James Schummer

Research Page

Contact Information

Curriculum Vitae (pdf)

Current Work

• "Surplus Sharing with several Projects" (with François Maniquet).
  • This is work in progress.
  
  
• "Assignment of Arrival Slots" (with Rakesh V. Vohra).
  • This is work in progress. We will be presenting our preliminary results at various upcoming conferences.
  
  
• "Voting with Money" (with Rakesh V. Vohra).
  • This is work in progress.
  • (July 2009) A preliminary version is available upon request. Hopefully it will be good enough to post soon.
  
  
• "An Ascending Vickrey Auction for Selling Bases of a Matroid" (with Sushil Bikhchandani, Sven de Vries, and Rakesh V. Vohra). (version: Aug 2008).
  • Download: jvick.pdf
  • 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.
  • This is a substantially revised version of CMS–EMS Discussion Paper 1368, which in turn is related to our published book article Linear Programming and Vickrey Auctions (2002).
  
  

Published Papers

• "Credible Deviations from Signaling Equilibria" (with Péter Esö).
  • International Journal of Game Theory (2009) 48:3, 411–430.
  • View at SpringerLink.
  • Download final version: CDC.pdf.
  • Our final “working paper version” contains more information, plus extra discussion about refinements that will 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 version. In the past we have received positive comments about 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.
  • 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.
  • Contact me for a copy.
  • 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)
  • Postscript: nonconc.ps
  • Adobe Acrobat: nonconc.pdf
• 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.)
  • Postscript: diss.ps
  • Postscript (gzipped): diss.ps.gz
  • Adobe Acrobat: diss.pdf

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