James Schummer

Bikhchandani, Sushil, Sven de Vries, James Schummer and Rakesh Vohra. 2011. An Ascending Vickrey Auction for Selling Bases of a Matroid. Operations Research. 59(2): 400-413.

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. [Extended abstract published as Bikhchandani, Sushil, Sven de Vries, James Schummer, and Rakesh V. Vohra (2008). Ascending auctions for integral (poly)matroids with concave nondecreasing separable values. In SODA 08: Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, pages 864-873.]

Eso, Peter and James Schummer. 2004. Bribing and signaling in second price auctions. Games and Economic Behavior. 47(2): 299-324.

We examine a specific form of collusive behavior in a 2-bidder, second-price auction (with independent private values). One bidder may bribe the other to commit to stay away from the auction (i.e., submit a bid of zero). First, we consider the situation where only a bribe of a fixed size may be offered. We show that there exist only two equilibria: one where bribing occurs with positive probability, and one where bribing does not occur. We show that an intuitive refinement of out-of-equilibrium beliefs rules out the no-bribe equilibrium. Second, we consider the case in which bribes of any size may be offered. We show that there is a unique equilibrium in continuous and weakly monotonic bribing strategies. In both setups (fixed or variable bribes) the bribing equilibrium leads to inefficient allocation of the good with positive probability.

Schummer, James and Rakesh Vohra. 2002. Strategy-Proof Location on a Network. Journal of Economic Theory. 104(2): 405-428.

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.

Schummer, James. 2000. Eliciting Preferences to Assign Positions and Compensation. Games and Economic Behavior. 30(2): 293-318.

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.

Bikhchandani, Sushil, Sven de Vries, James Schummer and Rakesh Vohra. 2011. An Ascending Vickrey Auction for Selling Bases of a Matroid. Operations Research. 59(2): 400-413.

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. [Extended abstract published as Bikhchandani, Sushil, Sven de Vries, James Schummer, and Rakesh V. Vohra (2008). Ascending auctions for integral (poly)matroids with concave nondecreasing separable values. In SODA 08: Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, pages 864-873.]

Eso, Peter and James Schummer. 2004. Bribing and signaling in second price auctions. Games and Economic Behavior. 47(2): 299-324.

We examine a specific form of collusive behavior in a 2-bidder, second-price auction (with independent private values). One bidder may bribe the other to commit to stay away from the auction (i.e., submit a bid of zero). First, we consider the situation where only a bribe of a fixed size may be offered. We show that there exist only two equilibria: one where bribing occurs with positive probability, and one where bribing does not occur. We show that an intuitive refinement of out-of-equilibrium beliefs rules out the no-bribe equilibrium. Second, we consider the case in which bribes of any size may be offered. We show that there is a unique equilibrium in continuous and weakly monotonic bribing strategies. In both setups (fixed or variable bribes) the bribing equilibrium leads to inefficient allocation of the good with positive probability.

Schummer, James and Rakesh Vohra. 2002. Strategy-Proof Location on a Network. Journal of Economic Theory. 104(2): 405-428.

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.

Schummer, James. 2000. Eliciting Preferences to Assign Positions and Compensation. Games and Economic Behavior. 30(2): 293-318.

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.