Market Design Working Group

October 8 and 9, 2010
Susan Athey and Parag Pathak of NBER and MIT, Organizers

Dirk Bergemann and Johannes Horner, Yale University
Should Auctions Be Transparent?

Bergemann and Horner investigate the role of market transparency in repeated first-price auctions. They consider a setting with private and independent values across bidders. The values are assumed to be perfectly persistent over time. They analyze the first-price auction under three distinct disclosure regimes regarding the bid and award history. Of particular interest is the minimal disclosure regime, in which each bidder only learns privately at the end of each round whether he won or lost the auction. In equilibrium, the winner of the initial auction lowers his bids over time, while losers keep their bids constant, in anticipation of the winner's lower future bids. This equilibrium is efficient, and all information eventually is revealed. Importantly, this disclosure regime does not give rise to pooling equilibria. The authors contrast the minimal disclosure setting with the case in which all bids are public, and the case in which only the winner's bids are public. In these settings, an inefficient pooling equilibrium with low revenues always exists with a sufficiently large number of bidders.

Simon Board, University of California, Los Angeles, and Andrzej Skrzypacz, Stanford University
Optimal Dynamic Auctions for Durable Goods: Posted Prices and Fire Sales

Board and Skrzypacz consider a seller who wishes to sell K goods by time T. Potential buyers enter IID over time and are patient. At any point in time, profit is maximized by awarding the good to the agent with the highest valuation exceeding a cutoff. These cutoffs are characterized by a one-period-look-ahead rule and are deterministic, depending only on the number of units and time remaining. The cutoffs decrease over time and in the inventory size, with the hazard rate of sales increasing as the deadline approaches. In the continuous time limit, the optimal allocation can be implemented by posted-prices with an auction at time T. Unlike the cutoffs, the prices depend on the history of past sales.

Mallesh Pai, University of Pennsylvania, and Rakesh Vohra, Northwestern University
Optimal Auctions with Financially Constrained Bidders

Pai and Vohra consider an environment where ex-ante symmetric potential buyers of an indivisible good have liquidity constraints, that is. they cannot pay more than their "budget" regardless of their valuation. A buyer's valuation for the good and her budget are her private information. The authors derive the symmetric constrained-efficient and revenue maximizing auctions for this setting. They show how to implement these via a standard auction (all pay) with a modified winning rule. In general, the optimal auction requires "pooling" both at the top and in the middle despite the maintained assumption of a monotonic hazard rate. Further, the auctioneer will never find it desirable in terms of revenue or social welfare to subsidize bidders with low budgets.

Lawrence Ausubel and Oleg V. Baranov, University of Maryland
Core-Selecting Auctions with Incomplete Information

Ausubel and Baranov consider a simple incomplete-information model with two goods, two "local" bidders, and one "global bidder". They examine a parametric family of distributions in which, at one extreme, the local bidders' valuations are independent and, at the other extreme, the local bidders' valuations are perfectly correlated. They perform a full equilibrium analysis for four different core-selecting auction formats. For the case of independent, uniformly-distributed valuations, they find that the VCG mechanism obtains 9 percent higher revenues and realizes 15 percent greater efficiency than the best core-selecting auction that they analyze. However, the comparison changes markedly when they introduce positive correlations in the local bidders' valuations. In particular, at the opposite extreme of perfect correlation, they find that the proxy auction obtains 33 percent higher revenues and realizes the same efficiency as the VCG mechanism. Moreover, it seems appropriate to posit that substantial correlations in bidders' valuations would be present in important applications such as spectrum auctions. Thus,they conclude that there may be good reasons for policymakers to select a core-selecting auction rather than a VCG mechanism. In the course of the analysis, rhey obtain closed-form solutions for the core-selecting pricing rules that they study. This enables them also to obtain revenue and efficiency rankings among the various rules. These rankings appear to be robust for the parameters of our model. The results may also provide useful guidance for policymakers.

Sven Seuken and David Parkes, Harvard University, and Denis Charles, Max Chickering, Mary Czerwinski, Kamal Jain, Sidd Puri, and Desney Tan, Microsoft Research
Hidden Market Design: A Peer-to-Peer Backup Market

Seuken, Parkes, Charles, Chickering, Czerwinski, Puri, and Jain take the problem of a market-based P2P backup application and carry it through market design, to implementation, to theoretical and experimental analysis. They introduce the "Hidden Market Design" paradigm, and use the P2P backup market as an illustrative example. The main idea of hidden markets is to hide the complexities of a market from the user to make the interaction as seamless as possible. They first describe the design of the P2P resource exchange market and the "hidden market" user interface they developed. Next they prove theorems on equilibrium existence and uniqueness. Third, they prove an impossibility result regarding the limited controllability of the equilibrium and show how to address this. Fourth, they present a price update algorithm that uses daily supply and demand information to move prices towards the equilibrium and they provide a theoretical convergence analysis. Finally, they present the results of a formative usability study of the new market user interface they developed. The market design is implemented as part of a Microsoft research project and an alpha version of the software has been tested successfully.

Gary E. Bolton, Penn State University; Ben Greiner, University of New South Wales; and Axel Ockenfels, University of Cologne
Engineering Trust: Reciprocity in the Production of Reputation Information

Bolton, Greiner, and Ockenfels note that reciprocal feedback distorts the production and content of reputation information, hampering trust and trade efficiency. Data from eBay and other sources combined with laboratory data provide a robust picture of how reciprocity can be guided by changes in the way feedback information flows through the system, leading to more accurate reputation information, more trust and more efficient trade.

Soohyung Lee, University of Maryland; Muriel Niederle, Stanford University and NBER, and Hye-Rim Kim and Woo-Keum Kim, Korea Marriage Culture Institute
Propose with a Rose? Signaling in Internet Dating Markets

In order to improve efficiency, several markets have mechanisms in place that allow agents to signal their preferences (for example, U.S. college application market and the economics junior market). However, empirically evaluating the impact of preference signaling proves difficult because of data limitations. Using a randomized field experiment, Lee, Niederle, Kim and Kim show that a signaling system can affect matching outcomes. In their study of online dating, participants can use a virtual "roses" to signal special interest in another participant. They find that attaching a rose to an offer increases the chance of acceptance, especially when the offer is made to medium attractive participants. Furthermore, participants endowed with more roses have a larger number of dates than their counterparts.

Yinghua He, Toulouse School of Economics
Gaming School Choice Mechanisms

Many public school choice programs use centralized mechanisms to match students with schools in the absence of market-clearing prices. Among them, the Boston mechanism is one of the most widely used. However, it is well-known that truth-telling may not be optimal under the Boston mechanism, which raises the concern that the mechanism may create a disadvantage to parents who do not strategize, or do not strategize well. Using a data set from Beijing, He investigates parents' strategic behaviors under the Boston mechanism and its welfare implications. School choice is modeled as a simultaneous game with parents' preferences being private information. The paper derives restrictions on parents' behavior under various assumptions on their information and sophistication, and the model is estimated using simulated maximum likelihood. The results suggest that parents' sophistication is heterogeneous; when parents have a greater incentive to behave strategically, they pay more attention to uncertainty and strategize better. There is no robust evidence that wealthier and/or more educated parents strategize better. If the Boston mechanism is replaced by the Deferred-Acceptance mechanism under which truth-telling is always optimal, the majority of the sophisticated parents who always play a best response are worse off, and almost none of them are better off. The reform benefits half of the naive parents who are always truth-telling under the Boston mechanism, while it also hurts about 20 percent of them.

Federico Echenique, SangMok Lee, and Matthew Shum, California Institute of Technology
Aggregate Matchings

Echenique, Lee, and Shum characterize the testable implications of stability for aggregate matchings. They consider data on matchings where individuals are aggregated, based on their observable characteristics, into types, and they know how many agents of each type match. They derive stability conditions for an aggregate matching and, based on these, provide a simple necessary and sufficient condition for an observed aggregate matching to be rationalizable (that is, such that preferences can be found so that the observed aggregate matching is stable). Subsequently, they use moment inequalities derived from the stability conditions to estimate bounds on agents' preferences using the cross-sectional marriage distributions across the U.S. states. They find that the rationalizing preferences of men and women are "antipodal", in that when men prefer younger women, women prefer younger men, and vice versa. This is consistent with the requirements of stability in non-transferable utility matching markets.

Fuhito Kojima, Stanford University; Parag Pathak; and Alvin E. Roth, Harvard University and NBER
Matching with Couples: Incentives and Stability in Large Markets

Accommodating couples has been a longstanding issue in the design of centralized labor market clearinghouses for doctors and psychologists, because couples view pairs of jobs as complements. A stable matching may not exist when couples are present. Kojima, Pathak, and Roth find conditions under which a stable matching exists with high probability in large markets. They present a mechanism that finds a stable matching with high probability, and which makes truth-telling by all participants an approximate equilibrium. They relate these theoretical results to the job market for psychologists, in which stable matchings exist for all years of the data, despite the presence of couples.

Itai Ashlagi, MIT and Alvin E. Roth, Harvard University and NBER
Participation (versus Free Riding) in Large Scale, Multi-Hospital Kidney Exchange

As multi-hospital kidney exchange consortia have been formed and a national exchange is contemplated, the set of "players" has grown from patients and their surgeons to include hospitals (or directors of transplant centers). Free riding has become possible, with hospitals having the option of participating in one or more kidney exchange networks but also of withholding some of their patient-donor pairs, and enrolling only those who are hardest to match, while conducting more easily arranged exchanges internally. This behavior has already started to be observed. Ashlagi and Roth extend and quantify some of the impossibility results for small markets that illustrate the tension between efficiency and incentives to participate fully, and explore how these extend to large markets, using the theory of random graphs. They show that the incentives to free ride by withholding pairs can be substantially ameliorated by the appropriate choice of mechanisms in large markets. It appears that achieving (close to) full participation will require some change in existing kidney exchange mechanisms when multiple hospitals are involved. However, the cost of making it individually rational for hospitals to participate is low in large markets, while the cost of failing to guarantee individually rational allocations could be large, in terms of lost transplants, if that causes hospitals to match their own internal pairs.

Michael Ostrovsky, Stanford University, and Michael Schwarz, Yahoo! Labs
Reserve Prices in Internet Advertising Auctions: A Field Experiment

Ostrovsky and Schwarz present the results of a large field experiment on setting reserve prices in auctions for online advertisements, guided by the theory of optimal auction design suitably adapted to the sponsored search setting. Consistent with the theory, following the introduction of new reserve prices revenues in these auctions have increased substantially.

Susan Athey; Dominic Coey, Stanford University; and Jonathan D. Levin, Stanford University and NBER
Subsidies and Set-Asides in Auctions

Set-asides and subsidies are used extensively in government procurement and natural resource sales. Athey, Coey, and Levin analyze these policies in an empirical model of Forest Service timber auctions. The model fits the data well both in-sample and out-of-sample. The estimates suggest that restricting entry to small businesses substantially reduces efficiency and revenue, although it does increase small business participation. A bidding subsidy for small business appears to be more effective at achieving distributional goals, increasing revenue and eliminating almost all of the efficiency loss. A small business bidding subsidy also increases the average profits of both large and small firms, compared to a set-aside policy. They explain these findings by connecting to the theory of optimal auction design.

Marek Pycia, University of California, Los Angeles, and Utku Unver, Boston College
Incentive Compatible Allocation and Exchange of Discrete Resources

Pycia and Unver study the allocation and exchange of discrete resources without monetary transfers. In market design literature, some problems that fall in this category are the house allocation problem with and without existing tenants, and the kidney exchange problem. The researchers introduce a new class of direct mechanisms that they call "trading cycles" with brokers and owners, and show that each mechanism in the class is group strategy-proof and Pareto efficient, and that each group strategy-proof and Pareto-efficient direct mechanism is in the class. As a corollary, they show that in pure exchange problems the well-known class of top trading cycles mechanisms contains all group strategy-proof, efficient, and individually rational mechanisms.