Robert Aumann

Israel Robert John Aumann (Frankfurt am Main, June 8, 1930) is an Israeli mathematician.

Aumann received the Nobel Prize in Economic Sciences in 2005 for his work on conflict and cooperation through game theory analysis. He shared the prize with Thomas Schelling.

Early years

Aumann was born in Frankfurt am Main (Germany) and fled to the United States with his family in 1938, two weeks before the Kristallnacht pogrom. He attended Rabbi Jacob Joseph School, a New York City Yeshiva.

Academic career

Aumann graduated in mathematics from the City College of New York in 1950. In 1952 he obtained a master's degree and in 1955 a doctorate in Mathematics, both from the Massachusetts Institute of Technology. Her doctoral thesis, Asphericity of Alternating Linkages , was about knot theory. Her advisor was George Whitehead, Jr.

In 1956 he joined the Faculty of Mathematics at the Hebrew University of Jerusalem and since 1989 he has been a visiting professor at Stony Brook University. He has been a visiting professor at the University of California, Berkeley (1971, 1985-1986), Stanford University (1975-1976, 1980-1981), and the Catholic University of Louvain (1972, 1978, 1984).

Mathematical and scientific contribution

Aumann's greatest contribution was in the area 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 classic Nash equilibrium. Furthermore, Aumann 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.

Aumann and Maschler used game theory to analyze Talmudic dilemmas. They were able to solve the mystery about the 'division problem', an ancient dilemma to explain Talmudic logic in the division of inheritance of a deceased husband among his three wives based on the value of the inheritance compared to its original value. The article in question was dedicated to Aumann's son, Shlomo, who died during the 1982 Lebanon War, while serving as tank gunner in the armored corps of the Israel Defense Forces.

Among Aumann's doctoral students are: Bezalel Peleg, David Schmeidler, Shmuel Zamir, Elon Kohlberg, Zvi Artstein, Benyamin Shitovitz, Eugene Wesley, Sergiu Hart, Abraham Neyman, Yair Tauman, Dov Samet, Ehud Lehrer, Yossi Feinberg, Itai Arieli, Uri Weiss and Yosef Zohar.

Controversy over Torah codes

Aumann has entered into the controversy of research into biblical codes. As a religious Jew and man of science, research into codes particularly interests him. He has partially endorsed the validity of the 'Great Rabbis Experiment'. by Doron Witztum, Eliyahu Rips and Yoav Rosenberg, published in Statistical Science. Aumann not only arranged for Rips to give a lecture on Torah codes at the Israeli Academy of Sciences and Humanities, but sponsored Witztum-Rips-Rosenberg's work for publication in the Proceedings of the National Academy of Sciences. The academy requires that a member sponsor any publication in its Proceedings; However, the work was rejected.

In 1996, a committee composed of Robert J. Aumann, Dror Bar-Natan, Hillel Furstenberg, Isaak Lapides and Rips was formed to examine the results reported by H.J. Gans on the existence of a "coded" in the Bible that predicted events that took place many years after the Bible was written. The committee performed two additional tests in the spirit of Gans's experiments. Both tests did not confirm the existence of the alleged code.

After a lengthy analysis of the experiment and the dynamics of the controversy, stating, for example, that "almost everyone included [in the controversy] was decided at the beginning of the game,", Aumann concluded:

"A priori, the Codes research thesis seems tremendously improbable... The research carried out under my own supervision did not confirm the existence of the codes, although it did not establish their non-existence either.. So I must return to my a priori estimate, that the phenomenon of the Codes is improbable.

Political opinions

These are some of the topics of Aumann's Nobel lecture, called "War and Peace":

1. War is not irrational, but must be studied scientifically to be understood, and eventually conquered;
2. The study of the repeated game diminishes importance to the "now" for the sake of the "after";
3. Simplistic pacification can provoke war, while the arms race, credible war threats and mutual destruction assured can prevent war in a reliable way.

Aumann is a member of Teachers for a Strong Israel (PSI), a right-wing political group. Aumann opposed the withdrawal from Gaza in 2005, claiming that it is a crime against the Gush Katif settlers and a serious threat to Israel's security. Aumann draws on a game theory case called the Blackmailer's Paradox to argue that ceding land to the Arabs is strategically foolish, based on mathematical theory. By presenting an inflexible demand, the Arab states force Israel to "give in to blackmail due to the perception that it will leave the negotiating room with nothing if it is inflexible."

As a consequence of his political opinions, and the use of his research to justify them, the decision to award him the Nobel Prize was criticized in the European press. A petition to annul his award gathered the signatures of 1,000 academics from around the world.

In a speech to a religious Zionist youth movement, Bnei Akiva, Aumann stated that Israel is in "deep trouble." He revealed his belief that the anti-Zionist Satmar Jews might have been right in their condemnation of the original Zionist movement. "I fear that the Satmar were right," he said, and quoted a verse from Psalm 127: "If the Lord does not build a house, his builders toil in it in vain." # 3. 4;. Aumann believes that the historical Zionist establishment failed to convey its message to its successors, because it was secular. The only way for Zionism to survive, according to Aumann, is for it to have a religious basis.

In 2008, Aumann joined the new political party Ahi, led by Effi Eitam and Yitzhak Levy.

Personal life

Aumann married Esther Schlesinger in April 1955 in Brooklyn. They had met in 1953, when Esther, who was from Israel, was visiting the United States. The couple had five children; the eldest, Shlomo, a student at Yeshiva Shaalvim, was killed in combat while serving in the Israel Defense Forces in the Lebanon War of 1982. Machon Shlomo Aumann, a Shaalvim-affiliated institute that reissues ancient manuscripts of Jewish legal texts, carries its name. Esther died of ovarian cancer in October 1998. In late November 2005, Aumann married Esther's widowed sister, Batya Cohn.

Aumann was a distant relative of Oliver Sacks.

Publications

Some of his most notable publications are listed:

• Values of Non-Atomic Games, Princeton University Press,Princeton, 1974 (with L.S. Shapley)
• Game Theory (in Hebrew), Everyman's University, Tel Aviv, 1981 (with Y. Tauman and S. Zamir), Vols. 1 " 2 "
• Lectures on Game Theory, Underground Classics in Economics, Westview Press, Boulder, 1989
• Handbook of Game Theory with economic applications, Vol 1–3, Elsevier, Amsterdam (coeditó S. Hart)
• Repeated Games with Incomplete Information, MIT Press, Cambridge, 1995 (with M. Maschler)
• Collected Papers, Vol 1–2, MIT Press, Cambridge, 2000
• Asphericity of alternating knots. Ann. of Math. (2) 64 1956 374—392
• «Game theoretic analysis of a bankruptcy problem from the Talmud». Journal of Economic Theory (in English) 36 (2): 195-213. August 1, 1985. ISSN 0022-0531. doi:10.1016/0022-0531(85)90102-4. Consultation on 14 July 2021.