Game Theory – Robert John Aumann
Robert John Aumann is an Israeli/American mathematician and a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew University of Jerusalem in Israel. He also holds a visiting position at Stony Brook University and is one of the founding members of the Center for Game Theory in Economics at Stony Brook.
Aumann received the Nobel Memorial Prize in Economics in 2005 for his work on conflict and cooperation through game-theory analysis. He shared the prize with Thomas Schelling.
Aumann's greatest contribution was in the realm of repeated games, which are situations in which players encounter the same situation over and over again.
Aumann was the first to define the concept of correlated equilibrium in game theory, which is a type of equilibrium in non-cooperative games that is more flexible than the classical Nash equilibrium. Furthermore, Aumann has introduced the first purely formal account of the notion of common knowledge in game theory. He collaborated with Lloyd Shapley on the Aumann-Shapley value. He is also known for his agreement theorem, in which he argues that under his given conditions, two Bayesian rationalists with common prior beliefs cannot agree to disagree.[1]
Aumann and Maschler used Game Theory also to analyze Talmudic dilemmas.[2] They were able to solve the mystery about the "division problem", a long-time dilemma of explaining the Talmudic rationale in dividing the heritage of a late husband to his three wives, depending on the worth of the heritage compared to its original worth.[3] The article in that matter was dedicated to a son of Aumann, Shlomo, who was killed during the 1982 Lebanon War while serving as a tank gunner in the Israel Defense Forces's armored corps.
These are some of the themes of Aumann's Nobel lecture, named "War and Peace":[4]
1. War is not irrational, but must be scientifically studied in order to be understood, and eventually conquered;
2. Repeated game study de-emphasizes the "now" for the sake of the "later";
3. Simplistic peacemaking can cause war, while arms race, credible war threats and mutually assured destruction can reliably prevent war.
