MANAGERIAL ECONOMICS & DECISION SCIENCES
James J. O'Connor Professor of Decision and Game Sciences
Professor of Math.
Director of the Center for Strategic Decision Making
Ehud Kalai advanced the frontiers of game theory and its interface with economics, social choice, operations research and computer science. His work opened and expanded our understanding of bargaining, strategic learning, large games and related subjects. The research is reported in over sixty scientific papers published by the leading game theory, economics, and operations journals.
Holding an AB in mathematics (U. of Calif. Berkeley, 1967), MS and PhD in statistics and mathematics (Cornell, 1971, 72), Kalai joined Northwestern University in 1975 after serving as assistant professor at Tel Aviv University. He is the James J. O’Connor Distinguished Professor of Decision and Game Sciences in the Kellogg School of Management and (courtesy) Professor of Mathematics in the College of Arts and Sciences. Past chair of the department of Managerial Economics and Decision Sciences, Kalai is the founding director of the Center for Strategic Decision Making, the founding organizer of the prestigious Nancy L. Schwartz Memorial Lecture series, and repeated winner of Outstanding Teacher awards in Kellogg’s Executive Programs.
Kalai is the founding Editor of Games and Economic Behavior, the top journal in game theory today, co-founder and president of the international Game Theory Society, and Fellow of the Econometric Society. He was awarded the Oskar Morgenstern Research Professorship at New York University, the Sherman Fairchild Distinguished Scholar position at the California Institute of Technology, and numerous NSF and other research grants. His consulting activities included Baxter Health Care Systems, Kaiser Permanente, Arthur Anderson, First Chicago, Sonnenschein, Nath and Rosenthal and Israel Defense Forces among others.
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A critical survey of game theory, its achievements and possible future directions, presented in the Second World Congress of The Game Theory Society in Marseilles, 2004
The sensitivity of Nash equilibrium to strategic and informational details presents a difficulty in applying it to games which are not fully specified. Structurally-robust Nash equilibria are less sensitive to such details. Moreover, they arise naturally in important classes of games that have many semi-anonymous players. The paper describes this condition and its implications.
With many semi-anonymous players, the equilibria of simultaneous-move games are "extensively robust." This means that the equilibria survive even if the simultaneous-play assumption is relaxed to allow for a large variety of extensive modifications. Such modifications include sequential play with partial and differential revelation of information, commitments, multiple revisions of choices, cheap talk announcements, and more.
In joint decision making, similarly minded people may take opposite positions. Consider the example of a marriage in which one spouse gives generously to charity while the other donates nothing. Such “polarization” may misrepresent what is, in actuality, a small discrepancy in preferences. It may be that the donating spouse would like to see 10% of their combined income go to charity each year, while the apparently frugal spouse would like to see 8% donated. A simple game-theoretic analysis suggests that the spouses will end up donating 10% and 0%, respectively. By generalizing this argument to a larger class of games, we provide strategic justification for polarization in many situations such as debates, shared living accommodations, and disciplining children. In some of these examples, an arbitrarily small disagreement in preferences leads to an arbitrarily large loss in utility for all participants. Such small disagreements may also destabilize what, from game-theoretic point of view, is a very stable equilibrium.
In a recurring game, a stage game is played sequentially by different groups of players. Each group receives publicly available information about the play of earlier groups. Not knowing the population distribution of player types (representing individual preferences and behavior), society members start with a prior probability distribution over a set of possible type-distributions. Late groups update their beliefs by considering the public information regarding the play of earlier groups. We study the limit beliefs and play of late groups and the relationships to the true (realized) type-distribution and equilibria of the true Bayesian stage game
The paper deals with three related issues: (1) It introduces a measure of partial subgame perfection for equilibria of repeated games. (2) It illustrates that the folk-theorem discontinuity generated by small complexity costs, as exhibited by Abreu and Rubinstein, does not exist in the presence of any level of perfection. (3) It shows that reactive strategy equilibria, such as tit-for-tat, cannot be subgame perfect, even partially so. As a corollary, this shows a need to use full automata rather than exact automata when studying complexity and perfection in repeated games.
A class of characteristic function games arising from maximum flow problems is introduced and is shown to coincide with the class of totally balanced games. The proof relies on the max flow-min cut theorem of Ford and Fulkerson and on the observation that the class of totally balanced games is the span of the additive games with the minimum operation.
An n-person social choice problem is considered in which the alternatives are n dimensional vectors with the ith component of such a vector being the part of the alternative effecting individual i alone. Assuming that individuals are selfish (i is indifferent between any two alternatives that have the same ith component) we characterize all the families of permissible individual preferences that admit nondictatorial Arrow-type social welfare functions. We also show that the existence of such a function for a given family of preferences is independent of n provided that is greater than one.
A central question in game theory and artificial intelligence is how a rational agent should behave in a complex environment, given that it cannot perform unbounded computations. We study strategic aspects of this question by ormulating a simple model of a game with additional costs (computational or otherwise) for each strategy. First we connect this to zero-sum games, proving a counter-intuitive generalization of the classic min-max theorem to zero-sum games with the addition of strategy costs. We then show that potential games with strategy costs remain potential games. Both zero-sum and potential games with strategy costs maintain a very appealing property: simple learning dynamics converge to equilibrium
Game Theory is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in game theory. We hear their views on game theory, its aim, scope, use, the future direction of game theory and how their work fits in these respects. Interviewees:Aumann,van Benthem, Bicchieri, Binmore, Brandenburger, Camerer, Grafen, Hammerstein, Hart, Kalai, Kreps, Moulin, Parikh, Rubinstein, Samuelson, Schelling, Skyrms, Sugden, Young .
Conditional commitments are used by players who wish to strengthen their strategic positions. We propose a model of conditional commitments that unifies earlier models and avoids the pitfalls and circularities of such commitments. A commitment folk theorem shows that the potential of conditional commitment is essentially unlimited. All feasible and individually-rational payoffs of a two-person strategic game can be attained at the equilibria of one (universal) voluntary commitment game that uses simple commitment devices.
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 survey discusses recent findings on the robustness of Nash equilibria of strategic games with many semianonymous players. It describes the notion of structural robustness and its general consequences , as well as implications to particular games, such as ones played on the web and market games.
How should a coalition of cooperating players allocate payoffs to its members? This question arises in a broad range of situations and evokes an equally broad range of issues. For example, it raises technical issues in accounting, if the players are divisions of a corporation, but involves issues of social justice when the context is how people behave in society. Despite the breadth of possible applications, coalitional game theory offers a unified framework and solutions for addressing such qsts. This article presents some of its major models and proposed solutions.
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.
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.
Analytical Approach to Uncertainty introduces elementary probability theory as a tool for modeling uncertainty in business, with illustrations from decision theory and statistics.
Game Theory (MECSX-460-0)
Game Theory studies strategic interaction and conflict resolution in competitive and cooperative environments. Principles of strategic reasoning and related mathematical formulas are taught through real-life examples and in-class games, giving students an edge in external business competition and in internal organization management.
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