Games and Economic Theory

Robert J. Aumann is an eminent scientist. He is one of the greatest thinkers on all aspects of rationality in decision-making. Aumann has played an essential and indispensable role in shaping game theory and much of economic theory, to become the great success it is today. He promotes a unified view of the very wide domain of rational behavior, a domain that encompasses areas of many apparently disparate disciplines, like economics, political science, biology, psychology, mathematics, philosophy, computer science, law, and statistics. Aumann’s research is characterized by an unusual combination of breadth and depth. His scientific contributions are path-breaking, innovative, comprehensive, and rigorous – from the discovery and formalization of the basic concepts and principles, through the development of the appropriate tools and methods for their study, to their application in the analysis of various specific issues. Some of his contributions require very deep and complex technical analysis; others are (as he says at times) “embarrassingly trivial” mathematically, but very profound conceptually. They are all insightful and thought-provoking, and go into the roots and heart of the central issues. It is science at its best. Half a century ago, the collaboration of the mathematician John von Neumann and the economist Oskar Morgenstern resulted in the 1944 publication of their book Theory of Games and Economic Behavior. This is the starting point of the scientific discipline called “game theory.” What is game theory? A better name, suggested by Aumann [55, p. 460], is perhaps “interactive decision theory”. The object of study is the interaction of decision-makers (“players”) whose decisions affect each other. The analysis is from a “rational” viewpoint; that is, each participant would like to obtain those outcomes he prefers most. When there is only one player, this usually leads to a well-defined optimization problem. In contrast, in the multi-person setup of game theory, the preference ranking of a player over the outcomes

[1]  Robert J. Aumann,et al.  EXISTENCE OF COMPETITIVE EQUILIBRIA IN MARKETS WITH A CONTINUUM OF TRADERS , 2020, Classics in Game Theory.

[2]  M. Dufwenberg.  Game theory. , 2011, Wiley interdisciplinary reviews. Cognitive science.

[3]  Polly S Nichols,et al.  Agreeing to disagree. , 2005, General dentistry.

[4]  R. Aumann,et al.  Epistemic Conditions for Nash Equilibrium , 1995 .

[5]  Robert J. Aumann,et al.  Perspectives on Bounded Rationality , 1992, TARK.

[6]  John C. Harsanyi,et al.  Общая теория выбора равновесия в играх / A General Theory of Equilibrium Selection in Games , 1989 .

[7]  R. Aumann,et al.  Cooperation and bounded recall , 1989 .

[8]  Wan-Jin Kim.  On the Rate of Convergence of the Core , 1986 .

[9]  R. Aumann,et al.  Game theoretic analysis of a bankruptcy problem from the Talmud , 1985 .

[10]  Robert J. Aumann,et al.  AN AXIOMATIZATION OF THE NON-TRANSFERABLE UTILITY VALUE , 1985 .

[11]  R. Aumann.  On the Non-transferable Utility Value: A Comment on the Roth-Shafer Examples [Values for Games without Side Payments: Some Difficulties with Current Concepts] [On the Existence and Interpretation of Value Allocations] , 1985 .

[12]  R. Aumann,et al.  Voting for Public Goods , 1983 .

[13]  Roy Radner,et al.  Approximate Purification of Mixed Strategies , 1983, Math. Oper. Res..

[14]  R. Aumann,et al.  Power and taxes in a multi-commodity economy (updated) , 1978 .

[15]  Robert J. Aumann,et al.  Power and Taxes in a multi-commodity economy , 1977 .

[16]  R. Aumann,et al.  Core and value for a public-goods economy: An example , 1977 .

[17]  Robert J. Aumann,et al.  Power and Taxes , 1977 .

[18]  Robert J. Aumann,et al.  The St. Petersburg paradox: A discussion of some recent comments , 1977 .

[19]  R. Aumann.  An elementary proof that integration preserves uppersemicontinuity , 1976 .

[20]  R. J. Aumann,et al.  Cooperative games with coalition structures , 1974 .

[21]  Bezalel Peleg,et al.  A note on Gale's example , 1974 .

[22]  R. Aumann.  Subjectivity and Correlation in Randomized Strategies , 1974 .

[23]  M. Lings,et al.  Articles , 1967, Soil Science Society of America Journal.

[24]  Robert J. Aumann,et al.  Chapter 1. A Survey of Cooperative Games Without Side Payments , 1967 .

[25]  R. Aumann.  INTEGRALS OF SET-VALUED FUNCTIONS , 1965 .

[26]  Bezalel Peleg,et al.  A method for computing the kernel of $n$-person games , 1965 .

[27]  Robert J . Aumann,et al.  28. Mixed and Behavior Strategies in Infinite Extensive Games , 1964 .

[28]  F. J. Anscombe,et al.  A Definition of Subjective Probability , 1963 .

[29]  R. Aumann.  Borel structures for function spaces , 1961 .

[30]  R. Aumann.  Almost Strictly Competitive Games , 1961 .

[31]  R. Aumann,et al.  THE BARGAINING SET FOR COOPERATIVE GAMES , 1961 .

[32]  R. Aumann.  The core of a cooperative game without side payments , 1961 .

[33]  Robert J. Aumann,et al.  Linearity of unrestrictedly transferable utilities , 1960 .

[34]  Robert J. Aumann,et al.  Spaces of measurable transformations , 1960 .

[35]  R. Aumann.  Acceptable points in games of perfect information. , 1960 .

[36]  R. Aumann,et al.  VON NEUMANN-MORGENSTERN SOLUTIONS TO COOPERATIVE GAMES WITHOUT SIDE PAYMENTS , 1960, Classics in Game Theory.

[37]  Joseph B. Kruskal,et al.  Assigning quantitative values to qualitative factors in the naval electronics problem , 1959 .

[38]  Joseph B. Kruskal,et al.  The coefficients in an allocation problem , 1958 .

[39]  R. Aumann.  Asphericity of Alternating Knots , 1956 .

[40]  J. S. Mateo.  The Shapley Value , 2012 .

[41]  G. Patil,et al.  Rejoinder , 2004, Environmental and Ecological Statistics.

[42]  R. Aumann,et al.  Endogenous Formation of Links Between Players and of Coalitions: An Application of the Shapley Value , 2003 .

[43]  R. Aumann.  Backward induction and common knowledge of rationality , 1995 .

[44]  Robert J. Aumann,et al.  Long-Term Competition - A Game-Theoretic Analysis , 1994, Essays in Game Theory.

[45]  R. Aumann.  Economic Applications of the Shapley Value , 1994 .

[46]  Partha Dasgupta,et al.  Economic Analysis of Markets and Games: Essays in Honor of Frank Hahn , 1992 .

[47]  R. Aumann.  Correlated Equilibrium as an Expression of Bayesian Rationality Author ( s ) , 1987 .

[48]  R. Aumann.  Arrow — the Breadth, Depth, and Conscience of the Scholar: an Interview , 1987 .

[49]  R. Aumann,et al.  Values of Markets With Satiation Or Fixed Prices , 1986 .

[50]  1 What Is Game Theory Trying to Accomplish ? , 1985 .

[51]  R. Aumann.  Survey of Repeated Games , 1981 .

[52]  Recent Developments in the Theory of the Shapley Value , 1978 .

[53]  R. Aumann,et al.  Orderable Set Functions and Continuity. III: Orderability and Absolute Continuity , 1977 .

[54]  R. Aumann.  Values of Markets with a Continuum of Traders , 1975 .

[55]  15 Measurable Utility and the Measurable Choice Theorem , 1969 .

[56]  R. Aumann.  Random measure preserving transformations , 1965 .

[57]  R. Aumann,et al.  A variational problem arising in economics , 1965 .

[58]  M. Shelly,et al.  Subjective Programming , 1964 .

[59]  R. Aumann.  Markets with a continuum of traders , 1964 .

[60]  Robert J. Aumann,et al.  UTILITY THEORY WITHOUT THE COMPLETENESS AXIOM: A CORRECTION , 1964 .

[61]  Robert J. Aumann,et al.  Some Thoughts on the Theory of Cooperative Games , 1963 .

[62]  Would you.  Economic Theory and Mathematical Method : An Interview , 2022 .