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Choice Screen Auctions
Author(s):
Michael Ostrovsky, Stanford University and NBER
Abstract:

Choice screen auctions have been recently deployed in 31 European countries, allowing consumers to choose their preferred search engine on Google's Android platform instead of being automatically defaulted to Google's own search engine. Ostrovsky shows that a seemingly minor detail in the design of these auctions--whether they are conducted on a "per appearance" or a "per install" basis--plays a major role in the mix and characteristics of auction winners, and, consequently, in their expected overall market share. Ostrovsky also shows that "per install" auctions distort the incentives of alternative search engines toward extracting as much revenue as possible from each user who installs them, at the expense of lowering the expected number of such users. The distortion becomes worse as the auction gets more competitive and the number of bidders increases. Empirical evidence from Android choice screen auctions conducted in 2020 is consistent with his theoretical results.

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This paper was distributed as Working Paper 28091, where an updated version may be available.

The Value of Excess Supply in Spatial Matching Markets
Author(s):
Mohammad Akbarpour, Stanford University
Yeganeh Alimohammadi, Stanford University
Shengwu Li, Harvard University
Amin Saberi, Stanford University
Abstract:

Akbarpour, Alimohammadi, Li, and Saberi study dynamic matching in a spatial setting. Drivers are distributed at random on some interval. Riders arrive in some (possibly adversarial) order at randomly drawn points. The platform observes the location of the drivers, and can match newly arrived riders immediately, or can wait for more riders to arrive. Unmatched riders incur a waiting cost c per period. The platform can match riders and drivers, irrevocably. The cost of matching a driver to a rider is equal to the distance between them. The researchers quantify the value of slightly increasing supply. Akbarpour, Alimohammadi, Li, and Saberi prove that when there are (1 + ϵ) drivers per rider (for any ϵ > 0), the cost of matching returned by a simple greedy algorithm which pairs each arriving rider to the closest available driver is O(log3 (n)), where n is the number of riders. On the other hand, with equal number of drivers and riders, even the ex post optimal matching does not have a cost less than Θ(√n). Their results shed light on the important role of (small) excess supply in spatial matching markets.

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Randomized FIFO Mechanisms
Author(s):
Francisco Castro, University of California, Los Angeles
Hongyao Ma, Columbia University
Hamid Nazerzadeh, University of Southern California
Chiwei Yan, University of Washington
Abstract:

Castro, Ma, Nazerzadeh, and Yan study the matching of jobs to workers in a queue, e.g. a ridesharing platform dispatching drivers to pick up riders at an airport. Under FIFO dispatching, the heterogeneity in trip earnings incentivizes drivers to cherry-pick, increasing riders' waiting time for a match and resulting in a loss of efficiency and reliability. Castro, Ma, Nazerzadeh, and Yan first present the direct FIFO mechanism, which offers lower-earning trips to drivers further down the queue. The option to skip the rest of the line incentivizes drivers to accept all dispatches, but the mechanism would be considered unfair since drivers closer to the head of the queue may have lower priority for trips to certain destinations. To avoid the use of unfair dispatch rules, the researchers introduce a family of randomized FIFO mechanisms, which send declined trips gradually down the queue in a randomized manner. Castro, Ma, Nazerzadeh, and Yan prove that a randomized FIFO mechanism achieves the first best throughput and the second best revenue in equilibrium. Extensive counterfactual simulations using data from the City of Chicago demonstrate substantial improvements of revenue and throughput, highlighting the effectiveness of using waiting times to align incentives and reduce the variability in driver earnings.

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Choices and Outcomes in Assignment Mechanisms: The Allocation of Deceased Donor Kidneys
Author(s):
Nikhil Agarwal, Massachusetts Institute of Technology and NBER
Charles Hodgson, Yale University
Paulo J. Somaini, Stanford University and NBER
Abstract:

While the mechanism design paradigm emphasizes notions of efficiency based on agent preferences, policymakers often focus on alternative objectives. School districts emphasize educational achievement, and transplantation communities focus on patient survival. It is unclear whether choice-based mechanisms perform well when assessed based on these outcomes. This paper evaluates the assignment mechanism for allocating deceased donor kidneys on the basis of patient life-years from transplantation (LYFT). Agarwal, Hodgson, and Somaini examine the role of choice in increasing LYFT and compare equilibrium assignments to benchmarks that remove choice. Their model combines choices and outcomes in order to study how selection affects LYFT. Agarwal, Hodgson, and Somaini show how to identify and estimate the model using instruments derived from the mechanism. The estimates suggest that the design in use selects patients with better post-transplant survival prospects and matches them well, resulting in an average LYFT of 8.78, which is 0.92 years more than a random assignment. However, the aggregate LYFT can be increased to 13.84. Realizing the majority of the gains requires transplanting relatively healthy patients, who would have longer life expectancies even without a transplant. Therefore, a policymaker faces a dilemma between transplanting patients who are sicker and those for whom life will be extended the longest.

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This paper was distributed as Working Paper 28064, where an updated version may be available.

Flow Trading
Author(s):
Eric Budish, University of Chicago and NBER
Peter Cramton, University of Cologne
Albert "Pete" Kyle, University of Maryland
Jeongmin (Mina) Lee, Washington University in St. Louis
David Malec, University of Maryland
Abstract:

Budish, Cramton, Kyle, Lee, and Malec propose a new market design for trading financial assets. The design combines three elements: (1) Traders submit persistent piecewise-linear downward-sloping demand curves to trade in shares per second (Kyle and Lee (2017)). (2) Markets clear using frequent batch auctions held at regular intervals, such as once per second (Budish, Cramton, and Shim (2015)). (3) Traders may submit orders to trade portfolios of assets, expressed as arbitrary linear combinations with positive and negative weights, as if they were one asset. Thus, relative to the status quo design: time is discrete instead of continuous, prices and quantities are continuous instead of discrete, and traders can directly trade portfolios. Market clearing quantities and prices are the solution to a quadratic program with linear constraints, constructed by attributing preferences to orders and maximizing imputed gains
from trade. Clearing prices and quantities are shown to exist, with the latter unique. Calculating prices is shown to be computationally feasible. Microfoundations for portfolio orders are provided. The market design has several potential benefits relative to the status quo: (1) traders can directly express many common trading demands, which reduces costs and complexity; (2) it reduces the importance of speed; (3) it allows liquidity and price discovery to be easily linked across related assets; and (4) it improves fairness and transparency, as all executable orders trade at the same prices at the same time.

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The Equilibrium Existence Duality: Equilibrium with Indivisibilities and Income Effects
Author(s):
Elizabeth C. Baldwin, University of Oxford
Omer Edhan, University of Manchester
Ravi Jagadeesan, Stanford University
Paul D. Klemperer, University of Oxford
Alexander Teytelboym, University of Oxford
Abstract:

Baldwin, Edhan, Jagadeesan, Klemperer, and Teytelboym show that, with indivisible goods, the existence of competitive equilibrium fundamentally depends on agents' substitution effects, not their income effects. Their Equilibrium Existence Duality allows us to transport results on the existence of competitive equilibrium from settings with transferable utility to settings with income effects. One consequence is that net substitutability--which is a strictly weaker condition than gross substitutability--is sufficient for the existence of competitive equilibrium. Baldwin, Edhan, Jagadeesan, Klemperer, and Teytelboym also extend the "demand types" classification of valuations to settings with income effects and give necessary and sufficient conditions for a pattern of substitution effects to guarantee the existence of competitive equilibrium.

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Linear Pricing Mechanisms without Convexity
Author(s):
Paul Milgrom, Stanford University
Mitchell Watt, Stanford University
Abstract:

Milgrom and Watt introduce two new linear pricing mechanisms that lead to feasible, budget-balanced and approximately efficient outcomes even when preferences or production sets are not convex and Walrasian equilibrium does not exist. One mechanism permits different prices for buyers and sellers; the other uses a single price vector but permits some agents to be rationed. In these mechanisms, both the inefficiency-to-value ratio and the maximum benefit any single agent can gain from false reporting tend quickly to zero as the numbers of producers and consumers increase.

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Designing a Combinatorial Financial Options Market
Author(s):
Xintong Wang, Harvard University
David Pennock, Microsoft Research
Nikhil Devanur, Amazon
David M. Rothschild, Microsoft Research
Biaoshuai Tao, Shanghai Jiao Tong University
Michael Wellman, University of Michigan
Abstract:

Financial options are contracts that specify the right to buy or sell an underlying asset at a strike price by an expiration date. Standard exchanges offer options of predetermined strike values and trade options of different strikes independently, even for those written on the same underlying asset. Such independent market design can introduce arbitrage opportunities and lead to the thin market problem. The paper first proposes a mechanism that consolidates and matches orders on standard options related to the same underlying asset, while providing agents the flexibility to specify any custom strike value. The mechanism generalizes the classic double auction, runs in time polynomial to the number of orders, and poses no risk to the exchange, regardless of the value of the underlying asset at expiration. Empirical analysis on real-market options data shows that the mechanism can find new matches for options of different strike prices and reduce bid-ask spreads. Extending standard options written on a single asset, Wang, Pennock, Devanur, Rothschild, Tao, and Wellman propose and define a new derivative instrument -- combinatorial financial options that offer contract holders the right to buy or sell any linear combination of multiple underlying assets. Wang, Pennock, Devanur, Rothschild, Tao, and Wellman generalize their single-asset mechanism to match options written on different combinations of assets, and prove that optimal clearing of combinatorial financial options is coNP-hard. To facilitate market operations, Wang, Pennock, Devanur, Rothschild, Tao, and Wellman propose an algorithm that finds the exact optimal match through iterative constraint generation, and evaluate its performance on synthetically generated combinatorial options markets of different scales. As option prices reveal the market's collective belief of an underlying asset's future value, a combinatorial options market enables the expression of aggregate belief about future correlations among assets.

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Price Discovery in Waiting Lists:
A Connection to Stochastic Gradient Descent
Author(s):
Itai Ashlagi, Stanford University
Jacob D. Leshno, University of Chicago
Amin Saberi, Stanford University
Pengyu Qian, Purdue University
Abstract:

Waiting lists allocate items by offering agents a choice among items with associated waiting times. These waiting times serve as prices that are formed by the stochastic arrivals and departures of agents. Ashlagi, Leshno, Saberi, and Qian study the allocative efficiency under such dynamically adjusting prices by drawing a connection between this price adjustment process and the stochastic gradient descent optimization algorithm. Ashlagi, Leshno, Saberi, and Qian show that the loss due to price fluctuations is bounded by the granularity of price changes. Additional conditions allow us to identify markets where the loss is close to the bound or exponentially small. Their results show that a simple price adjustment heuristic can perform well, but may be slow to adjust to changes in demand because of a trade-off between the speed of adaptation and loss from price fluctuations.

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Market Design for Distributional Objectives in (Re) assignment: An Application to Improve the Distribution of Teachers in Schools
Author(s):
Julien Combe, CREST - Ecole polytechnique
Umut M. Dur, North Carolina State University
Olivier Tercieux, Paris School of Economics
Camille Terrier, University of Lausanne
M. Utku Ünver, Boston College
Abstract:

Centralized (re)assignment of workers to jobs is increasingly common both in the public sector (for teachers, doctors, police officers, judicial clerks, administrators,...) and in the private sector (for company-wide job rotations). Many of these markets suffer from distributional concerns (e.g., experienced teachers are not equally distributed across schools). This raises a new challenge: How to leverage key features of centralized (re)assignment systems--such as mechanism and priorities--to reach distributional objectives? Combe, Dur, Tercieux, Terrier, and Ünver propose a model and two new (re)assignment mechanisms that improve both individual welfare and distributional welfare measures over an initial allocation. While both mechanisms are strategy-proof, one achieves two-sided Pareto efficiency (and in particular worker optimality) and the other achieves a novel stability property. Combe, Dur, Tercieux, Terrier, and Ünver then quantify the performance of their mechanisms in a real-life application: teacher reassignment where the unequal distribution of experienced teachers in schools is a widespread concern around the world. Public schools in disadvantaged districts often have fewer experienced teachers than those in more privileged districts. After estimating teacher preferences using French data, Combe, Dur, Tercieux, Terrier, and Ünver show that their efficient mechanism successfully reduces the teacher experience gap compared to other mechanisms and to the current French mechanism.

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Mechanism Design meets Priority Design: Redesigning the US Army's Branching Process
Author(s):
Kyle Greenberg, United States Military Academy at West Point
Parag A. Pathak, Massachusetts Institute of Technology and NBER
Tayfun Sönmez, Boston College
Abstract:

Army cadets obtain occupations through a centralized process. Three objectives - increasing retention, aligning talent, and enhancing trust - have guided reforms to this process since 2006. West Point's mechanism for the Class of 2020 exacerbated challenges implementing Army policy aims. Greenberg, Pathak, and Sönmez formulate these desiderata as axioms and study their implications theoretically and with administrative data. Greenberg, Pathak, and Sönmez show that the Army's objectives not only determine an allocation mechanism, but also a specific priority policy, a uniqueness result that integrates mechanism and priority design. These results led to a re-design of the mechanism, now adopted at both West Point and ROTC.

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This paper was distributed as Working Paper 28911, where an updated version may be available.

Decentralizing Centralized Matching Markets: Implications from Early Offers in University Admissions
Author(s):
Julien Grenet, Paris School of Economics
YingHua He, Rice University
Dorothea Kübler, WZB
Abstract:

The matching literature often recommends market centralization under the assumption that agents know their own preferences and that their preferences are fixed. Grenet, He, and Kübler find counterevidence to this assumption in a quasi-experiment. In Germany's university admissions, a clearinghouse implements the early stages of the Gale-Shapley algorithm in real time. Grenet, He, and Kübler show that early offers made in his decentralized phase, although not more desirable, are accepted more often than later ones. These results, together with survey evidence and a theoretical model, are consistent with students' costly learning about universities. Grenet, He, and Kübler propose a hybrid mechanism to combine the advantages of decentralization and centralization.

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Participants

Yeganeh Alimohammadi, Stanford University
Nick Arnosti, University of Minnesota
Lawrence Ausubel, University of Maryland
Elizabeth C. Baldwin, University of Oxford
Oleg V. Baranov, University of Colorado, Boulder
Martin Bichler, Technical University of Munich
Emmanuele Bobbio, Bank of Italy
Simon M. Brandkamp, University of Cologne
Gianluca Brero, Harvard University
Ozan Candogan, University of Chicago
Francisco Castro, University of California, Los Angeles
Ettore Damiano, University of Toronto
David Delacretaz, University of Oxford
Nikhil Devanur, Amazon
Omer Edhan, University of Manchester
Aytek Erdil, University of Cambridge
Ron Harstad, University of Missouri
Ravi Jagadeesan, Stanford University
Yash Kanoria, Columbia University
Onur Kesten, University of Sydney
Bettina Klaus, University of Lausanne
Flip Klijn, Institute for Economic Analysis
Dorothea Kübler, WZB
Jeongmin (Mina) Lee, Washington University in St. Louis
Jacob D. Leshno, University of Chicago
Fei Li, University of North Carolina Chapel Hill
Hongyao Ma, Columbia University
Mohammad Mahdian, Google Research
David Malec, University of Maryland
Antonio Miralles, Universita' degli Studi di Messina
Herve Moulin, University of Glasgow
Noam Nisan, Hebrew University of Jerusalem
Mariann Ollar, University of Edinburgh
David Pennock, Microsoft Research
Marek Pycia, University of Zurich
Pengyu Qian, Purdue University
Daniel Quint, University of Wisconsin
Marzena Rostek, University of Wisconsin- Madison
David M. Rothschild, Microsoft Research
Maher Said, New York University
James Schummer, Northwestern University
Sven Seuken, University of Zurich
Kentaro Tomoeda, University of Technology Sydney
Rakesh Vohra, University of Pennsylvania
Xintong Wang, Harvard University
Mitchell Watt, Stanford University
Alexander Westkamp, University of Cologne
Robert Wilson, Stanford University
Chiwei Yan, University of Washington
Ji Hee Yoon, University College London

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