Quem foi Robert Aumann?
Robert Aumann nasceu em 1930 em Frankfurt, Alemanha. É um dos teóricos mais destacados da Teoria de Jogos. Foi agraciado com o Prémio Nobel em 2005, juntamente com Thomas Schelling “por ter ampliado a nossa compreensão do conflito e da cooperação através do análise da Teoria de Jogos”.
Robert Aumann era judeu e emigrou para os Estados Unidos onde foi doutorado em matemática em 1955, no Massachusetts Institute of Technology (MIT).
Atualmente trabalham na Universidad Hebrea de Jerusalém.
Os desenvolvimentos da teoria dos jogos iniciaram-se em 1959 analisam as diferenças entre os jogos com a repetição finita e infinita. En 1960, com Bezalel Peleg, formalizou a noção de jogo de coligações sem transferência de utilidade. Em 1963, com Michael Maschler, introduziu o conceito de “conjunto de barganha”. Em 1974 identificou o “equilibrio correlacionado” em jogos bayesianos. Em 1975 demonstrou um teorema de convergência para o valor de Shapley. Em 1976 definiu formalmente o conceito de “conhecimento comum”.
Para Robert Aumann, a teoria de jogos é “a teoria mais geral” da Ciência Económica.
Principais obras e papers
“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.
“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.
“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.
“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.
