Market Design

October 28-29, 2016
Michael Ostrovsky of Stanford University and Parag A. Pathak of MIT, Organizers

Darrell Duffie, Stanford University and NBER, and Haoxiang Zhu, MIT and NBER

Size Discovery (NBER Working Paper No. 21696)

Size-discovery trade mechanisms allow large quantities of an asset to be exchanged at a price that does not respond to price pressure. Primary examples include "workup" in Treasury markets, "matching sessions" in corporate bond and CDS markets, and blocktrading "dark pools" in equity markets. By freezing the execution price and giving up on market-clearing, size-discovery mechanisms overcome concerns by large investors over their price impacts. Price-discovery mechanisms clear the market, but cause investors to internalize their price impacts, inducing costly delays in the reduction of position imbalances. Duffie and Zhu show how augmenting a price-discovery mechanism with a size-discovery mechanism improves allocative efficiency.

Ahmad Peivandi, Georgia State University

Participation and Unbiased Pricing in CDS Settlement Mechanisms

The centralized market for the settlement of credit default swaps (CDS), which governs more than $12 trillion's worth of outstanding CDS contracts, has been criticized for mispricing the defaulted bonds that underlie the contracts. Peivandi takes a mechanism design approach to the market for the settlement of CDS contracts and characterizes robust settlement mechanisms that deliver unbiased prices for the underlying assets. All robust settlement mechanisms are the payoff equivalent of a posted price mechanism. Because forced participation in the settlement mechanism is not possible, this approach requires the development of a new notion of the core of games of incomplete information. This new notion can be applied to mechanism design environments in which side trades are allowed or when joining the mechanism is a cooperative decision.

Laura Doval, Yale University

A Theory of Stability in Dynamic Matching Markets

Doval studies dynamic matching markets where matching opportunities arrive over time, and matching is one-to-one and irreversible. The proposed stability notion, dynamic stability, incorporates a backward induction notion to an otherwise cooperative model, which takes into account the time at which the arriving agents can form binding agreements. Dynamically stable matchings may fail to exist in two-sided economies (e.g., adoption markets), and in the allocation of objects with priorities (e.g., public housing). However, dynamically stable matchings always exist in one-sided economies (e.g., deceased-donor organ allocation). The non-existence result reveals a new form of unraveling in matching markets: agents wish to delay the time at which they are matched so as to improve their matching prospects. These findings rationalize why clearing houses in different markets adopt very different rules to deal with the event in which agents reject a current offer to wait for a better match. In particular, in two-sided markets and in the allocation of objects with priorities, to guarantee that efficiency is achieved, the central clearing house needs to restrict agents' option to wait for a better match.

Hugo Hopenhayn, University of California at Los Angeles and NBER, and Maryam Saeedi, Carnegie Mellon University

Bidding Dynamics in Auctions

Hopenhayn and Saeedi study biding dynamics where values and bidding opportunities follow an unrestricted joint Markov process, independent across agents. Bids cannot be retracted, as is frequently the case in auctions. The researchers' main methodological contribution is that they construct a mapping from this general stochastic process into a distribution of values that is independent of the type of auction considered. The equilibria of a static auction with this distribution of values is used to characterize the equilibria of the dynamic auction, making this general class very tractable. As a result of the option of future rebidding, early bids are shaded and under mild conditions increase toward the end of the auction. These results are consistent with repeated bidding and skewness of the time distribution of winning bids, two puzzling observations in dynamic auctions. As an application, the researchers estimate the model by matching moments from eBay auctions.

Christina Aperjis, Power Auctions LLC; Lawrence Ausubel, University of Maryland; Oleg Baranov, University of Colorado Boulder; and Thayer Morrill, North Carolina State University

Efficient Procurement Auctions with Increasing Returns

For procuring from sellers with decreasing returns, there are known efficient dynamic auction formats. In this paper, Baranov, Aperjis, Ausubel, and Morrill design an efficient dynamic procurement auction for the case where goods are homogeneous and bidders have increasing returns. Their motivating example is the procurement of vaccines, which often exhibit large fixed costs and small constant marginal costs. The auctioneer names a price and bidders report the interval of quantities that they are willing to sell at that price. The process repeats with successively lower prices, until the efficient outcome is discovered. The researchers demonstrate an equilibrium that is efficient and generates VCG prices.

Tibor Heumann, Princeton University

Ascending Auction with Multidimensional Signals

Heumann studies an ascending auction in which agents bid for an indivisible good and observe multidimensional Gaussian signals. He provides novel predictions of ascending auctions that arise only when agents observe multidimensional signals. The first novel prediction is that an ascending auction can have multiple symmetric equilibria. Each equilibria induces a different allocative efficiency and different profits for the seller. The second novel prediction is that, with multidimensional signals, public signals can be detrimental for profits (even in symmetric environments). In fact, a precise enough public signal can induce profits arbitrarily close to 0. Both of these novel predictions arise in a model with two-dimensional signals that combines a classic model of private values and a classic model of common values. Hence, the only difference between the model Heumann studies and the classic models of ascending auctions is the multidimensionality of the information structure. The equilibrium is solved using a two-step procedure. The first step is to project the signals into a one-dimensional equilibrium statistic. The second step is to solve for the equilibrium as if agents observed only the equilibrium statistic (and hence, as if agents observe one-dimensional signals). The equilibrium statistic can also be used to solve other trading mechanisms (e.g. supply function equilibria, generalized VCG mechanisms and other multi-unit auctions).

John Hatfield, University of Texas at Austin, and Scott Duke Kominers, Harvard University

Hidden Substitutes

In this paper, Hatfield and Kominers show that preferences exhibiting some forms of complementarity in fact have an underlying substitutable structure. In the setting of many-to one matching with contracts, they identify “hidden” substitutabilities in agents’ preferences; this makes stable and strategy-proof matching possible in new settings with complementarities, even though stable outcomes are not guaranteed, in general, when complementarities are present. These results give new insight into a range of market design settings, including the allocation of teachers to traineeships in Germany.

Gabriel Carroll and Ilya Segal, Stanford University

Robustly Optimal Auctions with Unknown Resale Opportunities

Carroll and Segal study robust revenue maximization by the designer of a single-object auction who has Bayesian beliefs about bidders' independent private values but is ignorant about post-auction resale opportunities (including possible leakage of private information). The researchers show the optimality of a "Vickrey auction with bidder specific reserve prices" proposed by Ausubel and Cramton (2004), which allocates the object efficiently provided that at least one of the bidders has bid above his reserve price. In this auction, truthful bidding and no resale is an ex post equilibrium for any individually rational resale procedure. The researchers show optimality of this auction for a "worst-case"resale procedure in which the highest-value bidder learns all other bidders'values and has full bargaining power. The proof involves construction of Lagrange multipliers on the incentive constraints representing non-local deviations in which a bidder underbids to lose and then purchases from the auction's winner.

Songzi Du, Simon Fraser University

Robust Mechanisms Under Common Valuation

Du studies robust mechanisms to sell a common-value good. Du assumea that the mechanism designer knows the prior distribution of the buyers' common value but is unsure of the buyers' information structure about the common value. The researcher uses linear programming duality to derive mechanisms that guarantee a good revenue among all information structures and all equilibria. The mechanism maximizes the revenue guarantee when there is one buyer. As the number of buyers tends to infinity, the revenue guarantee of the mechanism converges to the full surplus.

Shengwu Li, Stanford University

Obviously Strategy-Proof Mechanisms

What makes some strategy-proof mechanisms easier to understand than others? To address this question, Li proposes a new solution concept: A mechanism is obviously strategy-proof (OSP) if it has an equilibrium in obviously dominant strategies. This has a behavioral interpretation: A strategy is obviously dominant if and only if a cognitively limited agent can recognize it as weakly dominant. It also has a classical interpretation: A choice rule is OSP-implementable if and only if it can be carried out by a social planner under a particular regime of partial commitment. Li fully characterizes the set of OSP mechanisms in a canonical setting, with one-dimensional types and transfers. A laboratory experiment tests and corroborates the theory.

Marek Pycia, University of California at Los Angeles, and Peter Troyan, University of Virginia

Obvious Dominance and Random Priority

In environments without transfers, such as refugee resettlement, school choice, organ transplants, course allocation, and voting, Pycia and Troyan show that random priority is the unique mechanism that is obviously strategy-proof, Pareto efficient, and symmetric; hence providing an explanation for the popularity of this mechanism. The researchers also construct the full class of obviously strategy-proof mechanisms, and explain why some of them are more popular than others via a natural strengthening of obvious strategy-proofness.

Benjamin Roth, MIT, and Ran Shorrer, Pennsylvania State University

Making it Safe to Use Centralized Markets: Epsilon-Dominant Individual Rationality and Applications to Market Design

Roth and Shorrer take the view that centralizing a market is akin to designing a mechanism to which people may voluntarily sign away their decision rights. Volunteers send a message to the mechanism which can credibly act on their behalf but those who retain their decision rights act on their own accord in a decentralized manner. In this general setting the researchers ask when it is possible to guarantee agents will use a mechanism despite the voluntary nature of participation. Their first result is negative and derives from adverse selection concerns. Near any game with at least one pure strategy equilibrium the researchers prove there is another game in which no mechanism can eliminate the equilibrium of the original game.

Michal Feldman, Hebrew University of Jerusalem; Nicole Immorlica, Northwestern University; Brendan Lucier and Vasilis Syrgkanis, Microsoft Research; and Tim Roughgarden, Stanford University

Efficiency Guarantees in Large Markets

Feldman, Immorlica, Lucier, Roughgarden, and Syrgkanis present an analysis framework for bounding inefficiency in markets with many agents. The researchers use this framework to demonstrate that, in many markets, the efficiency in the large is much smaller than the worst-case bound. The researchers' framework also differentiates between markets with similar worst-case performance, such as simultaneous uniform-price auctions and greedy combinatorial auctions, thereby providing new insights about which markets are likely to perform well in realistic settings.

David Delacretaz, University of Melbourne; Scott Duke Kominers, Harvard University; and Alexander Teytelboym, University of Oxford

Refugee Resettlement

Paul Milgrom, Stanford University

Deferred Acceptance Auctions Without Substitutes

Tommy Andersson, Lund University, and Lars Ehlers, Université de Montréal

Assigning Refugees to Landlords in Sweden: Stable Maximum Matchings

The European refugee crisis began in 2015. In an attempt to reduce pressure on member states located at the external border of the European Union, the European Commission decided on a temporary European relocation scheme. However, several obstacles for successful integration remain and Andersson and Ehlers focus on one of these obstacles, namely the problem of finding housing for refugees once they have been relocated to a European Union membership state. In particular, the focus is restricted to the situation in Sweden during 2015–2016 and it is demonstrated that market design can play an important role in a partial solution to the problem. More specifically, because almost all accommodation options are exhausted in Sweden, the paper investigates a matching system, closely related to the system adopted by the European NGO "Refugees Welcome," and proposes an easy-to-implement algorithm that finds a stable maximum matching. Such matching guarantees that the maximum number of refugees are assigned to private landlords and that no refugee strictly prefers some landlord to their current match when, at the same time, that specific landlord strictly prefers that refugee to his current match.

NBER Videos

National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email:

Contact Us