MANAGERIAL ECONOMICS & DECISION SCIENCES
Associate Professor of Managerial Economics & Decision Sciences
James Schummer joined Kellogg in 1997 after getting his PhD in Economics from the University of Rochester. His general areas of research include game theory and mechanism design.
Within those areas, Professor Schummer's work ranges from foundational models, yielding qualitative insights, to more practical models, yielding more direct advice. A central theme in his work is the question: Taking incentives into account, how can goods best be (re)allocated? Professor Schummer's past work on auctions is an example of this. He is currently working on voting models, and the allocation of airport landing slots to airlines.
Mechanism Design
Probability
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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. This concept generalizes the notion of ``overdemanded" sets of objects introduced by Demange, Gale, and Sotomayor (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).
Though some environments yield reasonable allocation rules that are implementable in dominant strategies (i.e., strategy-proof),a significant number yield impossibility results.On the other hand, while there are general possibility results for implementation in Nash or Bayesian equilibrium, these equilibrium concepts make strong assumptions about the players' knowledge. Since such assumptions may not be practical in various design scenarios, we formulate a solution concept built on one premise: Players who do not have much to gain by manipulating will not bother to do so. For an exchange economy model, we search for efficient rules that never provide players with large gains from manipulation. Though the rules we describe are inequitable, they are significantly more flexible than those that satisfy the stronger condition of strategy-proofness, even when the allowable gains from manipulation are made arbitrarily small. This demonstrates a type of non-robustness in previous impossibility results.
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.
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.
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.
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 rule that have been most commonly discussed in the literature.
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.
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.
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, [9]; Hylland, [12]) – 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.
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.]
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.
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.
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.
This course counts toward the following majors: Decision Sciences.
Provides frameworks for reasoning about decisions in uncertain environments. Case studies and experiments are used to motivate the importance of probabilistic reasoning to avoid the systematic biases that cloud managers' decision making. Formal probabilistic tools are introduced and their relevance to modern business issues is conveyed via cases, exercises, and class experiments. Some of the applications include: inventory management with uncertain demand, principal-agent models, herd behavior, selection bias, rare events, real options and risk. The course is self-contained, and should be of value to all students, including those with prior exposure to formal probability models.
Pricing Strategies (MECN-446-0)
This course counts toward the following majors: Analytical Consulting, Decision Sciences, Entrepreneurship & Innovation, Managerial Economics.
This course provides students with a comprehensive framework for formulating and implementing pricing strategies. Techniques that take account of the often imprecise and uncertain information to which management has access are useded to analyze the influence of costs, demand and competition on the pricing decision. Also discussed are research methods that can complement managerial judgment and the importance of maintaining consistency with other elements of the marketing mix. Special attention is devoted to the design of pricing schemes that segment the market, such as peak-load pricing, product bundling and nonlinear pricing. The course also studies vertical pricing problems (transfer pricing, pricing and distribution), legal constraints on pricing and industrial pricing (bidding). Actual pricing schemes in various industries and selected cases are used for illustrative and analytical purposes.
Prerequisites: MECN-430, MKTG-430.
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