Robert J. Aumann

The 2005 John von Neumann Theory Prize is awarded by the Institute for Operations Research and the Management Sciences to Robert J. Aumann of the Hebrew University of Jerusalem in recognition of his fundamental contributions to game theory and related areas.

Beginning with the 1944 publication of von Neumann’s Theory of Games and Economic Behavior (with Oskar Morgenstern), game theory has played an important role in operations research and management science, providing a framework for the analysis of complex systems where multiple decision-makers, driven by individual incentives, operate. Aumann has played an essential and indispensable role in game theory’s development for almost half a century. The common theme in Aumann’s work is a unified view of rational behavior. His scientific contributions are characterized by an unusual combination of depth and breadth: they are path-breaking, innovative, comprehensive and rigorous. Aumann’s work introduced basic concepts and principles, created appropriate tools for their study, developed theoretic foundations for significant ideas, established important relationships and analyzed various particular applications.

Specific contributions include:

• Modeling perfect competition in multi-agent systems with many participants through games with a continuum of players. He has studied various game-theoretic tools in this framework (partly in collaboration with others, including Lloyd Shapley), inspiring others to apply it to the Internet, traffic routing and congestion.
• Introducing the concept of correlated equilibrium – an important mechanism in game theory engineering that is natural in its formulation, is based on intuitive dynamics, is tractable (computable) and has an appealing convexity structure.
• Formulating the interaction of information among agents and formalizing the notion of common knowledge. Ideas Aumann introduced are fundamental in the understanding of the strategic value of information in multi-agent systems.
• Laying the foundations for the theory of repeated games that model long-term interactions among decision-makers. Aumann’s book, Repeated Games with Incomplete Information, co-authored with Michael Maschler, won the Lanchester Prize in 1995.
• Introducing the bargaining set in coalitional games (with Michael Maschler) and the extensive study of cooperative games with transferable and nontransferable utility.
• Developing an axiomatic foundation of subjective quantification of uncertainty.

Aumann is a member of the US National Academy of Science and of the Israeli Academy of Sciences and Humanities. He has received honorary doctorates from the University of Bonn, Université Catholique de Louvain and the University of Chicago, in addition to numerous prizes. He was the Founding Area Editor in Game Theory of Mathematics of Operations Research and is the Founding President of the Game Theory Society, reflecting his central and fundamental role in guiding and leading the development of the study of decision-making in multi-agent systems.

Aumann and Maschler, with the collaboration of Richard E. Sterns, were honored for their book Repeated Games with Incomplete Information, published by MIT press in 1995.

The Lanchester Prize Committee cited the work of Aumann and Maschler as "representing a landmark contribution to the theory of repeated games, which has profoundly influenced economic thinking in recent decades." The theory about relationships between rational decision makers involving repeated interaction over time, developed by Aumann and Maschler, places particular emphasis on the strategic use of information between the parties. Their theory delineates how much to reveal and how much to conceal, when exactly to do it, whether or not to believe the revealed information, and so forth. The award further cites: "An important conclusion is that the 'solution space' of a game typically expands when it is played repeatedly; much more subtle forms of cooperations and stability arise in repeated interaction than in single-shot games.

"In addition to its many and varied insights into applied problems, the theory developed in this book involves deep and subtle mathematics, with significant contributions to convexity theory, probability and stochastic processes. The quality of exposition for such highly mathematical material, in which results turn on delicate distinctions, is also exemplary."