Ehud Kalai
Ehud Kalai

Professor Emeritus of Managerial Economics & Decision Sciences
Director of the Center for Games and Economic Behavior

Print Overview

Ehud Kalai is a prominent American game theorist and mathematical economist known for his contributions to game theory and its interface with economics, social choice, computer science and operations research. He is the James J. O'Connor Distinguished Professor of Decision and Game Sciences at Northwestern University, where he has taught since 1975.

Kalai moved from Israel to the US in 1963. He received his AB in mathematics from the University of California Berkeley (1967) and an MS (1971) and a PhD (1972) in statistics and mathematics from Cornell University. After serving as an assistant professor of statistics at Tel Aviv University (1972-1975), he was hired by Northwestern University to establish a research group in game theory. He is the founding director of the Kellogg Center of Game Theory and Economic Behavior and the executive director of the Nancy L. Schwartz Memorial Lecture series.

Kalai is the founding Editor of Games and Economic Behavior, the leading journal in game theory. With Robert J. Aumann, Kalai founded the Game Theory Society and served as its president from 2003 to 2006. He is a fellow of the American Academy of Arts and Sciences and of the Econometric Society, was awarded an Honorary Doctorate by the University of Paris (2010), the Sherman Fairchild Distinguished Scholar position at the California Institute of Technology (1993), and was appointed the Oskar Morgenstern Research Professor at New York University (1991).

In cooperative game theory, the Kalai-Smorodinsky solution reopened the study of bargaining by showing that the long unchallenged Nash solution is not unique. He later axiomatized the Egalitarian solution to bargaining problems and, with D. Samet, formulated its extension to general (NTU) cooperative games, unifying it with the Shapley (TU) Value. In non cooperative game theory, the Kalai-Lehrer model of rational learning showed that rational players with truth-compatible beliefs eventually learn to play Nash equilibria of repeated games. In particular, in Bayesian equilibria of repeated games all relevant private information eventually becomes common knowledge. Kalai's work on large games showed that the equilibria of Bayesian games with many players are structurally robust, thus large games escape major pitfalls in game-theoretic modeling.

Kalair is also known for seminal collaborative research on flow games and totally balanced games; strategic complexity and its implications in economics and political systems; arbitration, strategic delegation and commitments; extensions of Arrow's Impossibility Theorem in social choice; competitive service speed in queues; and on rational strategic polarization in group decision making.

Selected publications:

Cooperative Game Theory
"Other Solutions to Nash's Bargaining Problems," Econometrica, 1975 (with M. Smorodinsky) "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, 1977 "Monotonic Solutions to General Cooperative Games," Econometrica, 1985 (with D. Samet)

Non cooperative Game Theory
"Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, 1988 (with W. Stanford) "Rational Learning Leads to Nash Equilibrium," Econometrica, 1993 (with E. Lehrer) "Large Robust Games," Econometrica, 2004

Probability and Learning
"Bayesian Representations of Stochastic Processes Under Learning: deFinetti Revisited," Econometrica, 1999 (with M. Jackson and R. Smorodinsky)

"The Kinked Demand Curve, Facilitating Practices, and Oligopolistic Coordination," 1986, Northwestern DP (with M. Satterthwaite; published by Kluwer, 1996) "Observable Contracts: Strategic Delegation and Cooperation," International Economic Review, 1991 (with C. Fershtman and K. Judd) "Complexity Considerations in Market Behavior," The RAND Journal of Economics, 1993 (with C. Fershtman)

Social Choice
"Aggregation Procedure for Cardinal Preferences: A Formulation and Proof of Samuelson's Impossibility Conjecture," Econometrica, 1977 (with D. Schmeidler) "Characterization of Domains Admitting Non-Dictatorial Social Welfare Functions and Non-Manipulable Voting Procedures," Journal of Economic Theory, 1977 (with E. Muller) "Path Independent Choices," Econometrica, 1980 (with N. Megiddo)

Operations Research / Computer Science
"Totally Balanced Games and Games of Flow," Mathematics of Operations Research, 1982 (with E. Zemel) "Optimal Service Speeds in a Competitive Environment," Management Science, 1992 (with M. Kamien and M. Rubinovitch) "Partially-Specified Large Games," Lecture Notes in Computer Science, 2005

Mathematical Psychology
"Strategic Polarization," Journal of Mathematical Psychology, 2001 (with A. Kalai)

Areas of Expertise
Game Theory

Print Vita
PhD, 1972, Mathematics, Statistics, Cornell University
MS, 1971, Mathematics, Statistics, Cornell University
AB, 1967, Mathematics, University of California, Berkeley

Academic Positions
The James J. O'Connor Distinguished Professor of Decision and Game Sciences, Managerial Economics and Decision Sciences, Kellogg School of Management, Northwestern University, 2001-present
Professor, Mathematics, College of Arts and Sciences, Northwestern University, 1990-present
The Charles E. Morrison Professor of Decision Sciences, Kellogg School of Management, Northwestern University, 1982-2001
Professor, Kellogg School of Management, Northwestern University, 1978-1982
Associate Professor, Kellogg School of Management, Northwestern University, 1976-1978
Visiting Assistant Professor, Kellogg School of Management, Northwestern University, 1975-1976
Assistant Professor, Statistics, Tel Aviv University, 1972-1975

Honors and Awards
Prize in Game Theory in Honor of Ehud Kalai, Game Theory Society
Fellow, Society for the Advancement of Economic Theory, 2011, ongoing
Fellow, American Academy of Arts and Sciences, 2012, ongoing

Editorial Positions
Editor-in-Chief, Games and Economic Behavior, 1988-Present
Editorial Board Member, The International Journal of Game Theory, 1985
Founder, Games and Economic Behavior, 1988

Print Research
Research Interests
Game theory, mathematical economics

Kalai, Ehud and J. Deb. 2015. Stability in large Bayesian games with heterogeneous players. Jorunal of Economic Theory. 157: 1041-1055.
Kalai, Ehud. 2013. The High Priest of Game Theory. The American Mathematical Monthly. 120(5)
Kalai, Ehud and A. Kalai. 2013. Cooperation in Strategic Games Revisited. Quarterly Journal of Economics.
Kalai, Ehud and A. Kalai. 2011. Cooperation in Two Person Games, Revisited. Association for Computing Machinery, SIGecom Exchanges. 10(1): 13-16.
Kalai, Ehud and A. Kalai. 2011. Cooperation and Competition in Strategic Games with Private Information. Proceedings of the 11th Conference on Electronic Commerce of the Association for Computing Machinery.: 345-346.
Kalai, Adam, Ehud Kalai, Ehud Lehrer and Dov Samet. 2010. A Commitment Folk Theorem. Games and Economic Behavior. 69(1): 127-137.
Gossner, Olivier, Ehud Kalai and Robert Weber. 2009. Information Independence and Common Knowledge. Econometrica. 77(4): 1317-1328.
Kalai, Ehud. 2009. Technical Perspective: The Complexity of Computing Nash Equilibrium. Communications of the Association for Computing Machinery. 52(2): 88.
Kalai, Ehud. 2008. The Presidential Address of the Second World Congress of Game Theory. Games and Economic Behavior. 63(2): 421-430.
Ben-Sasson, Eli, Adam Kalai and Ehud Kalai. 2007. An Approach to Bounded Rationality. Advances in Neural Information Processing Systems. 19: 145-152.
Kalai, Ehud. 2005. Partially-Specified Large Games. Lecture Notes in Computer Science. 3828: 3-13.
Kalai, Ehud. 2004. Large Robust Games. Econometrica. 72(6): 1631-1665.
Kalai, Ehud and Eilon Solan. 2003. Randomization and Simplification in Dynamic Decision Making. Journal of Economic Theory. 111(2): 251-264.
Kalai, Adam and Ehud Kalai. 2001. Strategy Polarization. Journal of Mathematical Psychology. 45(4): 656-663.
Jackson, Matthew O. and Ehud Kalai. 1999. Reputation versus Social Learning. Journal of Economic Theory. 88(1): 40-59.
Kalai, Ehud and John Ledyard. 1998. Repeated Implementation. Journal of Economic Theory. 83(2): 308-317.
Jackson, Matthew O., Ehud Kalai and Rann Smorodinsky. 1999. Bayesian Representations of Stochastic Processes Under Learning: deFinetti Revisited. Econometrica. 67(4): 875-893.
Kalai, Ehud, Ehud Lehrer and Rann Smorodinsky. 1999. Calibrated Forecasting and Merging. Games and Economic Behavior. 29(1/2): 151-159.
Jackson, Matthew O. and Ehud Kalai. 1997. Social Learning in Recurring Games. Games and Economic Behavior. 21(1-2): 102-134.
Fershtman, Chaim and Ehud Kalai. 1997. Unobserved Delegation. International Economic Review. 38(4): 763-744.
Kalai, Ehud and Ehud Lehrer. 1995. Subjective Games and Equilibria. Games and Economic Behavior. 8(1): 123-163.
Kalai, Ehud and Ehud Lehrer. 1994. Weak and Strong Merging of Opinions. Journal of Mathematical Economics. 23(1): 73-86.
Kalai, Ehud and Ehud Lehrer. 1993. Subjective Equilibrium in Repeated Games. Econometrica. 61(5): 1231-1240.
Gilboa, Itzhak, Ehud Kalai and Eitan Zemel. 1993. The Complexity of Eliminating Dominated Strategies. Mathematics of Operations Research. 18(3): 553-565.
Baron, David and Ehud Kalai. 1993. The Simplest Equilibrium of a Majority-Rule Division Game. Journal of Economic Theory. 61(2): 290-301.
Fershtman, Chaim and Ehud Kalai. 1993. Complexity Considerations and Market Behavior. RAND Journal of Economics. 24(2): 224-235.
Kalai, Ehud, Morton Kamien and Michael Rubinovitch. 1992. Optimal Service Speeds in a Competitive Environment. Management Science. 38(8): 1154-1163.
Kalai, Ehud and Alejandro Neme. 1992. The Strength of a Little Perfection. International Journal of Game Theory. 20(4): 335-355.
Fershtman, Chaim, Kenneth L. Judd and Ehud Kalai. 1991. Observable Contracts: Strategic Delegation and Cooperation. International Economic Review. 32(3): 551-559.
Gilboa, Itzhak, Ehud Kalai and Eitan Zemel. 1990. On the Order of Eliminating Dominated Strategies. Operations Research Letters. 9(2): 85-89.
Kalai, Ehud, Dov Samet and William Stanford. 1988. A Note on Reactive Equilibria in the Discounted Prisoners' Dilemma. International Journal of Game Theory. 17(3): 177-186.
Kalai, Ehud and Dov Samet. 1987. On Weighted Shapley Values. International Journal of Game Theory. 16(3): 205-222.
Kalai, Ehud. 1987. Strategic Behavior and Competition: An overview. Journal of Economic Theory. 39(1): 1-13.
Kalai, Ehud and William Stanford. 1988. Finite Rationality and Interpersonal Complexity in Repeated Games. Econometrica. 56(2): 397-410.
Kalai, Ehud and William Stanford. 1985. Conjectural Variations Strategies in Accelerated Cournot Games. International Journal of Industrial Organization. 3(3): 133-152.
Kalai, Ehud and Dov Samet. 1985. Monotonic Solutions to General Cooperative Games. Econometrica. 53(2): 307-327.
Kalai, Ehud and Dov Samet. 1985. Unanimity Games and Pareto Optimality. International Journal of Game Theory. 14(1): 41-50.
Kalai, Ehud and Dov Samet. 1984. Persistent Equilibria in Strategic Games. International Journal of Game Theory. 13(3): 129-144.
Kalai, Ehud and Eitan Zemel. 1982. Generalized Network Problems Yielding Totally Balanced Games. Operations Research. 30(4): 998-1008.
Kalai, Ehud and Eitan Zemel. 1982. Totally Balanced Games and Games of Flow. Mathematics of Operations Research. 7(3): 476-478.
Kalai, Ehud. 1981. Preplay Negotiations and the Prisoners' Dilemma. Mathematical Social Sciences. 1(4): 375-379.
Kalai, Ehud and Nimrod Megiddo. 1980. Path Independent Choices. Econometrica. 48(3): 781-784.
Kalai, Ehud and Zvi Ritz. 1980. Characterization of the Private Alternatives Domains Admitting Arrow Social Welfare Functions. Journal of Economic Theory. 22(1): 23-36.
Kalai, Ehud, Eitan Muller and Mark Satterthwaite. 1979. Social Welfare Functions when Preferences are Convex and Continuous: Impossibility Results. Public Choice. 34(1): 87-98.
Kalai, Ehud, Andrew Postlewaite and John Roberts. 1979. A Group Incentive Compatible Mechanism Yielding Core Allocations. Journal of Economic Theory. 20(1): 13-22.
Kalai, Ehud, Andrew Postlewaite and John Roberts. 1979. Barriers to Trade and Disadvantageous Middlemen: Nonmonotonicity of the Core. Journal of Economic Theory. 19(1): 200-209.
Kalai, Ehud and Robert Rosenthal. 1978. Arbitration of Two-Party Disputes under Ignorance. International Journal of Game Theory. 7(2): 65-72.
Anbar, Dan and Ehud Kalai. 1978. A One-Shot Bargaining Problem. International Journal of Game Theory. 7(1): 19-30.
Kalai, Ehud and Eitan Muller. 1977. Characterization of Domains Admitting Non-Dictatorial Social Welfare Functions and Non-Manipulable Voting Procedures. Journal of Economic Theory. 16(2): 457-469.
Kalai, Ehud. 1977. Non-Symmetric Nash Solutions for Replications of 2-Person Bargaining. International Journal of Game Theory. 6(3): 129-133.
Kalai, Ehud. 1977. Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons. Econometrica. 45(7): 1623-1630.
Kalai, Ehud and David Schmeidler. 1977. An Admissible Set Occurring in Various Bargaining Situations. Journal of Economic Theory. 14(2): 402-411.
Kalai, Ehud and David Schmeidler. 1977. Aggregation Procedure for Cardinal Preferences: A Formulation and Proof of Samuelson's Impossibility Conjecture. Econometrica. 45(6): 1431-1438.
Kalai, Ehud, Elisha A. Pazner and David Schmeidler. 1976. Collective Choice Correspondences as Admissible Outcomes of Social Bargaining Processes. Econometrica. 44(2): 233-240.
Kalai, Ehud. 1975. On Game-Type Subsets. International Journal of Game Theory. 4(3): 141-150.
Kalai, Ehud. 1975. Excess Functions for Cooperative Games Without Sidepayments. SIAM Journal on Applied Mathematics. 29(1): 60-71.
Kalai, Ehud and Rann Smorodinsky. 1975. On a Game-Theoretic Notion of Complexity for Compact Convex Sets. Proceedings of the American Mathematical Society. 49(2): 416-420.
Kalai, Ehud and Rann Smorodinsky. 1975. Other Solutions to Nash's Bargaining Problems. Econometrica. 43(3): 513-518.
Working Papers
Shmaya, Eran and Ehud Kalai. 2017. Large strategic dynamic interactions.
Kalai, Ehud. 2002. Ex-Post Stability in Large Games.
Kalai, Ehud. 2000. Private Information in Large Games.
Book Chapters
Kalai, Ehud. 2008. "Large Games: Structural Robustness." In The New Palgrave Dictionary of Economics, edited by Steven Derlauf, Larry Blume, Hampshire, UK: Palgrave Macmillan, 2nd.
Kalai, Ehud. 2008. "Games in Coalitional Form." In New Palgrave Dictionary of Economics, 2nd Edition, edited by Steven N. Durlauf and Lawrence E. Blume, McMillan.
Kalai, Ehud. 2007. "A Personal View of Game Theory." In Game Theory, Five Questions, edited by V.F. Hendricks, P.G. Hansen, Automatic Press/ VIP.
Jackson, Matthew O. and Ehud Kalai. 1999. "Social Learning in Recurring Games." In Social Organization and Mechanism Design, edited by Claude d, De Boeck & Larcier s.a..
Jackson, Matthew O. and Ehud Kalai. 1997. "Recurring Bullies, Trembling and Learning." In Understanding Strategic Interaction: Essays in Honor of Reinhard Selten, edited by W. Albers, W. Guth, P. Hammerstein, B. Moldovanu, and E. Van Damme, Springer-Verlag.
Kalai, Ehud. 1993. "A Rational Game Theory Framework for the Analysis of Legal and Criminal Decision Making." In Inside the Juror: The Psychology of Juror Decision Making, edited by R. Hastie, 235-241. Oxford University Press.
Kalai, Ehud and Ehud Lehrer. 1999. "Rational Learning Leads to Nash Equilibrium." In Recent Development in Game Theory, edited by E. Maskin, 183-209. Edward Elgar Publishing.
Kalai, Ehud and Mark Satterthwaite. 1994. "The Kinked Demand Curve, Facilitating Practices, and Oligopolistic Coordination." In Imperfections and Behavior in Economic Organizations, edited by R. P. Gilles and P. H. M. Ruys, 15-38. Kluwer.
Kalai, Ehud and Dov Samet. 1992. "Types Decomposition and Perfect Implementations." In Rational Interaction, Essays in Honor of John C. Harsanyi, edited by Reinhard Selten, Springer-Verlag.
Kalai, Ehud. 1990. "Bounded Rationality and Strategic Complexity in Repeated Games." In Game Theory and Applications, edited by Ichiishi Tatsuro, Neyman Abraham, Tauman Yair, Academic Press.
Kalai, Ehud and Dov Samet. 1988. "Weighted Shapley Values." In The Shapley Value, Essays in Honor of Lloyd S. Shapley, edited by Alvin E. Roth, 83-100. Cambridge University Press.
Kalai, Ehud. 1985. "Solutions to the Bargaining Problem." In Social Goals and Social Organization, Essays in Memory of Elisha A. Pazner, edited by Hurwicz, Schmeidler and Sonnenschein, 77-106. Cambridge University Press.
Kalai, Ehud, Andrew Postlewaite and John Roberts. 1979. "Arbitration of Exchange Situations with Public Goods." In Applied Game Theory, edited by S. J. Brams, A. Schotter, G. Schwo, vol. 1, Wu: Physica Verlag.
Kalai, Ehud. "Games, Computers, and O.R.." Proceedings of the Seventh Annual ACM-SIAM Symposium on Discrete Algorithms.
Kalai, Ehud. "Games and Economic Behavior (Editorial)." Games and Economic Behavior.
Kalai, Ehud. 1998. Frontiers of Research in Economic Theory : The Nancy L. Schwartz Memorial Lectures, 1983-1997. Cambridge University Press.

Print Teaching
Teaching Interests
Quantitative methods and decision theory with managerial applications
Executive MBA
Analytical Approach to Uncertainty (MECNX-433-0)

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.