Robert J. Aumann

A boy who fled Nazi Germany in 1938 grew up to prove, in mathematics, why long-term relationships make cooperation possible.

The Nobel citation: “for having enhanced our understanding of conflict and cooperation through game-theory analysis”

Born: June 8, 1930, Frankfurt-on-the-Main, Germany
Shared with: Thomas C. Schelling
Affiliation at the time: University of Jerusalem, Center for RationalityHebrew, Israel

Economics prize

2005

Shared with 1 other laureate.

Age that year

75years

Born in 1930.

Sources cited

Fact-checked September 24, 2026.

His family left Frankfurt for New York in 1938, shortly before Kristallnacht, and his parents lost all their assets in the move.
His doctorate was in knot theory, which he called absolutely useless; fifty years later his grandson studied knots in medical school because DNA can tangle.
In the mid-1960s he advised a US arms-control project alongside three future Nobel laureates: John Harsanyi, Reinhard Selten and Gerard Debreu.
He says his best-known work with the public is a 1985 paper, written with Michael Maschler, that used game theory to explain a puzzling rule in the Talmud.
He brought 34 family members to Stockholm, where his Nobel ceremony began just minutes after the Jewish Sabbath ended.

The breakthrough

Why cooperation can last when people keep meeting again

Game theory is the mathematics of situations where your best choice depends on what others choose. A classic puzzle is that two sides can both lose by each grabbing a short-term advantage, even though cooperating would leave both better off. Aumann was the first to build a full, rigorous theory of games that are played over and over without a fixed end. He pinned down precisely which results can be sustained when the same players keep meeting. The core idea is simple: when there is always a tomorrow, cheating today invites punishment later, so repetition works like a contract that no court has to enforce. Think of a shopkeeper who could overcharge a tourist once, but treats neighbors fairly because they will come back every week. The catch is patience. If the players care too much about today and too little about the future, cooperation falls apart. With Lloyd Shapley he later showed that the threats holding cooperation together can also be believable; Ariel Rubinstein reached a similar result independently. With Michael Maschler he extended the theory to repeated games where one side knows something the other does not, such as a rival's true military strength. He also gave a precise definition of common knowledge, meaning what everyone knows that everyone knows, and introduced correlated equilibrium, which helps explain why a neutral mediator can help both sides.^{[1],[2],[3],[4],[5]}

“Science is exploration – exploration for the sake of exploration, and for nothing else.”

Robert J. Aumann, From his Nobel autobiography, after recalling that the 'useless' knot theory of his doctorate had come to be taught in medical school.^[1]

What it meant for humanity

Aumann's work is theory, not a product, so its effect on lives is indirect: it changed how scholars and policymakers think about when people and nations will cooperate. The Royal Swedish Academy of Sciences described repeated-game theory as the standard tool social scientists now use to study cooperation that lasts over time. It helps explain why cooperation is harder when there are many players, when they meet rarely, when the relationship may soon end, or when no one can see what the others are doing. The Academy's prize materials listed applications ranging from price wars, trade wars and firms colluding to keep prices high to farmers sharing pastures or irrigation water, and countries entering environmental agreements or settling territorial disputes. It also said the approach clarifies why institutions such as merchant guilds, wage negotiations and trade agreements exist at all. His idea of correlated equilibrium gives a reason why rival parties can both gain from a neutral mediator who talks to them separately. His definition of common knowledge opened a field that now reaches into economics, computer science, philosophy and logic. Some of this work began as advice to the US Arms Control and Disarmament Agency during Cold War negotiations with the Soviet Union, though Aumann himself doubts it changed policy much. He also helped found the Hebrew University's Center for the Study of Rationality in 1991, which brings together mathematicians, economists, biologists, psychologists, philosophers and lawyers. Beyond scholars, he has lectured on his game-theory explanation of a Talmudic bankruptcy rule to high school students, synagogue groups and yeshivas, linking an ancient legal text to modern mathematics.

The Royal Swedish Academy of Sciences described repeated-game theory as the standard tool social scientists now use to study long-term cooperation.^[3]
The Nobel press release said the approach helps explain price wars, trade wars, the management of shared resources, and institutions from merchant guilds to international trade agreements.^[2]
Correlated equilibrium, a concept Aumann introduced, shows why rival negotiators can both gain from a neutral mediator, even one who tells each side different things.^[3]
His 1976 paper 'Agreeing to Disagree' gave common knowledge a precise definition and, in his interviewer Sergiu Hart's words, set off a large literature reaching into computer science, philosophy and logic.^[5]
His book with Michael Maschler on repeated games with incomplete information, first written as reports for the US arms-control agency, won the 1995 Lanchester Prize for the best operations research book.^[1]

Impact in numbers

Aumann gave social science a precise answer to an old question: why do selfish people and rival nations sometimes cooperate? His theory of repeated games shows that an ongoing relationship can enforce cooperation without any court, as long as the parties are patient enough to value the future. The Royal Swedish Academy of Sciences calls it the standard framework for studying long-run cooperation, used to understand cartels, trade disputes, shared natural resources and territorial conflicts. His definitions of common knowledge and correlated equilibrium became basic tools in economics, computer science and philosophy, and his work with Maschler grew out of Cold War arms-control research. These ideas shape how experts reason about negotiation and institutions, but their effect on real decisions is diffuse and indirect, so no honest number can be put on lives or dollars changed. Just as clearly, his use of the same reasoning to back hardline positions in the Israeli-Palestinian conflict shows that game theory can be enlisted for contested political conclusions.

MathematicsEconomyPeaceFundamental science

No number is given here on purpose. Some contributions cannot be counted honestly, and we would rather describe them than invent a figure.

The double edge

No physical harm is tied to Aumann's mathematics, but his use of it in politics has drawn sharp criticism. In his Nobel lecture he argued, in general terms, that disarming can make war more likely and that wanting peace immediately can prevent it. In later talks he applied that reasoning to Israel's conflict with the Palestinians from a hawkish position, and he has said Israel's continued military government in the West Bank shows it does not want the land enough. About 1,000 academics from some 50 countries signed a petition asking the Swedish Academy to reverse his prize and Thomas Schelling's, accusing Aumann of using his analysis to justify the occupation. In 2006, in dismay at the Gaza withdrawal, he said he feared the anti-Zionist Satmar sect had been right. He also headed a committee that tested claims of hidden codes in the Bible, after years in which he thought a strong case had been made for them; in 2004 he concluded the tests did not confirm the codes and that he found them improbable.

Moderate
Petition to withdraw his Nobel Prize
Around 1,000 academics from about 50 countries sent the Swedish Academy a petition asking it to reverse the 2005 awards to Aumann and Thomas Schelling. They said Aumann used his analysis to justify Israel's occupation and the oppression of Palestinians. The prize was presented as planned.^[7]
Moderate
Game theory enlisted for hardline politics
In his Nobel lecture Aumann argued that disarming can cause war and that insisting on peace now may mean never getting it. In later talks and interviews he applied such reasoning to the Israeli-Palestinian conflict, called the treatment of evacuated Gaza settlers a national disgrace, and said Israel's military government in the West Bank shows the country does not want the land enough.^[4],[6],[8]
Minor
Involvement in the Bible codes debate
Aumann headed a committee that tested claims of hidden predictive codes in the Hebrew Bible. He wrote in 2004 that for many years he had thought a strong case had been made for the codes, until critics showed the data could have been manipulated. Research under his supervision failed to confirm the codes, though it did not disprove them, and he concluded they were improbable.^[9]

Against the odds

Aumann was not yet three when Hitler came to power in January 1933. Germany then had about 523,000 Jews, and over the next five years Nazi laws stripped them of civil rights, while the regime took more and more of emigrants' property through heavy exit taxes and limits on moving money abroad. His family had planned to leave in 1933, but were persuaded the danger would pass, a mistake he later said was hard to see from inside the crisis. In 1938 they managed, not easily, to get US visas and left Frankfurt for New York shortly before the Kristallnacht pogrom. Demand for US visas far outstripped the places on offer: by mid-1939, 309,000 German, Austrian and Czech Jews had applied for 27,000 US quota places. His parents lost all their assets and worked extremely hard to make a living, yet still sent both sons to Jewish schools and college. His father, a decorated German veteran of World War I, had seen the country his family had lived in for centuries turn on them. Later tragedy came in Israel: in 1982 his eldest son, Shlomo, was killed in action as a soldier in the Lebanon War.

1938
Exile
With life for Jews in Nazi Germany growing ever more dangerous, the family secured US visas only with difficulty and emigrated from Frankfurt to New York shortly before Kristallnacht.^{[1],[5],[6],[10]}
1938
Poverty
His parents lost all their assets in leaving Germany and arrived in New York with no money, working very hard to make ends meet.^[1],[5],[6]
1982
War
His eldest son, Shlomo, was killed in action while serving in the Israeli army during the 1982 Lebanon War.^[1],[5]

What Jews faced around 2005

Open borders and a rising tide of attacks

With the Soviet Union gone, about 1 million emigrants from the former USSR eventually settled in Israel and 300,000 had reached the United States by 2000, and Syria let its last Jews leave in 1992. Terrorism against Jewish targets continued: bombings in Buenos Aires killed 29 at Israel's embassy in 1992 and 85 at the AMIA community center in 1994, and synagogues were attacked in Djerba in 2002 and Istanbul in 2003. About 1,000 Israelis were killed during the Second Intifada of 2000 to 2005, many in suicide bombings.

2003Istanbul synagogue bombings. Truck bombs exploded minutes apart outside Istanbul's Beth Israel and Neve Shalom synagogues during Sabbath prayers. Twenty-eight people died, including the two bombers and six Jewish victims, and more than 300 were wounded.
2002El Ghriba synagogue bombing, Djerba. A suicide bomber acting for al-Qaeda detonated a truck of gas canisters at the ancient El Ghriba synagogue on the Tunisian island of Djerba. Accounts give 19 to 21 dead, including 14 German tourists, and more than 30 wounded.
2000Second Intifada. A major Palestinian uprising against Israel and its occupation began in September 2000 and lasted until early 2005. Palestinian militant groups carried out about 138 suicide bombings, mostly against Israeli civilians, and Israel mounted large military operations. About 1,000 Israelis and 3,000 Palestinians, combatants and civilians, were killed.

The full timeline

Jewish background

Both parents JewishReligiously observant

Aumann was born in Frankfurt into an Orthodox Jewish family. His father, a textile merchant whose family had lived in Germany for centuries, and his mother, who grew up in London, identified with the Agudat Yisrael movement, which then opposed a Jewish state. He attended Jewish schools in New York, including the Rabbi Jacob Joseph yeshiva high school, and as a teenager became an ardent Zionist. He moved to Jerusalem in 1956 and remains a religiously observant Jew who studies Talmud, keeps the Sabbath, and uses the Hebrew name Yisrael. He opened his Nobel banquet speech with a Hebrew blessing and quoted Jewish sources in his Nobel lecture.^{[1],[4],[5],[6]}

Key dates

June 8, 1930
Born in Frankfurt am Main, Germany, to an Orthodox Jewish family.^[1],[2]
1938
Family flees Nazi Germany for New York, shortly before Kristallnacht, losing all their assets.^[1],[6]
1950
Earns a bachelor's degree in mathematics at the City College of New York.^[1],[11]
1955
Completes a PhD in knot theory at MIT and marries Esther Schlesinger in Brooklyn; then turns to game theory at a Princeton consulting group.^[1],[2],[11]
1956
Moves to Israel and joins the mathematics faculty of the Hebrew University of Jerusalem.^[1],[11]
1959
Publishes 'Acceptable Points', perhaps the first rigorous general treatment of repeated games; its idea of strong equilibrium was cited in the Nobel announcement.^[1],[4]
1964
Publishes 'Markets with a Continuum of Traders' in Econometrica, a new way to model perfect competition.^[5]
1965
Around the mid-1960s, joins a US Arms Control and Disarmament Agency project, developing repeated games with incomplete information with Michael Maschler.^[1],[3]
1976
Publishes 'Agreeing to Disagree', defining common knowledge; that year he and Lloyd Shapley also prove the Perfect Folk Theorem.^[4],[5]
1982
His eldest son, Shlomo, is killed in action in the Lebanon War.^[1],[5]
1985
With Maschler, publishes a game-theory explanation of a bankruptcy problem in the Babylonian Talmud.^[1]
1991
Helps found the Center for the Study of Rationality at the Hebrew University.^[5],[11]
December 10, 2005
Receives the Prize in Economic Sciences, shared with Thomas Schelling, for game-theory analysis of conflict and cooperation.^[2],[7]

Sources

1.Robert J. Aumann – Biographical · NobelPrize.org (Nobel Prize Outreach), 2006
2.Press release: The Prize in Economic Sciences 2005 · The Royal Swedish Academy of Sciences / NobelPrize.org, 2005
3.The Prize in Economic Sciences 2005: Supplementary information (Conflict and cooperation through the lens of game theory) · The Royal Swedish Academy of Sciences / NobelPrize.org, 2005
4.War and Peace (Prize Lecture, December 8, 2005) · NobelPrize.org (Les Prix Nobel 2005), 2005
5.An Interview with Robert Aumann (interviewed by Sergiu Hart) · Macroeconomic Dynamics (author's version, Hebrew University of Jerusalem), 2005
6.Jerusalemites – Yisrael Aumann · World Mizrachi (HaMizrachi magazine), David Olivestone, 2022
7.Anti-Israel protests against Nobel prize award · European Jewish Press (archived by the Internet Archive), 2005
8.Nobel laureate: Satmars were right about Israel · Ynetnews, 2006
9.Analyses of the Gans Committee Report (Discussion Paper 365) · Center for the Study of Rationality, Hebrew University of Jerusalem, 2004
10.German Jewish Refugees, 1933–1939 · United States Holocaust Memorial Museum, Holocaust Encyclopedia
11.Curriculum Vitae: Robert J. Aumann · The Hebrew University of Jerusalem (Aumann's faculty page), 2025

Fact-checked on September 24, 2026 by a separate AI fact-checking pass that re-opened the sources, with 9 corrections made. How we check

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