Robert J. Aumann (1930-)

Premio Nobel  2005

Robert Aumann es uno de los teóricos más destacados de la Teoría de Juegos.  El Premio Nobel le ha sido concedido compartiéndolo con Thomas Schelling "por haber ampliado nuestra comprensión del conflicto y la cooperación mediante el análisis de la Teoría de Juegos".

Robert Aumann y Martínez Coll
en Stony Brook, USA, julio 1991

Judío, nacido en Frankfurt, Alemania, emigró a los Estados Unidos donde se doctoró en matemáticas en 1955, en el Massachusetts Institute of Technology (MIT). Actualmente trabaja en la Universidad Hebrea de Jerusalén. Tiene la doble nacionalidad, USA e Israel.

Sus desarrollos de la Teoría de los Juegos se iniciaron en 1959 al analizar las diferencias entre los juegos con repetición finita e infinita. En 1960, con Bezalel Peleg, formalizó la noción de juego de coaliciones sin transferencia de utilidad. En 1963, con Michael Maschler, introdujo el concepto de "bargaining set". En 1974 identificó el "equilibrio correlacionado" en juegos bayesianos. En 1975 demostró un teorema de convergencia para el valor de Shapley. En 1976 definió formalmente el concepto de "conocimiento común".

Para Robert Aumann, la teoría de juegos es "la teoría más general" de la ciencia económica.

OBRAS

• "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.