Escape from Frankfurt
Robert John Aumann, Yisrael Aumann in Hebrew, was born in Frankfurt am Main in June 1930 into a comfortably off Orthodox Jewish family. His father was a wholesale textile merchant whose family had lived in Germany for centuries, and who had fought for Germany in the First World War and been decorated. His mother had grown up in London and earned a degree at University College London, a rare achievement for a woman of her generation.
As the Nazi regime tightened its grip, his parents saw, in Aumann’s words, the handwriting on the wall. In 1938 they obtained American visas with some difficulty and emigrated to New York, about two weeks before the Kristallnacht pogrom. In the move they lost nearly all their assets and had to work very hard to make a living, but they gave Robert and his brother an excellent Jewish and secular education.
A yeshiva boy who loved Euclid
Aumann attended Jewish day schools, including the Rabbi Jacob Joseph School, a yeshiva high school on the Lower East Side. There a remarkable mathematics teacher, Abraham Gansler, taught him to love the subject, above all the axioms, theorems and proofs of Euclid’s geometry. At the City College of New York he majored in mathematics, graduating in 1950, and devoured number theory precisely because, he later said, it was natural, simple to state, extraordinarily deep, and absolutely useless.
He went on to the Massachusetts Institute of Technology, earning a master’s degree in 1952 and a PhD in 1955. His doctoral thesis, under George Whitehead, was in knot theory, another branch of pure mathematics he valued for its apparent uselessness. Fifty years later, he recalled with delight, his grandson telephoned from medical school to ask about knots, because knotted DNA can lead to cancer.
From decoys to game theory
After his PhD Aumann took a job with an operations-research group affiliated with Princeton University that did practical consulting work. One problem he was given was how to defend a city against a squadron of aircraft, a few carrying nuclear weapons and most of them decoys. He remembered conversations at MIT with the young John Nash about game theory, the mathematics of strategic decision-making, and decided it was the right tool. He studied just enough to solve the problem, and then found himself captivated by the subject in its own right.
Meanwhile his Zionism was turning into a plan. He and his brother had decided, when the State of Israel was founded in 1948, to make their lives there; his brother went in 1950. In 1953 Aumann met Esther Schlesinger, a young Israeli visiting the United States, and they married in Brooklyn in April 1955. In the autumn of 1956 he took up a post as an instructor in mathematics at the Hebrew University of Jerusalem, where he has remained ever since.
The mathematics of repeated encounters
Aumann’s most celebrated contribution is to the theory of repeated games, situations in which the same players face the same strategic choice again and again. A single encounter between self-interested parties can easily end in mutual betrayal, as in the famous prisoner’s dilemma. But when people know they will meet again, the calculation changes: cheating today can be punished tomorrow, and cooperation can become the rational choice.
In a 1959 paper, “Acceptable Points in General Cooperative n-Person Games”, written partly during summers at the US National Bureau of Standards, Aumann produced what he called perhaps the first rigorous general treatment of repeated games, showing that the stable outcomes of an infinitely repeated game coincide with cooperative outcomes of the one-shot game. Around the same time he became aware of what became known as the “Folk Theorem” of repeated games, but, he later admitted, he thought it too simple to publish, which he called a big mistake. With Lloyd Shapley he later sharpened the theory, and with his longtime collaborator Michael Maschler he developed the theory of repeated games with incomplete information, in which one side knows more than the other, work begun in the 1960s for the US Arms Control and Disarmament Agency as it prepared for nuclear negotiations with the Soviet Union.
Common knowledge and other ideas
Aumann’s influence reaches well beyond repeated games. He gave the first formal mathematical definition of “common knowledge”, not just that everyone knows something, but that everyone knows that everyone knows it, and so on without end, and proved the striking “agreement theorem”: rational people who start from the same prior beliefs and whose opinions are common knowledge cannot agree to disagree. He introduced “correlated equilibrium”, a solution concept that explains, among other things, why it can help rival parties to use an impartial mediator who gives them different information. With Shapley he wrote Values of Non-Atomic Games (1974), on games with very many players, such as markets and elections.
He also delighted in applying game theory to Jewish texts. In a 1985 paper with Maschler, “Game-Theoretic Analysis of a Bankruptcy Problem from the Talmud”, he solved a long-standing puzzle in the Babylonian Talmud (Ketubot 93a) about how to divide an estate among three widows when it cannot satisfy all their claims, showing that the Talmud’s seemingly inconsistent rulings follow a precise modern solution concept, the nucleolus. He has lectured on it, by his own count, dozens if not hundreds of times, to scientists, schoolchildren, synagogue groups and Talmudic academies.
From price wars to peace
In 2005 Aumann shared the Nobel Memorial Prize in Economic Sciences with the American economist Thomas Schelling, “for having enhanced our understanding of conflict and cooperation through game-theory analysis.” The Royal Swedish Academy of Sciences noted that Aumann was the first to conduct a full-fledged formal analysis of infinitely repeated games, identifying exactly which outcomes can be upheld in long-run relationships.
The practical reach of that work is wide. Repeated-game theory helps explain why cooperation is harder with many participants, infrequent contact or short time horizons; why firms can sustain high prices without formal collusion; why price wars and trade wars break out; how communities manage shared pastures and irrigation systems; and why institutions from medieval merchant guilds to modern trade agreements take the shapes they do. It is now the standard framework in the social sciences for analysing long-term cooperation.
Faith, family and controversy
Aumann is a deeply observant Jew who sees no conflict between his faith and his science, and he has spoken of studying Talmud with a study partner for decades. His family life has known great joy and great sorrow. He and Esther had five children; their eldest son, Shlomo, a yeshiva student serving as a tank gunner, was killed in action in the 1982 Lebanon War. Esther died of ovarian cancer in 1998. In November 2005, about a week before receiving the Nobel Prize, Aumann married her widowed sister, Batya Cohn. He is a cousin of the late neurologist and writer Oliver Sacks.
His public views have often provoked debate. Aumann has drawn on game theory to argue for a hard line in Israel’s negotiations with its neighbours, opposed Israel’s 2005 withdrawal from Gaza, and been associated with right-wing religious Zionist groups. His Nobel lecture, titled “War and Peace”, argued that war must be studied scientifically in order to be prevented. Critics in Europe objected to the award on political grounds, and a petition calling for it to be withdrawn gathered signatures from academics around the world. He also engaged with the controversial “Bible codes” research; after a committee he served on failed to confirm the claims, he concluded that the codes phenomenon was improbable.
A builder of Israeli science
In 1990 Aumann was among the founders of the Center for Rationality at the Hebrew University, an interdisciplinary centre built around game theory that brings together economists, mathematicians, psychologists, computer scientists, biologists, lawyers and philosophers. He has supervised a generation of leading game theorists, including Sergiu Hart, Abraham Neyman, David Schmeidler and Yair Tauman, and helped make Jerusalem one of the world’s centres of the field. He has also held visiting positions at Princeton, Yale, Berkeley, Stanford, Louvain, Stony Brook and New York University.
His honours include the Harvey Prize (1983), the Israel Prize in economics (1994), the EMET Prize (2002) and membership of the US National Academy of Sciences and the Israel Academy of Sciences and Humanities. He has written well over eighty research papers and six books.
“One tremendous joyride”
In the autobiography he wrote for the Nobel Foundation, Aumann insisted that science is the product of many minds and that much of his prize belonged to his collaborators. He described his life as one magnificent tapestry, into which even the worst times, his son’s death, his wife’s death, had somehow been woven. Among its pleasures he listed the excitement of research, teaching, climbing rock faces, skiing expert slopes, cooking for friends, studying Talmud with a granddaughter, and seeing the flag of Israel flying beside Sweden’s over the Grand Hotel in Stockholm.
Aumann’s enduring legacy is a body of mathematics that explains one of the oldest puzzles of human society: why selfish individuals, rival firms and even hostile nations can sometimes find their way to lasting cooperation, and why, without the shadow of the future, they so often fail to.
Sources & further reading
Robert J. Aumann, Biographical, NobelPrize.org · Press release: The Prize in Economic Sciences 2005, NobelPrize.org · Robert Aumann, Brief biography, Hebrew University of Jerusalem · Robert Aumann, Wikipedia · Researched from the sources above and checked against them. Spotted an error? Tell us.
A life of tikkun olam. This is part of tikkun olam, the Jewish idea of repairing the world, and every one of us can add to it.