Aumann's greatest contribution was in the realm ofrepeated games, which are situations in which players encounter the same situation over and over again.
Aumann andMaschler used game theory to analyzeTalmudic dilemmas.[6] They were able to solve the mystery about the"division problem", a long-standing 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.[7] The article in that matter was dedicated to a son of Aumann, Shlomo, who was killed during the1982 Lebanon War, while serving as atank gunner in theIsrael Defense Forces's armored corps.
Aumann has entered the controversy ofBible codes research. In his position as both areligious Jew and a man of science, the codes research holds special interest to him. He has partially vouched for the validity of the "Great Rabbis Experiment" by Doron Witztum,Eliyahu Rips, and Yoav Rosenberg, which was published inStatistical Science. Aumann not only arranged for Rips to give a lecture on Torah codes in theIsrael Academy of Sciences and Humanities, but sponsored the Witztum-Rips-Rosenberg paper for publication in theProceedings of the National Academy of Sciences. The academy requires a member to sponsor any publication in its Proceedings; the paper was turned down however.[8]
In 1996, a committee consisting ofRobert J. Aumann,Dror Bar-Natan,Hillel Furstenberg, Isaak Lapides, and Rips, was formed to examine the results that had been reported by H.J. Gans regarding the existence of "encoded" text in the bible foretelling events that took place many years after the Bible was written. The committee performed two additional tests in the spirit of the Gans experiments. Both tests failed to confirm the existence of the putative code.
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. So I must return to mya priori estimate, that the Codes phenomenon is improbable".[9]
These are some of the themes of Aumann's Nobel[1] lecture, named "War and Peace":[10]
War is not irrational, but must be scientifically studied in order to be understood, and eventually conquered;
Repeated game study de-emphasizes the "now" for the sake of the "later";
Simplistic peacemaking can cause war, while an arms race, credible war threats and mutually assured destruction can reliably prevent war.
Aumann is a member ofProfessors for a Strong Israel (PSI), a right-wing political group. Aumann opposedthe disengagement from Gaza in 2005 claiming that it was a crime againstGush Katif settlers and a serious threat to the security of Israel. Aumann drew on a case ingame theory called theBlackmailer Paradox to argue that giving land to the Arabs is strategically foolish based on the mathematical theory.[11] By presenting an unyielding demand, he claims that the Arab states will force Israel to "yield toblackmail due to the perception that it will leave the negotiating room with nothing if it is inflexible".
As a result of his political views, and his use of his research to justify them, the decision to give him the Nobel prize[1] was criticized in the European press. A petition to cancel his prize garnered signatures from 1,000 academics worldwide.[12]
In a speech to the religious Zionist youth movement,Bnei Akiva, Aumann got that Israel is in "deep trouble" due to his belief that anti-ZionistSatmar Jews might have been right in their condemnation of the original Zionist movement. "I fear the Satmars were right", he said, and quoted a verse fromPsalm 127: "Unless the Lord builds a house, its builders toil on it in vain." Aumann feels that the historical Zionist establishment failed to transmit its message to its successors, because it was secular. The only way that Zionism can survive, according to Aumann, is if it has a religious basis.[13]
Aumann married Esther Schlesinger in April 1955 inBrooklyn. They had met in 1953, when Esther, who was from Israel, was visiting the United States. The couple had five children; the oldest, Shlomo, a student inYeshivat Shaalvim, was killed in action while serving as atank gunner in theIsrael Defense Forces's armored corps in the1982 Lebanon War.Machon Shlomo Aumann, an institute affiliated with Shaalvim that republishes old manuscripts of Jewish legal texts, was named after him. Esther died ofovarian cancer in October 1998. In late November 2005, Aumann married Esther's widowed sister, Batya Cohn.[1]
^Aumann, R.H.; Furstenberg, H.; Lapides, I.; Witztum, D."Analyses of the Gans Committee Report".The Federmann Center for the Study of Rationality. Retrieved20 April 2024.