http://ap.tbo.com/ap/breaking/MGBEJU4SMEE.htmlIsraeli, American Win Nobel for Economics
By MATT MOORE, AP Business Writer
STOCKHOLM, Sweden - Israeli-American Robert J. Aumann and American Thomas C. Schelling won the 2005 Nobel Memorial Prize in Economic Sciences on Monday for their work on game theories that help explain political and economic conflicts from arms races to price wars.
"Why do some groups of individuals, organizations and countries succeed in promoting cooperation while others suffer from conflict?" the Royal Swedish Academy of Sciences said.<snip>
Aumann and Schelling were cited for using game-theory analysis to "explain economic conflicts such as price wars and trade wars, as well as why some communities are more successful than others in managing common-pool resources."
"The repeated-games approach clarifies the raison d'etre of many institutions, ranging from merchant guilds and organized crime to wage negotiations and international trade agreements," the citations said.<snip>
The academy, in its citation, lauded Schelling for showing "that a party can strengthen its position by overtly worsening its own options, that the capability to retaliate can be more useful than the ability to resist an attack, and that uncertain retaliation is more credible and more efficient than certain retaliation."<snip>
"In many real-world situations, cooperation may be easier to sustain in a long-term relationship than in a single encounter. Analyses of short-run games are, thus, often too restrictive," the academy said. "Robert Aumann was the first to conduct a full-fledged formal analysis of so-called infinitely repeated games. His research identified exactly what outcomes can be upheld over time in long-run relations."<snip>
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A BIT MORE DETAIL:
John von Neumann and Oskar Morgenstern (1944) introduced the strategic normal game, strategic extensive game, the concept of pure/mixed strategies, coalitional games as well as the axiomatization of expected utility theory, which was so useful for economics under uncertainty. They employed the "maximin" solution concept derived earlier by John von Neumann (1928) to solve simple strategic, zero-sum normal games.
In 1950, John Nash introduced the concept of a "Nash Equilibrium" (NE), which became the organizing concept under Game Theory -- even though the concept actually stretched as far back as Cournot (1838). Nash followed this up in 1951 with the concept of a "Nash Bargaining Solution" (NBS) for coalitional games.
Then the floodgates opened for the refinement of Nash Equilibrium. In the field of non-cooperative games, R. Duncan Luce and Howard Raiffa (1957) provided the first popular textbook on game theory and, in it, they formalized the idea of the Iterated Elimination of Dominated Strategies (IEDS) method for Strategic Normal Games and introduced the concept of "Repeated Game" (static games which are played several times over). H.W. Kuhn (1953) introduced extensive games with "imperfect information" (i.e. where one does not know what moves have already been played by other players). William Vickrey (1961) provided the first formalization of "auctions". Reinhard Selten (1965) developed the concept of a "Subgame Perfect Equilibrium" (SPE) (i.e. elimination by backward induction) as a refined solution for extensive form games. John C. Harsanyi (1967-8) developed the concept of a "Bayesian Nash Equilibrium" (BNE) for Bayesian games (i.e. games with incomplete information - where there is some uncertainty surrounding moves, or where "nature" plays as well.)
In coalitional (co-operative) games further refinements also occurred. Lloyd Shapley (1953) introduced the concept of the "Shapley Value" and the "Core" (which had been originally conceived by F.Y. Edgeworth (1881)) as solutions to Coalitional Games. Throughout the early 1960s, Robert J. Aumann and Martin Shubik began to apply cooperative game theory extensively throughout economics (e.g. industrial organization, general equilibrium, monetary theory, etc.), and, in the process, went on to invent several solution concepts for coalitional games (e.g. Bargaining Set, Strong Equilibrium), "large games" with infinite players and early statements of the "Folk Theorems" (solution concepts for Repeated Games). David Schmeidler (1969) developed the "Nucleolus" solution for coalitional games.
Further developments emerged in the 1970s. John C. Harsanyi (1973) provided a remarkably insightful new interpretation of the concept of a "mixed strategy". Robert J. Aumann (1974) defined "Correlated Equilibrium" for Bayesian Games while Reinhard Selten (1975) introduced "Trembling Hand Equilibrium" for Bayesian Games. Further definitions came: Robert J. Aumann (1976) formally defined the concept of "Common Knowledge", opening a floodgate of literature, while B.D. Bernheim and D.G. Pearce (1984) formalized the concept of "rationalizability".
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Choice and Consequence by Thomas Schelling
Micro Motives and Macro Behavior (Fels Lectures on Public Policy Analysis) by Thomas C. Schelling
The Strategy of Conflict (Paperback)
by Thomas C. Schelling
4game theory (and the study of culture): the concept of focal points. He observed that in real life bargaining each player would rather make a concession than fail to reach any agreement at all. And there are a wide range of outcomes that would be preferable to both of them than no agreement at all. Now without some procedure to select among those acceptable alternatives, people might never come to a satisfactory agreement. This is where the key concept of "focal points" comes into play. Schelling defines focal points as "intuitively perceived mutual expectations, shared appreciations, preoccupations, obsessions, and sensitivities to suggestion." He criticized traditional game theorists for failing to recognize that "players" actually achieve much better coordination and cooperation when they are able to rely upon focal points. Although he does not make this analogy, it seems that focal points represent some sort of a "template" or "blueprint" that helps to unify understanding and coordinate action. However, for Schelling, "focal points" are quite arbitrary-whether and to what degree they serve to coordinate action and expectations is the key question.
This is one of the key insights in the book, but only one. He also has a fascinating discussion of threats, promises, and credibility and the relation of these issues to national security issues. The connection is explored further in Schelling's Arms and Influence.
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Aumann entered game theory in 1959 to carefully distinguish between infinitely and finitely repeated games. With Bezalel Peleg in 1960, Aumann formalized the notion of a coalitional game without transferable utility (NTU) - one of the organizing beacons of his later research. With Michael Maschler (1963), he introduced the concept of a "bargaining set". In 1974, Aumann went on to identify "correlated equilibrium" in Bayesian games. In 1975, Aumann went on to prove a convergence theorem for the Shapley value. In 1976, he formally defined the concept of "Common Knowledge". Also in 1976, in an unpublished paper with Lloyd Shapley, Aumann provided the perfect folk theorem using the limit of means criterion. His ruminations on the role of game theory in economic analysis are wonderfully laid out in Aumann (1985).
Major Works of Robert J. Aumann
"Acceptable Points in General Cooperative n-Person Games", 1959, in Contributions to the Theory of Games IV, Annals of Math. Study
"Von Neumann-Morgenstern Solutions to Cooperative Games Without Side Payments" with B. Peleg, 1960, Bulletin of the American Mathematical Society.
"Acceptable Points in Games of Perfect Information", 1960, Pacific Journal of Mathematics
"Linearity of Unrestrictedly Transferable Utilities", 1960, Naval Research Logistics Quarterly
"Spaces of Measurable Transformations", 1960, Bulletin of AMS
"The Core of a Cooperative Game Without Side Payments", 1961, Transactions of the American Mathematical Society
"Almost Strictly Competitive Games", 1961, Journal of the Society for Industrial and Applied Mathematics.
"Utility Theory Without the Completeness Axiom", 1962, Econometrica.
"A Definition of Subjective Probability" with F.J. Anscombe, 1963, Annals of Mathematical Statistics
"The Bargaining Set for Cooperative Games", with M. Maschler, 1964, in Advances in Game Theory,
"Mixed and Behavior Strategies in Infinite Extensive Games", 1964, in Advances in Game Theory.
Values of Non-Atomic Games, with L.S. Shapley, 1964.
"Markets with a Continuum of Traders", 1964, Econometrica.
"A Variational Problem Arising in Economics", with M. Perles, 1965, Journal of Mathematical Analysis and Applications.
"Integrals of Set-Valued Functions", 1965, Journal of Mathematical Analysis and Applications.
"A Method of Computing the Kernel of n-Person Games", with B. Peleg and P. Rabinovitz, 1965, Mathematics of Computation.
"Game-Theoretic Aspects of Gradual Disarmament", with M. Maschler, 1966, Mathematica
"Existence of a Competitive Equilibrium in Markets with a Continuum of Traders", 1966, Econometrica.
"A Survey of Cooperative Games Without Side Payments", 1967, in Essays in Mathematical Economics in Honor of Oskar Morgenstern.
"Random Measure Preserving Transformations", 1967, in Proceedings of the Fifth Berkeley Symposium.
"Measurable Utility and the Measurable Choice Theorem", 1969, in La D&eacut;cision.
"Some Thoughts on the Minimax Principle" with M. Maschler, 1972, Management Science.
"Disadvantegous Monopolies", 1973, JET.
"Subjectivity and Correlation in Randomized Strategies", 1974, JMathE.
Values of Non-Atomic Games, with L.S. Shapley, 1974.
"A Note on Gale's Example", with B. Peleg, 1974, JMathE.
"Cooperative Games with Coalition Structures", with J. Dréze, 1975, International Journal of Game Theory.
"Values of Markets with a Continuum of Traders", 1975, Econometrica.
"An Elementary Proof that Integration Preserves Uppersemicontinuity", 1976, JMathE.
"Agreeing to Disagree", 1976, Annals of Statistics.
"Solution Notions for Continuingly Competitive Situations", with L.S. Shapley, 1976.
"Orderable Set Functions and Continuity III: Orderability and Absolute Continuity", with Uri Rothblum, 1977, SIAM Journal on Control and Optimization.
"The St. Petersburg Paradox: A Discussion of some Recent Comments", 1977, JET.
"Power and Taxes", with M. Kurz, 1977, Econometrica.
"Core and Value for a Public Goods Economy: An example", with R.J. Gardner and R.W. Rosenthal, 1977, JET.
"On the Rate of Convergence of the Core", 1979, IER.
"Recent Developments in the Theory of the Shapley Value", 1978, in Proceedings of the International Congress of Mathematicians.
"Survey of Repeated Games", 1981, in Essays in Game Theory and Mathematical Economics in Honor of Oskar Morgenstern
"Approximate Purification of Mixed Strategies", with Katznelson, Radner, Rosenthal and Weiss, 1983, Mathematics of Operations Research
"Voting for Public Goods", with M. Kurz and A. Neyman, 1983, RES.
"An Axiomatization of the Non-Transferable Utility Value", 1985, Econometrica.
"Game Theoretic Analysis of a Bankruptcy Problem from the Talmud", with M. Maschler, 1985, JET.
"What is Game Theory Trying to Accomplish?", 1985, in Arrow and Honkaphola, editors, Frontiers in Economics.
"On the Non-Transferable Utility Value: A Comment on the Roth-Shafer Examples", 1985, Econometrica.
"Values of Markets with Satiation or Fixed Prices", with J. Dréze, 1986, Econometrica.
"Game Theory", 1987, in New Palgrave.
"Power and Public Goods", with M. Kurz and A. Neyman, 1987, JET.
"Correlated Equilibrium as an Expression of Bayesian Rationality", 1987, Econometrica.
"Endogenous Formation of Links between Players and of Coalitions: An Application of the Shapley value", with R.B. Myerson 1988, in Roth, editor, The Shapley Value.
"Cooperation and Bounded Recall", with S. Sorin, 1989, GamesEB.
Lectures on Game Theory, 1989.
"Nash Equilibria are Not Self-Enforcing", 1990, in Gabszewicz et al, editors, Economic Decision-Making
"Irrationality in Game Theory", 1992, in Dasgupta et al, editors, Economic Analysis of Markets and Games, Essays in Honor of Frank Hahn.
"Long-Term Competition: A game-theoretic analysis", with L.S. Shapley, 1994, in Gale et al, editors, Essays in Game Theory
"Backward Induction and Common Knowledge of Rationality", 1995, GamesEB.
Repeated Games of Incomplete Information with M. Maschler, 1995.
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