Robert Aumann

Last updated
Robert Aumann
ySHrAl Avmn 2010.jpg
Aumann in 2010
Born
Robert John Aumann

(1930-06-08) 8 June 1930 (age 89)
Nationality Israeli, American
Alma mater City College of New York
Massachusetts Institute of Technology
Awards Nobel Memorial Prize in Economics
John von Neumann Theory Prize
Harvey Prize in Science and Technology
Israel Prize for Economical Research
Scientific career
Fields Mathematical economics
Game theory
Doctoral advisor George Whitehead, Jr.
Doctoral students David Schmeidler
Sergiu Hart
Abraham Neyman
Yair Tauman

Robert John Aumann (Hebrew name: ישראל אומן, Yisrael Aumann; born June 8, 1930) 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 Stony Brook Center for Game Theory.

Hebrew names are names that have a Hebrew language origin, classically from the Hebrew Bible. They are mostly used by Jews and Christians, but many are also adapted to the Muslim world, particularly if a Hebrew name is mentioned in the Qur'an. A typical Hebrew name can have many different forms, having been adapted to the phonologies of many different languages. A common Jewish practice worldwide is to give a Hebrew name to a child that is used religiously throughout its lifetime.

Israel country in the Middle East

Israel, also known as the State of Israel, is a country in Western Asia, located on the southeastern shore of the Mediterranean Sea and the northern shore of the Red Sea. It has land borders with Lebanon to the north, Syria to the northeast, Jordan on the east, the Palestinian territories of the West Bank and Gaza Strip to the east and west, respectively, and Egypt to the southwest. The country contains geographically diverse features within its relatively small area. Israel's economic and technological center is Tel Aviv, while its seat of government and proclaimed capital is Jerusalem, although the state's sovereignty over Jerusalem has only partial recognition.

Americans Citizens, or natives, of the United States of America

Americans are nationals and citizens of the United States of America. Although nationals and citizens make up the majority of Americans, some dual citizens, expatriates, and permanent residents may also claim American nationality. The United States is home to people of many different ethnic origins. As a result, American culture and law does not equate nationality with race or ethnicity, but with citizenship and permanent allegiance.

Contents

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

The Nobel Memorial Prize in Economic Sciences, commonly referred to as the Nobel Prize in Economics, is an award for outstanding contributions to the field of economics, and generally regarded as the most prestigious award for that field. The award's official name is The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel.

Game theory is the study of mathematical models of strategic interaction among rational decision-makers. It has applications in all fields of social science, as well as in logic, systems science, and computer science. Originally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

Thomas Schelling American economist

Thomas Crombie Schelling was an American economist and professor of foreign policy, national security, nuclear strategy, and arms control at the School of Public Policy at University of Maryland, College Park. He was also co-faculty at the New England Complex Systems Institute. He was awarded the 2005 Nobel Memorial Prize in Economic Sciences for "having enhanced our understanding of conflict and cooperation through game-theory analysis."

Biography

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 the Rabbi Jacob Joseph School, a yeshiva high school in New York City. He graduated from the City College of New York in 1950 with a B.Sc. in Mathematics. He received his M.Sc. in 1952, and his Ph.D. in Mathematics in 1955, both from the Massachusetts Institute of Technology. His doctoral dissertation, Asphericity of Alternating Linkages, concerned knot theory. His advisor was George Whitehead, Jr.

Weimar Republic Germany state in the years 1918/1919–1933

The Weimar Republic is an unofficial historical designation for the German state from 1918 to 1933. The name derives from the city of Weimar, where its constitutional assembly first took place. The official name of the republic remained Deutsches Reich unchanged from 1871, because of the German tradition of substates. Although commonly translated as ’German Empire’, the word Reich here better translates as ’realm’, in that the term does not have monarchical connotations in itself. The Reich was changed from a constitutional monarchy into a republic. In English, the country was usually known simply as Germany.

United States Federal republic in North America

The United States of America (USA), commonly known as the United States or America, is a country comprising 50 states, a federal district, five major self-governing territories, and various possessions. At 3.8 million square miles, the United States is the world's third or fourth largest country by total area and is slightly smaller than the entire continent of Europe. With a population of over 327 million people, the U.S. is the third most populous country. The capital is Washington, D.C., and the most populous city is New York City. Most of the country is located contiguously in North America between Canada and Mexico.

<i>Kristallnacht</i> Pogrom against Jews throughout Nazi Germany on 9–10 November 1938

Kristallnacht or the Night of Broken Glass, also called the November Pogrom(s), was a pogrom against Jews carried out by SA paramilitary forces and civilians throughout Nazi Germany on 9–10 November 1938. The German authorities looked on without intervening. The name Kristallnacht comes from the shards of broken glass that littered the streets after the windows of Jewish-owned stores, buildings and synagogues were smashed.

In 1956 he joined the Mathematics faculty of the Hebrew University of Jerusalem and has been a visiting professor at Stony Brook University since 1989. He has held visiting professorship at the University of California, Berkeley (1971, 1985–1986), Stanford University (1975–1976, 1980–1981), and Universite Catholique de Louvain (1972, 1978, 1984). [1]

Hebrew University of Jerusalem Israeli University in Jerusalem

The Hebrew University of Jerusalem is Israel's second-oldest university, established in 1918, 30 years before the establishment of the State of Israel. The Hebrew University has three campuses in Jerusalem and one in Rehovot. The world's largest Jewish studies library is located on its Edmond J. Safra Givat Ram campus.

Stony Brook University Public university in Stony Brook, New York, United States

The State University of New York at Stony Brook, commonly referred to as Stony Brook University (SBU), is a public sea-grant and space-grant research university in Stony Brook, New York. It is one of four university centers of the State University of New York system.

University of California, Berkeley Public university in California, USA

The University of California, Berkeley is a public research university in Berkeley, California. It was founded in 1868 and serves as the flagship campus of the ten campuses of the University of California. Berkeley has since grown to instruct over 40,000 students in approximately 350 undergraduate and graduate degree programs covering numerous disciplines.

Mathematical and scientific contribution

Aumann at a meeting in 2008. Aumann-1080b.jpg
Aumann at a meeting in 2008.

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.

In game theory, a repeated game is an extensive form game that consists of a number of repetitions of some base game. The stage game is usually one of the well-studied 2-person games. Repeated games capture the idea that a player will have to take into account the impact of his or her current action on the future actions of other players; this impact is sometimes called his or her reputation. Single stage game or single shot game are names for non-repeated games.

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. [2]

In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. It was first discussed by mathematician Robert Aumann in 1974. The idea is that each player chooses their action according to their observation of the value of the same public signal. A strategy assigns an action to every possible observation a player can make. If no player would want to deviate from the recommended strategy, the distribution is called a correlated equilibrium.

In game theory, the Nash equilibrium, named after the mathematician John Forbes Nash Jr., is a proposed solution of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.

Common knowledge is a special kind of knowledge for a group of agents. There is common knowledge of p in a group of agents G when all the agents in G know p, they all know that they know p, they all know that they all know that they know p, and so on ad infinitum.

Aumann and Maschler used game theory to analyze Talmudic dilemmas. [3] 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. [4] 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.

Political views

These are some of the themes of Aumann's Nobel lecture, named "War and Peace": [5]

  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 an arms race, credible war threats and mutually assured destruction can reliably prevent war.

Aumann is a member in the Professors for a Strong Israel (PSI), a right-wing political group. Aumann opposed the disengagement from Gaza in 2005 claiming it is a crime against Gush Katif settlers and a serious threat to the security of Israel. Aumann draws on a case in game theory called the Blackmailer Paradox to argue that giving land to the Arabs is strategically foolish based on the mathematical theory. [6] By presenting an unyielding demand, the Arab states force Israel to "yield to blackmail 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 was criticized in the European press. A petition to cancel his prize garnered signatures from 1,000 academics worldwide. [7]

In a speech to a religious Zionist youth movement, Bnei Akiva, Aumann claimed 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 the Satmars were right", he said, and quoted a verse from Psalm 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. [8]

In 2008, Aumann joined the new political party Ahi led by Effi Eitam and Yitzhak Levy. [9]

Torah codes controversy

Aumann has entered the controversy of Bible codes research. In his position as both a religious 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 in Statistical Science. Aumann not only arranged for Rips to give a lecture on Torah codes in the Israel Academy of Sciences and Humanities, but sponsored the Witztum-Rips-Rosenberg paper for publication in the Proceedings of the National Academy of Sciences. The Academy requires a member to sponsor any publication in its Proceedings; the paper was turned down however. [10]

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. 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 my a priori estimate, that the Codes phenomenon is improbable". [11]

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 oldest, Shlomo, was killed in action while serving in the Israel Defense Forces in the 1982 Lebanon War. Esther died of ovarian cancer in October 1998. In late November 2005, Aumann married Esther's widowed sister, Batya Cohn. [12]

Honours and awards

Publications

See also

Related Research Articles

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References

  1. "CV (Robert J. Aumann)". Einstein Institute of Mathematics. Retrieved 4 June 2017.
  2. Aumann, Robert J. (1976). "Agreeing to Disagree". The Annals of Statistics. Institute of Mathematical Statistics. 4 (6): 1236–1239. doi:10.1214/aos/1176343654. ISSN   0090-5364. JSTOR   2958591.
  3. Aumann, Robert J. (2003). "Risk Aversion in the Talmud" (PDF). Economic Theory . Springer-Verlag. 21 (2–3): 233–239. doi:10.1007/s00199-002-0304-9 . Retrieved July 29, 2015.
  4. Aumann, Yisrael (1999). "B'Inyan Mi SheHayah Nasui Shalosh Nashim" בענין מי שהיה נשוי שלוש נשים [Regarding One who was Married to Three Wives](pdf). מוריה (Moriah) (in Hebrew). Jerusalem: Machon Yerushalayim. 22 (3–4): 98–107. Retrieved July 29, 2015.[ verification needed ]
  5. Robert Aumann's Nobel Prize in Economics lecture, Stockholm, 8 December 2005
  6. Aumann, Robert (July 3, 2010). "Game Theory and negotiations with Arab countries". Aish.com.
  7. "Archived copy". Archived from the original on 2010-12-15. Retrieved 2010-02-05.CS1 maint: archived copy as title (link)
  8. http://www.ynetnews.com/articles/0,7340,L-3205817,00.html
  9. http://fr.jpost.com/servlet/Satellite?pagename=JPost/JPArticle/ShowFull&cid=1202246357040 Archived 2012-01-04 at the Wayback Machine http://www.eitam.org.il/info_en.asp?id=2062535187 Archived 2008-06-26 at the Wayback Machine
  10. Szpiro, George G. (2006), The Secret Life of Numbers: 50 Easy Pieces on how Mathematicians Work and Think, National Academies Press, p. 190, ISBN   9780309096584 .
  11. Aumann, R.H., H. Furstenberg, I. Lapides, and D. Witztum (July 2004). "Analyses of the 'Gans' Committee Report (#365)" (PDF). Center for the Study of Rationality, The Hebrew University of Jerusalem. Archived from the original (PDF) on 2006-06-25. Retrieved 2006-06-20.Cite journal requires |journal= (help)CS1 maint: multiple names: authors list (link)
  12. "Robert J. Aumann – Autobiography". Nobelprize.org.
  13. "Book of Members, 1780–2010: Chapter A" (PDF). American Academy of Arts and Sciences. Retrieved 27 April 2011.
  14. "Israel Prize Official Site – Recipients in 1994 (in Hebrew)".
  15. Nemmers Prize Recipients Archived 2006-02-22 at the Wayback Machine Northwestern University
  16. "The EMET Prize for Art, Science and Culture in the Social Sciences".
  17. "Recipients of Yakir Yerushalayim award (in Hebrew)". Archived from the original on 2013-10-22. City of Jerusalem official website
Awards
Preceded by
Finn E. Kydland
Edward C. Prescott
Laureate of the Nobel Memorial Prize in Economics
2005
Served alongside: Thomas C. Schelling
Succeeded by
Edmund S. Phelps