MANAGERIAL ECONOMICS & DECISION SCIENCES
Frederic E. Nemmers Professor of Decision Sciences
Robert J. Weber is the Frederic E. Nemmers Distinguished Professor of Decision Sciences at the Kellogg School of Management, Northwestern University. Educated at Princeton and Cornell, he was a faculty member of the Cowles Foundation for Research in Economics at Yale, and taught in the Yale School of Organization and Management, prior to joining the Kellogg faculty in 1979.
His general area of research is game theory, with a primary focus on the effects of private information in competitive settings. Much of his research has been centered on the theory and practice of competitive bidding and auction design. His 1982 paper, "A Theory of Auctions and Competitive Bidding" (Econometrica 50, co-authored with P.R. Milgrom), is considered a seminal work in the field. He served as an external consultant on a 1985 project leading to revisions in the procedures used to auction petroleum extraction leases on the U.S. outer continental shelf, and he co-organized (with representatives of the Federal Reserve Board and the U.S. Treasury) the 1992 public forum which led to changes in the way the Treasury auctions its debt issues. Since 1993, he has represented private clients during both the rule-making and bidding phases of the FCC's sale of licenses of spectrum for the provision of personal communications services.
In the early 1970s, Professor Weber proposed an alternative to the traditional "plurality rule" for elections involving more than two candidates. This alternative, "approval voting", has generated a substantial body of research, has been adopted by a number of professional organizations, and has been used in several public elections. Recent work in this area includes "A Theory of Voting Equilibria" (American Political Science Review 87, 1993, co-authored with R. Myerson), and "Approval Voting" (Journal of Economic Perspectives 9(1), 1995).
Professor Weber has also conducted research on negotiation and arbitration. Among his activities have been preparation of a research survey for the American Arbitration Association, and development of classroom materials for the National Institute for Dispute Resolution. He is a founding member of the Center for Research on Dispute Resolution at Northwestern University, and has served on the editorial board of the International Journal of Game Theory. In 1990 he was designated the outstanding professor of the year by the students in Kellogg's Managers' Program, and in 1998 he received the Sidney J. Levy Teaching Award. In 2008, he was chosen as Alumni Professor of the Year.
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A topical overview, and review of Vijay Krishna's book.
A general problem is to study two-person zero-sum games with stochastic movement among subgames in which the subgame being played is not precisely known, but in which information about this aspect may be gathered or partially revealed by the strategy choices of the players, the actual game being played, and chance.
We report the results of elections conducted in a laboratory setting, modelled on a threecandidate example due to Borda. By paying subjects conditionally on election outcomes, we create electorates with (publicly) known preferences. We compare the results of experiments with and without non-binding pre-election polls under plurality rule, approval voting, and Borda rule. We also refer to a theory of voting “equilibria,” which makes sharp predictions concerning individual voter behavior and election outcomes. We find that Condorcet losers occasionally win regardless of the voting rule or presence of polls. Duverger's law (which asserts the predominance of two candidates) appears to hold under plurality rule, but close three-way races often arise under approval voting and Borda rule. Voters appear to poll and vote strategically. In elections, voters usually cast votes that are consistent with some strategic equilibrium. By the end of an election series, most votes are consistent with a single equilibrium, although that equilibrium varies by experimental group and voting rule.
Do polls simply measure intended voter behavior or can they affect it and, thus, change election outcomes? Do candidate ballot positions or the results of previous elections affect voter behavior? We conduct several series of experimental, three-candidate elections and use the data to provide answers to these questions. In these elections, we pay subjects conditionally on election outcomes to create electorates with publicly known preferences. A majority (but less than two-thirds) of the voters are split in their preferences between two similar candidates, while a minority (but plurality) favor a third, dissimilar candidate. If all voters voted sincerely, the third candidate — a Condorcet loser — would win the elections. We find that pre-election polls significantly reduce the frequency with which the Condorcet loser wins. Further, the winning candidate is usually the majority candidate who is listed first on the poll and election ballots. The evidence also shows that a shared history enables majority voters to coordinate on one of their favored candidates in sequences of identical elections. With polls, majority-preferred candidates often alternate as election winners.
The U.S. Treasury could raise more revenue if it changed the way it auctions its debt. Under the current procedure, all bidders whose competitive bids for Treasury securities are accepted pay the prices they bid; different winning bidders, that is, pay different prices. Instead, economic theory says, all winning bidders should all pay the same price—that of the highest bid not accepted, or the price that just clears the market. This procedural change would increase the revenue that Treasury auctions raise primarily because it would decrease the amount of resources that bidders would spend collecting information about what other bidders are likely to do. It would also reduce the incentives for traders to attempt to manipulate the securities market.
We study games with incomplete information from a point of view which emphasizes the empirical predictions arising from game-theoretic models. Using the notion of "distributional" strategies, we prove four main theorems: (i) a mixed-strategy Nash equilibrium existence theorem, (ii) a pure-strategy equilibrium existence theorem, (iii) a pure-strategy ∈-equilibrium existence theorem, and (iv) a theorem describing how the set of equilibria of a game varies with the parameters of the game.
A model of competitive bidding is developed in which the winning bidder's payoff may depend upon his personal preferences, the preferences of others, and the intrinsic qualities of the object being sold. In this model, the English (ascending) auction generates higher average prices than does the second-price auction. Also, when bidders are risk-neutral, the second-price auction generates higher average prices than the Dutch and first-price auctions. In all of these auctions, the seller can raise the expected price by adopting a policy of providing expert appraisals of the quality of the objects he sells.
In this paper, we explore bidders' incentives to gather information in auctions, when there is one bidder with only public information and another with some private information. We find that the bidder with only public information makes no profit at equilibrium, while the bidder with private information generally makes positive profits. Moreover, the informed bidder's profits rise when he gathers extra information, and the increase in greater when the information is collected overtly than when it is collected covertly. When the uniformed bidder can observe some of the better-informed bidder's information, he prefers to make his observations covertly. If the seller has access to some of the better-informed bidder's information, or if he has affiliated information of his own, he can raise the expected price by adopting a policy of making that information public. However, there are cases where a policy of publicizing his information would lower the expected price. The distinguishing feature of these latter cases seems to be that the seller's information is complementary to the information of the better-informed bidder.
A semivalue is a symmetric positive linear operator on a space of games, which leaves the additive games fixed. Such an operator satisfies all of the axioms defining the Shapley value, with the possible exception of the efficiency axiom. The class of semivalues is completely characterized for the space of finite-player games, and for the space pNA of nonatomic games.
The complexity of the attainable set of utility outcomes of a market (with finitely many traders) is defined as the least number of commodities involved in any market giving the same set. This notion is investigated both for the case of quasiconcave and concave utility functions. It is shown that, in either case, there is a dense collection of attainable sets, each having complexity at most n(n−1)/2.
A set is convexifiable if there exists a strictly increasing, continuous rescaling of the coordinate axes which makes the set convex. Several classes of sets are investigated with regard to this property. It is shown that every convexifiable compactly generated set is the attainable set of a market in which the traders have quasiconcave utility functions.
We study notions of independence of the private information available to different agents in a Bayesian environment and their connection to common knowledge. We describe three game theoretic applications that give rise to such notions, and clarify their relationships to each other.
This chapyer presents an axiomatic development of values for games involving a fixed finite set of players. We primarily seek methods for evaluating the prospects of individual players, and our results center around the class of "probabilistic" values. In the process of obtaining our results, we examine the role played by each of the Shapley axioms ins restricting the set of value functions under consideration, and we trace in detail the logical path leading the Shapley value.
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.
Managerial Decision Analysis (DECS-438-A)
This course presents the standard approach taken in all Kellogg courses in dealing with risk and uncertainty. The principal focus is on the language of probability, random variables, decision trees and commonly encountered probability distributions. A number of applications are explored, with most analysis performed using spreadsheets.
Prerequisite: One-Year-student status.
Statistical Decision Analysis (DECS-439-B)
The study of statistics at Kellogg has two complementary goals: The first is to master the two languages of statistics: How to measure how much an estimate can be trusted and how to measure the weight of evidence with respect to a claim that has been made. The objective is to become knowledgeable consumers of statistical reports, effective managers of those doing the statistical "dirty work" and confident critics of statistics done badly. The other goal is to become facile at performing regression analysis, a tool for understanding the types of relationships all managers must deal with. A spreadsheet-based statistical analysis package is provided to all students.
Prerequisite: One-Year-student status.
Strategic Decision Making (DECS-452-0)
This course counts toward the following majors: Analytical Consulting, Decision Sciences.
Decision makers face two types of uncertainty: uncertainty about the state of nature (how much oil is on a tract of land) and uncertainty about the strategic behavior of other decision makers (what pricing strategy a competitor will follow). This course focuses on strategic uncertainty and the uses decision makers can make of the concepts of game theory to guide their decisions. Topics include bargaining and arbitration, collusion and competition, joint cost allocation, market entry and product differentiation, and competitive bidding. Role-playing exercises and case analysis are used.
Statistical Decision Analysis explores the use of sample data for estimating,predicting, forecasting and making business decisions.
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