Kellogg James Schummer

Research Page

Contact Information

James Schummer
MEDS, Kellogg School of Management
Northwestern University
Evanston, IL 60208–2009, USA

Phone: 847-491-5151
Fax:     847-467-1220
MEDS Dept.: 847-491-3603

Curriculum Vitae (pdf)

Work in Progress

  • “Influencing Waiting Lists.”
    • Download Waiting.pdf (version: May 2016).
    • Abstract: Scarce goods (donor organs, public housing, etc.) are often allocated through waiting lists, especially when monetary transfers are undesirable. Arriving objects are offered to priority-ordered agents who may defer the object to the next agent in line in order to wait for a better one. We consider the welfare implications of arbitrarily influencing such deferral decisions (by force, by “nudging,” etc.). When agents are patient, uninfluenced (equilibrium) behavior is Pareto-dominant; this conclusion strengthens as agents' risk-aversion increases. When risk-neutral agents are impatient, however, influence results in a welfare tradeoff between earlier and later agents in the queue. The results have implications for the “organ spoilage” problem in waiting lists for donor organs, where useful lower-quality organs spoil in the time that it takes to process the deferrals by agents early in the queue. Removing the right to defer such organs appears to solve the wastage problem by increasing utilization. But for some parameters (e.g. extremely high risk-aversion) such solutions could paradoxically lower the welfare of some agents it is intended to help. Fortunately the parameters that result in this phenomenon appear to be atypical in real world settings.
    • Featured in Kellogg Insight, Dec 2016.

  • “Revenue from Matching Platforms” (with Phillip Marx).
    • Manuscript is in preparation.
    • Abstract: We consider revenue maximization for one-to-one matching platforms. Heterogeneous agents from two sides of a market use the platform to form pairs, yielding non-transferable value. The platform charges a match-contingent fee to each of the two sides and commits to a matching mechanism. We particularly consider the implications of committing to stable mechanisms, under which it is known that agents on the “short” side of the market capture relatively more value than those on the long side, at least when preferences are independently drawn (Ashlagi et al., 2017). Despite this fact, we show that a platform does not want to price discriminate across the two sides of the market based on their relative sizes. Next we show that the stable platform”s expected revenue is well-approximated using an exact expression for revenue under a constrained serial dictatorship mechanism. The approximation shows that the platform”s “cost of imposing stability” vanishes in large markets. Finally we consider how correlation in agents” preferences affects our results, and further separates our one-to-one heterogeneous matching model from classic models of pricing in two-sided markets.

  • “Sequential Preference Revelation in Incomplete Information Settings” (with Rodrigo Velez).
    • Manuscript available very soon!
    • Abstract: Strategy-proof, direct revelation mechanisms provide an incentive for agents to truthfully report preferences in a simultaneous revelation game. When preferences are elicited sequentially, however, an agent's report leaks information about the distribution of preferences to agents who have yet to report. We show in a Bayesian example that sequential reporting mechanisms can create a situation in which an agent has a strict disincentive to report preferences truthfully, even when the underlying social choice function is strategy-proof and non-bossy. Notably, such examples do not exist under complete information (Marx and Swinkles, 1997 GEB). The example is also robust to forward induction requirements. Our main results then rule out such phenomena under generic “Cartesian support” assumptions. Under these assumptions, when the underlying social choice function is strategy-proof and non-bossy, agents obtain outcomes that are welfare-equivalent to truthful ones. in any sequential equilibrium of the sequential game. Furthermore we argue that, starting from any such equilibrium, an agent can switch to truthful behavior without affecting this conclusion; this adds robustness to the notion that that planners can safely recommend truth-telling behavior in such mechanisms.

  • “The Role of Characterizations in Market Design” (with Shigehiro Serizawa).
    • This is a book chapter for an upcoming compilation of articles on The Future of Market Design. Details will be forthcoming.

  • “Voting with Money” (with Rakesh V. Vohra).
    • This is some old work. Preliminary results are available upon request.

Published Papers

  • “Incentives in Landing Slot Problems” (with Azar Abizada).
    • Journal of Economic Theory (2017) 170, 29–55.
    • View at
    • Online appendix.
    • Working paper version (Jan. 2017, includes online appendix).
    • Abstract: During weather-induced airport congestion, landing slots are reassigned based on flights’ feasible arrival times and cancelations. We consider the airlines’ incentives to report such information and to execute cancelations, creating positive spillovers for other flights. We show that such incentives conflict with Pareto-efficiency, partially justifying the FAA’s non-solicitation of delay costs. We provide mechanisms that, unlike the FAA’s current mechanism, satisfy our incentive properties to the greatest extent possible given the FAA’s own design constraints. Our mechanisms supplement Deferred Acceptance with a “self-optimization” step accounting for each airline's granted right to control its assigned portion of the landing schedule.

  • “Assignment of Arrival Slots” (with Rakesh V. Vohra).
    • American Economic Journal: Microeconomics (2013) 5:2, 164–185.
    • Download: slots-AEJM.pdf.
    • View at AEAweb.
    • Abstract: During inclement weather, the FAA reassigns vacated airport landing slots within a certain time interval. We consider this mechanism design problem when a pre-existing landing schedule defines certain property rights for the airlines. This particular problem has been analyzed from an operational perspective, where the motivation for the FAA’s current mechanism—the Compression Algorithm—rests on incentives and property rights. This paper appears to be the first to rigorously formalize these two notions for this application. Our results show that the Compression Algorithm satisfies a certain form of incentive compatibility but fails a certain interpretation of property rights. We then provide an example of a mechanism that satisfies both conditions; proofs of this use a different but related matching model. Neither mechanism, however, would always gives airlines the incentive to vacate unusable landing slots if airlines can prevent the slot’s inclusion in either of these trading algorithms.
    • Featured in Kellogg Insight, May 2012.

  • “An Ascending Vickrey Auction for Selling Bases of a Matroid” (with Sushil Bikhchandani, Sven de Vries, and Rakesh V. Vohra).
    • Operations Research (2011) 59:2, 400–413.
    • Download: Matroid-OR2011.pdf. Also see the e-Companion.
    • View at Informs Online.
    • Abstract: Consider selling bundles of indivisible goods to buyers with concave utilities that are additively separable in money and goods. We propose an ascending auction for the case when the seller is constrained to sell bundles whose elements form a basis of a matroid. It extends easily to polymatroids. Applications include scheduling (Demange, Gale, and Sotomayor, 1986), allocation of homogeneous goods (Ausubel, 2004), and spatially distributed markets (Babaioff, Nisan, and Pavlov, 2004). Our ascending auction induces buyers to bid truthfully, and returns the economically efficient basis. Unlike other ascending auctions for this environment, ours runs in pseudo-polynomial or polynomial time. Furthermore we prove the impossibility of an ascending auction for nonmatroidal independence set-systems.

  • “Credible Deviations from Signaling Equilibria” (with Péter Esö).
    • International Journal of Game Theory (2009) 38:3, 411–430.
    • View at SpringerLink.
    • Download final version: CDC.pdf.
    • Our final “working paper version” contains more information plus extra discussion about refinements that does not appear in the published version. For those interested in a deeper reading on this topic, within the context of the refinements literature, I recommend reading this pre-editorialized version. In the past we have received positive comments about the helpfulness of this version’s extra discussion.
    • The supplemental appendix proves some claims and provides more examples.
    • Abstract: In Sender-Receiver games with costly signaling, some equilibria are vulnerable to deviations which could be “unambiguously” interpreted by the Receiver as coming from a unique set of possible Sender-types. The vulnerability occurs when the types in this set are the ones who gain from the deviation, regardless of the posterior beliefs the Receiver forms over that set. We formalize this idea and use it to characterize a unique equilibrium outcome in two classes of games. First, in monotonic signaling games, only the Riley outcome is immune to this sort of deviation. Our result therefore provides a plausible story behind the selection made by Cho and Kreps’ (1987) D1 criterion on this class of games. Second we examine a version of Crawford and Sobel’s (1982) model but with costly signaling and finite type sets, where standard refinements have no effect. We show that only a Riley-like separating equilibrium is immune to these deviations.

  • “Mechanism Design without Money” (with Rakesh V. Vohra).
    • This is a chapter in the book Algorithmic Game Theory (Nisan, Roughgarden, Tardos, Vazirani, eds.), Cambridge University Press, 2007.
    • Update: Want a free PDF of the entire book? Go to the publisher's catalog page and click on the Resources button half way down. Enjoy!
    • Abstract: Despite impossibility results on general domains, there are some classes of situations in which there exist interesting dominant-strategy mechanisms. While some of these situations (and the resulting mechanisms) involve the transfer of money, we examine some that do not. Specifically, we analyze: problems where agents have single-peaked preferences over a 1-dimensional public policy space; problems where agents can trade/consume a single, indivisible private good; and problems where agents must match with each other.

  • “On Ascending Vickrey Auctions for Heterogeneous Objects” (with Sven de Vries and Rakesh V. Vohra).
    • Journal of Economic Theory (2007) 132:1, 95–118.
    • View at ScienceDirect.
    • Download the prepublication version.
    • Abstract: We construct an ascending auction for heterogeneous objects by applying a primal-dual algorithm to a linear program that represents the efficient-allocation problem for this setting. The auction assigns personalized prices to bundles, and asks bidders to report their preferred bundles in each round. A bidder’s prices are increased when he belongs to a “minimally undersupplied” set of bidders. We consider this concept to be the natural generalization of an “overdemanded” set of objects, introduced by Demange et al. (1986) for the one-to-one assignment problem. Under a submodularity condition, the auction implements the Vickrey–Clarke–Groves outcome; we show that this type of condition is somewhat necessary to do so. When classifying the ascending-auction literature in terms of their underlying algorithms, our auction fills a gap in that literature. We relate our results to the recent work of Ausubel and Milgrom (2002).
    • Try out a javascript applet which executes the auction algorithm derived in the paper!

  • “Almost-dominant Strategy Implementation”
    • Games and Economic Behavior (2004) 48, 154–170.
    • View at ScienceDirect.
    • Download the prepublication version.
    • Abstract: We examine the consequences of relaxing strategy-proofness (a form of dominant strategy implementation) by allowing instances of “small” gains from manipulation. In 2-agent exchange economies, this relaxation is shown to have a discontinuous effect on the range of efficient rules. This demonstrates a type of non-robustness in previous impossibility results. When small gains are measured with respect to a single good, we show that a particular rule is, unambiguously, most equitable among all efficient rules satisfying the relaxed condition.

  • “Bribing and Signaling in Second-price Auctions” (with Péter Esö)
    • Games and Economic Behavior (2004) 47, 299–324.
    • View at ScienceDirect.
    • Download the prepublication version.
    • The Working Paper version (Oct. 2002) contains related results.
    • We have some unpublished supplemental notes on variations of the model in this paper.
    • Abstract: We examine whether a two-bidder, second-price auction for a single good (with private, independent values) is immune to a simple form of collusion, where one bidder may bribe the other to commit to stay away from the auction (i.e. submit a bid of zero). In either of two cases—where the potential bribe is fixed or allowed to vary—the only robust equilibria involve bribing. In the fixed-bribe case, there is a unique such equilibrium. In the variable bribes case, all robust equilibria involve low briber-types revealing themselves through the amount they offer, while all high types offer the same bribe; only one such equilibrium is continuous. Bribing in all cases causes inefficiency.

  • “Auctions for Procuring Options” (with Rakesh V. Vohra)
    • Operations Research (2003) 51, 41–51.
    • View at INFORMS.
    • Abstract: We examine the mechanism design problem for a single buyer to procure purchase-options for a homogeneous good when that buyer is required to satisfy an unknown future demand. Suppliers have 2-dimensional types in the form of commitment costs and production costs. The efficient schedule of options depends on the distribution of demand. To implement an efficient outcome, we introduce a class of mechanisms which are essentially pivotal mechanisms (Vickrey–Clarke–Groves) with respect to the expected costs of the suppliers. We show that the computational task of running such mechanisms is not burdensome. Our discussion uses electricity markets as an example.

  • “Linear Programming and Vickrey Auctions” (with Sushil Bikhchandani, Sven de Vries, and Rakesh V. Vohra)
    • In Mathematics of the Internet: E-auction and Markets, an IMA Volume in Mathematics and its Applications, Dietrich and Vohra, ed., Springer, 2002.
    • Abstract: The Vickrey sealed bid auction occupies a central place in auction theory because of its efficiency and incentive properties. Implementing the auction requires the auctioneer to solve n+1 optimization problems, where n is the number of bidders. In this paper we survey various environments (some old and some new) where the payments bidders make under the Vickrey auction correspond to dual variables in certain linear programs. Thus, in these environments, at most two optimization problems must be solved to determine the Vickrey outcome. Furthermore, primal-dual algorithms for some of these linear programs suggest ascending auctions that implement the Vickrey outcome.

  • “Strategy-proof Location on a Network” (with Rakesh V. Vohra)
    • Journal of Economic Theory (2002) 104, 405–428.
    • View at ScienceDirect.
    • Download the prepublication version.
    • Abstract: We consider rules that choose a location on a graph (e.g. a road network) based on agents’ single-peaked preferences. First, we characterize the class of strategy-proof, onto rules when the graph is a tree. Such a rule is based on a collection of generalized median voter rules (Moulin, 1980) satisfying a consistency condition. Second, we characterize such rules for graphs containing cycles. We show that while such a rule is not necessarily dictatorial, the existence of a cycle grants some agent an amount of decisive power, unlike the case of trees. Rules for this case can be described in terms of a subclass of such rules for trees. Journal of Economic Literature Classification Numbers: C72, D78.

  • “Constrained Egalitarianism: A New Solution for Claims Problems” (with Y. Chun and W. Thomson)
    • Seoul Journal of Economics (2001) 14, 269–298.
    • Download.
    • Abstract: We propose a new rule to solve claims problems (O’Neill 1982) and show that this rule is best in achieving certain objectives of equality. We present three theorems describing it as the most “egalitarian” among all rules satisfying two minor requirements, “estate-monotonicity” and “the midpoint property.” We refer to it as the “constrained egalitarian” rule. We show that it is consistent and give a parametric representation of it. We also define several other rules and relate all of them to the rules that have been most commonly discussed in the literature. Journal of Economic Literature Classification Numbers: D63, D70.

  • “Manipulation through Bribes”
    • Journal of Economic Theory (2000) 91, 180–198.
    • This paper can be downloaded.
    • View at ScienceDirect.
    • Abstract: We consider allocation rules that choose both an outcome and transfers, based on the agents’ reported valuations of the outcomes. Under a given allocation rule, a bribing situation exists when agent j could pay agent i to misreport his valuations, resulting in a net gain to both agents. A rule is bribe-proof if such opportunities never arise. The central result is that when a bribe-proof rule is used, the resulting payoff to any one agent is a continuous function of any other agent’s reported valuations. We then show that on connected domains of valuation functions, if either the set of outcomes is finite or each agent’s set of admissible valuations is smoothly connected, then an agent’s payoff is a constant function of other agents’ reported valuations. Finally, under the additional assumption of a standard domain-richness condition, we show that a bribe-proof rule must be a constant function. The results apply to a very broad class of economies.

  • “Eliciting Preferences to Assign Positions and Compensation”
    • Games and Economic Behavior (2000) 30, 293–318.
    • View at ScienceDirect.
    • Abstract: We describe strategy-proof rules for economies where an agent is assigned a position (e.g., a job) plus some of a divisible good. For the 2-agent–2-position case we derive a robust characterization. For the multi-agent-position case, many “arbitrary” such rules exist, so we consider additional requirements. By also requiring coalitional strategy-proofness or nonbossiness, the range of a solution is restricted to the point that such rules are not more complex than those for the Shapley-Scarf housing model (no divisible good). Third, we show that essentially only constant solutions are immune to manipulations involving “bribes.” Finally, we demonstrate a conflict between efficiency and strategy-proofness. The results extend to models (without externalities) in which agents share positions

  • “Strategy-proofness versus Efficiency for Small Domains of Preferences over Public Goods”
    • Economic Theory (1999) 13, 709–722.
    • See this paper at SpringerLink.
    • Abstract: It has long been known that when agents have von Neumann–Morgenstern preferences over lotteries, there is an incompatibility between strategy-proofness and efficiency (Gibbard (1973), Hylland (1980))—a solution satisfying those properties must be dictatorial. We strengthen this result by showing that it follows from the same incompatibility on a series of much smaller domains of preferences.
      Specifically, we first show the incompatibility to hold on our smallest domain, in which two agents are restricted to have linear preferences over one private good and one public good produced from the private good (Kolm triangle economies). This result then implies the same incompatibility on increasingly larger domains of preferences, ending finally with the class of von Neumann–Morgenstern preferences over lotteries.

  • “Strategy-proofness versus Efficiency on Restricted Domains of Exchange Economies”
    • Social Choice and Welfare (1997) 14, 47–56.
    • See this paper at SpringerLink.
    • Abstract: Strategy-proofness has been shown to be a strong property, particularly on large domains of preferences. We therefore examine the existence of strategy-proof and efficient solutions on restricted, 2-person domains of exchange economies. On the class of 2-person exchange economies in which agents have homothetic, strictly convex preferences we show, as Zhou (1991) did for a larger domain, that such a solution is necessarily dictatorial. As this proof requires preferences exhibiting high degrees of complementarity, our search continues to a class of linear preferences. Even on this “small” domain, the same negative result holds. These two results are extended to many superdomains, including Zhou’s.

  • “Two Derivations of the Uniform Rule and an Application to Bankruptcy” (with William Thomson)
    • Economics Letters (1997) 55, 333–337.
    • View at ScienceDirect.
    • Abstract: We consider the problem of allocating a single infinitely divisible commodity to agents with single-peaked preferences, and establish two properties of the rule that has played the central role in the analysis of this problem, the uniform rule. Among the efficient allocations, it selects (1) the one at which the difference between the largest amount received by any agent and the smallest such amount is minimal, and (2) the one at which the variance of the amounts received by all the agents is minimal. We also show that an important solution for bankruptcy problems, the constrained equal-award solution, can be characterized by analogous minimization exercises, subject to different constraints.

Unpublished Manuscripts

  • “A Pedagogical Example of Non-concavifiable Preferences”
    (version: March 1998)
  • Dissertation: “Strategy-proof Allocation for Restricted Economic Domains”
    (My Ph.D. dissertation, completed at the University of Rochester in 1997, under the supervision of William Thomson.)

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