**Robert Aumann: Mathematics Major, City College Graduate, Nobel Laureate**

Prepared by:

Joseph Malkevitch

Department of Mathematics

York College (CUNY)

Jamaica, New York 11451

Email: malkevitch@york.cuny.edu (for additions, suggestions, and corrections)

Web page:

http://www.york.cuny.edu/~malk

Mathematicians who teach for CUNY (City University of New York) are extremely proud of the recent awarding of the Nobel Memorial Prize in Economics to Robert Aumann, Professor emeritus, Hebrew University (Jerusalem). Aumann is remarkable in a variety of ways. Not only was he trained as a "pure mathematician" but also he is an extremely religious man. None the less he has been able to co-exist in a world demanding the highest standards of "scientific" thinking yet at the same time being nurtured by his faith. Much of the information below has been drawn from an interview that Aumann gave to one of his doctoral students. Sergiu Hart, one of Robert Aumann’s 13 doctoral students has conducted an extensive __interview__ with Aumann which is available on the following web page:

http://www.ma.huji.ac.il/~hart/abs/aumann.html

Aumann was educated in New York City at City College (CCNY-CUNY) and is extremely articulate. This is a very fine interview both for getting a sense of Aumann as a person and for his work in game theory. It provides a nice introduction to a variety of different types of issues that are treated in the theory of games.

A few facts about Aumann. He was born in Germany and moved to the US with his parents to escape the tyranny of Hitler’s Germany. He was educated at City College, where he majored in Mathematics, and then he went to study at MIT. He took his graduate degrees there in Mathematics as well. He studied with George Whitehead in the field of algebraic topology. His doctoral thesis treated a problem in knot theory. He studied the properties of alternating links which is widely known. After finishing at MIT he took a postdoc at Princeton where he came in contact with a group of individuals working in the area of operations research and game theory. He decided he wanted to move to Israel rather than continue to work in the United States and he spent the major part of his career at Hebrew University in Jerusalem. He also visited Stanford University where he spent several sabbaticals. Aumann made fundamental contributions to many areas of mathematics economics and in particular to game theory. He shared the 2005 Nobel Memorial Prize in Economics with Thomas Schelling. Once, earlier, the Nobel Prize was given for work in Game Theory, to Rheinhard Selten, John Harsanyi, and John Nash.

Other major contributors to the Theory of Games were Oskar Morgenstern and John Von Neumann, who founded the modern theory. Other important contributors are David Gale and Lloyd Shapley.

Aumann is a very religious man, and his views on the ways that he has mixed being a first rate mathematician and being religious are very interesting. Some people were surprised when he did not win the Nobel Prize earlier. There was some speculation that his comments on the “bible codes” may have been in part responsible for this delay.

One especially nice paper of Aumann’s, joint with Michael Maschler is:

Game Theoretic Analysis of a Bankruptcy Problem from the Talmud, J. of Economic Theory, 36 (1985) 195-213.

In this paper Aumann and Maschler were inspired by thinking about some bankruptcy problems which appear in the Talmud to obtain new insights and algorithms to solve bankruptcy problems. Suppose there are two claimants A and B who have claims of $100 and $50 but there is only $110 available to try to resolve the claims. The intriguing idea that the Talmud suggests grows out of the following line of reasoning. Claimant A could argue to the "judge" who most distribute the $110 that since Claimant B is only asking for $50, that $110 - $50 = $60 (A's uncontested claim) should be assigned to A. Claimant B can make a similar argument that $110 - $100 = $10 (B's uncontested claim) must "belong" to B. The Talmud suggests the way to fairly assign the $110 is to give Claimant A, $60 + $20 = $80, and Claimant B $10 + $20 = $30. (These numbers add to $110.) These number are arrived at by taking $110 - ($60 + $10) = $40 and splitting this equally between A and B. Thus, each of A and B would get $20 and in addition the amount of the "uncontested claim" that they are entitled to. The intuitive idea is that each claimant be given his/her uncontested claim if any, and that any remaining amount be distributed by equally dividing it between the two claimants. Aumann and Maschler give an algorithm for generalizing this approach to bankruptcy problems where there are more than 2 claimants.

References:

Some good introductory books in game theory are:

Brams, S., Negotiation Games, Chapman and Hall, 1990.

Davis, M., Game Theory, Basic Books, 1993.

Luce, R. and H. Raiffa, Games and Decision, Wiley, 1957 (Dover reprint.)

Owen, G., Game Theory, Second Edition, Academic Press, 1982.

Straffin, P., Game Theory and Strategy, Mathematical Association of America, Washington, 1993.

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