### Who Is Robert J. Aumann?

Robert J. Aumann is a mathematician who received the 2005 Nobel Prize in Economics along with his co-recipient, Thomas Schelling. Aumann's most lauded contributions to the fields of math and economics have been in the realm of game theory.

### Key Takeaways

- Robert Aumann is a mathematician who has made important contributions to the field of game theory.
- Aumann's work focuses on the theory of repeated games under various conditions of information and knowledge available to the players.
- He was awarded the 2005 Nobel Prize in Economics for his contribution to the understanding of repeated cooperative and competitive games.

### Understanding Robert J. Aumann

Aumann was born in Germany in 1930. In 1938, his family fled to the U.S. to escape the Nazis. He eventually moved to Jerusalem, where he has lived and worked ever since.

Aumann earned his PhD from the Massachusetts Institute of Technology in 1955, focusing on the mathematical theory of rope knots. From there, he went on to work for the Analytical Research Group at Princeton, where his work focused on the theoretical problem of defending a city from aerial attack. At that time he began to focus on game theory, a tool he had encountered through the mathematician John Nash while at MIT. In 1956, Aumann took a position as instructor of mathematics at the Hebrew University of Jerusalem.

#### Religious Work

Aumann is a religious Jew and has gained attention outside of the fields of math and economics for using game theory to analyze dilemmas in the Talmud, or Jewish scripture. He also briefly stirred controversy for his interest in bible or Torah codes. However, after delving into experimentation and research with peers, Aumann determined that the experiment failed to confirm the existence of any definitive code.

Aumann has given lectures within Israel on the importance of maintaining religious belief in order to keep the state alive. He has long been a vocal proponent of Israel as a Jewish state and cited game theory as he argued against the Israeli withdrawal from Gaza in 2005.

### Contributions

Aumann's most noted contributions lie in the field of game theory.

#### Repeated Games and the Folk Theorem

Robert Aumann first grabbed the attention of the mathematics world with his work on repeated games, which he published as a set of theories in 1959. He later developed and published his Folk Theorem. Taken together, these publications describe the relationship between equilibrium behavior in repeated games and cooperative behavior, the basis for the concept of correlated equilibrium.

#### Correlated Equilibrium

Aumann was the first person to articulate correlated equilibrium as a phenomenon. Correlated equilibrium is similar to Nash's Equilibrium, though considered more flexible. In a correlated equilibrium, the players in a game choose based on some piece of public information available to each player and assuming that the other players will not deviate from their best strategy given the same information. A repeated game where each player knows the past choices of the other players can converge to a correlated equilibrium.

#### Incomplete Information

In collaboration with Michael Maschler, Aumann explored the theory of games with incomplete information. This involves games where the players do not have the same information, and the information that they have may be dependent or independent of the other players' choices and information. Aumann's work in this area would go on to help shape U.S. arms control negotiation strategy during the Cold War.