Elon Kohlberg is the Royal Little Professor of Business Administration at the Harvard Business School. His research is mainly in Game Theory, in particular the study of non-cooperative equilibrium.
Professor Kohlberg has taught many courses in the MBA, Ph.D., and executive programs at Harvard Business School, including, Managerial Economics, Competitive Decision Making, Strategy, and Finance. He is currently teaching the Advanced Microeconomics course in the doctoral program, as well as the elective MBA course Games of Chance and Games of Strategy.
Professor Kohlberg serves on the board of directors of Medinol and Digi-Block, Inc. Previously, he served on the boards of Teva Pharmaceuticals and Ormat Technologies.
He received a B.Sc., M.Sc., and Ph.D. in mathematics from the Hebrew University of Jerusalem.
A game of threats on a finite set of players, N, is a function d that assigns a real number to any coalition, S ⊆ N, such that d(S) = -d(N\S). A game of threats is not necessarily a coalitional game as it may fail to satisfy the condition d(Ø) = 0. We show that analogs of the classic Shapley axioms for coalitional games determine a unique value for games of threats. This value assigns to each player an average of the threat powers, d(S), of the coalitions that include the player. Games of threats arise naturally in value theory for strategic games and may have applications in other branches of game theory.
Hillas, John, and Elon Kohlberg. "Foundations of Strategic Equilibria." In Handbook of Game Theory, edited by Robert J. Aumann and Sergiu Hart. Elsevier Science, 2002.
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Hausman, Jerry A., and Elon Kohlberg. "The Future Evolution of the Central Office Switching Industry." In Future Competition in Telecommunications, edited by Stephen P. Bradley and Jerry A. Hausman. Boston, MA: Harvard Business School Press, 1989.
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We examine a solution concept, called the “value," for n-person strategic games. In applications, the value provides an a-priori assessment of the monetary worth of a player's position in a strategic game, comprising not only the player's contribution to the total payoff but also the player's ability to inflict losses on other players. A salient feature is that the value takes account of the costs that “spoilers" impose on themselves. Our main result is an axiomatic characterization of the value. For every subset, S, consider the zero-sum game played between S and its complement, where the players in each of these sets collaborate as a single player, and where the payoff is the difference between the sum of the payoffs to the players in S and the sum of payoffs to the players not in S. We say that S has an effective threat if the minmax value of this game is positive. The first axiom is that if no subset of players has an effective threat then all players are allocated the same amount. The second axiom is that if the overall payoff to the players in a game is the sum of their payoffs in two unrelated games, then the overall value is the sum of the values in these two games. The remaining axioms are the strategic-game analogs of the classical coalitional-games axioms for the Shapley value: efficiency, symmetry, and null player.
Building on the work of Nash, Harsanyi, and Shapley, we define a cooperative solution for strategic games that takes account of both the competitive and the cooperative aspects of such games. We prove existence in the general (NTU) case and uniqueness in the TU case.
Our main result is an extension of the definition and the existence and uniqueness theorems to stochastic games—discounted or undiscounted.
Since the seminal paper of Shapley, the theory of stochastic games has been developed in many different directions. However, there has been practically no work on the interplay between stochastic games and cooperative game theory. Our purpose here is to make a first step in this direction. We show that the Harsanyi-Shapley-Nash cooperative solution to one-shot strategic games can be extended to stochastic games. While this extension applies to general n-person stochastic games, it does not rely on Nash equilibrium analysis in such games. Rather, it only makes use of minmax analysis in two-person (zero-sum) stochastic games. This will become clear in the sequel.
Noncooperative games are examined from the point of view of an outside observer who believes that the players are rational and that they know at least as much as the observer. The observer is assumed to be able to observe many instances of the play of the game; these instances are identical in the sense that the observer cannot distinguish between the settings in which different plays occur. If the observer does not believe that he will be able to offer beneficial advice then he must believe that the players are playing a correlated equilibrium, though he may not initially know which correlated equilibrium. If the observer also believes that, in a certain sense, there is nothing connecting the players in a particular instance of the game then he must believe that the correlated equilibrium they are playing is, in fact, a Nash equilibrium.
Kohlberg, Elon, and Philip J. Reny. "Independence on Relative Probability Spaces and Consistent Assessments in Game Trees." Harvard Business School Working Paper, No. 96-072, June 1996.
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Christenson, Charles, Elon Kohlberg, Arthur Schleifer Jr., Harborne W. Stuart Jr., Paul A. Vatter, and George Wu. "Quality Printing." Harvard Business School Case 896-002, August 1995.
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