Aumann received the Nobel Memorial Prize in Economic Sciences in 2005 for his work on conflict and cooperation through game theory analysis.

He is also known for Aumann's agreement theorem, in which he argues that under his given conditions, two Bayesian rationalists with common prior beliefs cannot agree to disagree.

[6] 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.

He has partially vouched for the validity of the "Great Rabbis Experiment" by Doron Witztum, Eliyahu Rips, and Yoav Rosenberg, which was published in Statistical Science.

[7] In 1996, a committee consisting of Robert J. Aumann, Dror Bar-Natan, Hillel Furstenberg, Isaak Lapides, and Rips, was formed to examine the results that had been reported by H.J.

After a long analysis of the experiment and the dynamics of the controversy, stating for example that "almost everybody included [in the controversy] made up their mind early in the game" Aumann concluded: "A priori, the thesis of the Codes research seems wildly improbable... Research conducted under my own supervision failed to confirm the existence of the codes – though it also did not establish their non-existence.

[10] By presenting an unyielding demand, he claims that the Arab states will force Israel to "yield to blackmail due to the perception that it will leave the negotiating room with nothing if it is inflexible".

[12] In 2008, Aumann joined the right-wing religious Zionist Ahi political party, which was led at the time by Effi Eitam and Yitzhak Levy.

The couple had five children; the oldest, Shlomo, a student in Yeshivat Shaalvim, was killed in action while serving as a tank gunner in the Israel Defense Forces's armored corps in the 1982 Lebanon War.

Machon Shlomo Aumann, an institute affiliated with Shaalvim that republishes old manuscripts of Jewish legal texts, was named after him.