improvement property, and a no complementarities condition. Finally, they show that substitutability implies the monotonicity conditions known as the Laws of Aggregate Supply and Demand.

Thành Nguyen, Purdue University, and Rakesh Vohra, University of Pennsylvania

Near Feasible Stable Matchings with Complementarities

The National Resident Matching program strives for a stable matching of medical students to teaching hospitals. With the presence of couples, stable matchings need not exist. For any student preferences, Nguyen and Vohra show that each instance of a stable matching problem has a 'nearby' instance with a stable matching. The nearby instance is obtained by perturbing the capacities of the hospitals. Specifically, given a reported capacity k_h for each hospital h, authors find a redistribution of the slot capacities k_h^' satisfying |k_h-k_h^'|<=4 for all hospitals h and sum_h k_h<=sum k_h^'<=sum_h k_h+9, such that a stable matching exists with respect to k^'. Their approach is general and applies to other type of complementarities, as well as matchings with contracts.

Jonathan D. Levin, Stanford University and NBER, and Andrzej Skrzypacz, Stanford University

Are Dynamic Vickrey Auctions Practical? Properties of the Combinatorial Clock Auction

The combinatorial clock auction is becoming increasingly popular for large-scale spectrum awards and other uses, replacing more traditional ascending or clock auctions. Levin and Skrzypacz describe some surprising properties of the auction, including a wide range of ex post equilibria with demand expansion, demand reduction and predation. These outcomes arise because of the way the auction separates allocation and pricing, so that bidders are asked to make decisions that cannot possibly affect their own auction outcome. The researchers' results obtain in a standard homogenous good setting where bidders have well-behaved linear demand curves, and suggest some practical difficulties with dynamic implementations of the Vickrey auction.

Ali Hortaçsu, University of Chicago and NBER; Jakub Kastl, Princeton University and NBER; and Allen Zhang, Department of the Treasury

Bid Shading and Bidder Surplus in the U.S. Treasury Auction System

Hortaçsu, Kastl, and Zhang analyze detailed bidding data from auctions of Treasury bills and notes conducted between July 2009 and October 2013. The U.S. Treasury uses a uniform price auction system, which the researchers model building on the share auction model of Wilson (1979) and Kastl (2012). The researchers' model takes into account informational asymmetries introduced by the primary dealership and indirect bidding system employed by the U.S. Treasury. Building on the methods developed by Hortaçsu (2002), Hortaçsu and McAdams (2010), Kastl (2011), and Hortaçsu and Kastl (2012), the authors estimate the amount of bid shading undertaken by the bidders under the assumption of bidder optimization. Their method also enables them to estimate the marginal valuations of bidders that rationalize the observed bids under a private value framework. They find that primary dealers consistently bid higher yields in the auctions compared to direct and indirect bidders. Their model allows them to decompose this difference into two components: difference in demand/willingness-to-pay, and difference in ability to shade bids. The researchers find that while primary dealer willingness-to-pay is similar to or even higher than direct and indirect bidders', their ability to bid-shade is higher, leading to higher yield bids. By computing the area under bidders' demand curves, the authors can also quantify the surplus that bidders derive from the auctions. They find that total bidder surplus across the sample period was, on average, 2.3 basis points. By comparing the actual allocation to the one corresponding to the maximum surplus, they also quantify the efficiency loss from the auctions, which was, on average, 2.25 basis points.

Nick Arnosti, Marissa Beck, and Paul Milgrom, Stanford University

Arnosti, Beck, and Milgrom model an online display advertising environment in which "performance" advertisers can measure the value of individual impressions, whereas "brand" advertisers cannot. If advertiser values for ad opportunities are positively correlated, second-price auctions for impressions can be very inefficient. Bayesian-optimal auctions are complex, introduce incentives for false-name bidding, and disproportionately allocate low-quality impressions to brand advertisers. The researchers introduce "modified second bid" auctions as the unique auctions that overcome these disadvantages. When advertiser match values are drawn independently from heavy tailed distributions, a modified second bid auction captures at least 94.8% of the first-best expected value. In that setting and similar ones, the benefits of switching from an ordinary second-price auction to the modified second bid auction may be large, and the cost of defending against shill bidding and adverse selection may be low.

Daniela Saban, Stanford University, and Gabriel Weintraub, Columbia University

Procurement Mechanisms for Differentiated Products

Saban and Weintraub consider the problem faced by a procurement agency that runs an auction-type mechanism to construct an assortment of differentiated products with posted prices, offered by strategic suppliers. Heterogeneous consumers then buy their most preferred alternative from the assortment as needed. Framework agreements (FAs), widely used in the public sector, take this form; the central government runs the initial auction and then the public organizations (hospitals, schools, etc.) buy from the selected assortment. This type of mechanism is also relevant in other contexts, including private procurement settings and the design of drug formularies. When evaluating the bids, the procurement agency must consider the optimal trade-off between offering a richer menu of products for consumers versus offering less variety, hoping to engage the suppliers in a more aggressive price competition. The researchers develop a mechanism design approach to study this problem. They characterize the optimal mechanism, which typically restricts the entry of close-substitute products to the assortment to induce more price competition among suppliers, without much damage to variety. They then use the optimal mechanism as a benchmark to evaluate the performance of the Chilean government procurement agency's current implementation of FAs, used to acquire US\$2 billion worth of goods per year. Through a combination of theoretical and numerical results the authors show how the performance of such FAs can be considerably improved by introducing simple modifications to current practice which, similarly to the optimal mechanism, increase price competition among close substitutes.

Steven Lalley, University of Chicago, and Glen Weyl, Microsoft Corporation

N individuals with independent private values must choose among two collective alternatives. A simple, detail-free mechanism, Quadratic Voting (QV), has been suggested based on heuristic arguments and experimental results to maximize utilitarian welfare. Lalley and Weyl prove that for any value distribution all symmetric Bayes-Nash equilibria of QV converge towards efficiency, with waste decaying generically as 1/N.

Canice Prendergast, University of Chicago

The Allocation of Food to Food Banks

Food banks throughout the U.S. provide nutrition to the needy. Yet the food that is distributed through food banks often originates with donors  large manufacturers or distributors  far from those needy clients. How that food is distributed to food banks across the country is the subject of this essay. Prendergast gives an informal description of an innovation introduced in 2005 by Feeding America (at the time the organization was called America's Second Harvest) that would better allow food bank preferences to be reflected in their allocations. Specifically, Feeding America transitioned from the centralized allocation process, where they would make decisions based on their perception of food bank need, to one where local affiliates would bid for food items. To do so, Feeding America constructed a specialized constructed currency called "shares" that are used to bid on loads of donated food. The process by which this change came about, its necessary idiosyncrasies, and its outcomes are described.

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