Israeli winner of Nobel Prize: Israel is No. 1 in game theory

[ygalg1]

By Tamara Traubman, Haaretz Correspondent, The Associated Press and Haaretz Service

Robert J. Aumann, who lives in Israel and holds dual American and Israeli citizenship, and Thomas C. Schelling, an American, have won the 2005 Nobel Prize in Economic Sciences, the Royal Swedish Academy of Sciences announced Monday.

Aumann, who is also known as Yisrael, told reporters that Israel has become the No. 1 world power in the field of game theory. Aumann, the eighth Israeli to receive the Nobel Prize, is a professor emeritus at the Hebrew University of Jerusalem's Institute of Mathematics and a member of the university's Center for Rationality.

Aumann and Schelling won the $1.3 million prize "for having enhanced our understanding of conflict and cooperation through game-theory analysis," the academy said.

"I think game theory creates ideas that are important in solving and approaching conflict in general," Aumann told the awards ceremony by telephone from Israel.

Asked whether it could help solve the Israeli-Palestinian conflict, he said: "I do hope that perhaps some game theory can be used and be part of this solution."

Aumann had not decided what to do with the prize money. "I am totally overwhelmed. I had absolutely no idea," he said.

Hebrew University President Prof. Menachem Magidor said the announcement of the prize "has brought pride and happiness to the university, to the State of Israel and to all of Israeli academia."

Through their work, Aumann, 75, and Schelling, 84, have helped to "explain economic conflicts such as price wars and trade wars, as well as why some communities are more successful than others in managing common-pool resources," the academy said in its citation.

"The repeated-games approach clarifies the raison d'etre of many institutions, ranging from merchant guilds and organized crime to wage negotiations and international trade agreements," it said.

Aumann was cited for his analysis of "infinitely repeated games" to identify what outcomes can be maintained over time.

"Insights into these issues help explain economic conflicts such as price wars and trade wars, as well as why some communities are more successful than others in managing common-pool resources," said the citation.

Aumann, who was born in Frankfurt, Germany, immigrated to New York with his family in 1938. He studied mathematics in New York and completed his undergraduate and graduate studies over there. He wrote his doctoral dissertation at MIT.

Schelling is a professor at the University of Maryland's department of economics and a professor emeritus at Harvard.

Upon earning his doctorate, Aumann moved to Princeton and began researching the games theory, then a field in its early days. He immigrated to Israel in 1956 and became a staff member at the Hebrew University Mathematics Institute, where he taught until his retirement.

In his research Aumann developed tools for accurate analysis of economic systems where player groups have great influence over the final result, while individual players have very little influence over the outcome of processes.

Last year, two biochemistry professors from the Technion, Aaron Ciechanover and Avram Hershko, won the Nobel Prize in chemistry. Two years ago, Daniel Kahneman, an American-born Israeli, won the Nobel Prize in economics for his studies on decision-making in situations of uncertainty. The other Israeli Nobel laureates are S.Y. Agnon, who won the prize for literature and was the first Israeli to win a Nobel, and Menachem Begin, Yitzhak Rabin and Shimon Peres, who won the Nobel peace prize.
http://www.haaretz.com/hasen/objects...?itemNo=633666

[ygalg1]

http://www.ynetnews.com/Ext/Comp/Art...153399,00.html

Israeli, U.S. economists win Nobel Prize

Robert Aumann, American Thomas Schelling win the 2005 Nobel economics prize on Monday for their ‘Game-theory analysis’, which can help resolve conflicts in trade and business - and even avoid war; Aumann, 75, was born in Germany but is an Israeli and U.S. citizen who teaches at the Hebrew University of Jerusalem
Reuters

Israel’s Robert Aumann and American Thomas Schelling won the 2005 Nobel economics prize on Monday for their “Game-theory analysis”, which can help resolve conflicts in trade and business - and even avoid war.



Their studies have found uses in “Security and disarmament policies, price formation on markets, as well as economic and political negotiations”, Said the Royal Swedish Academy of Sciences awarding the 10 million crown (USD 1.30 million) prize.



Aumann, 75, was born in Germany but is an Israeli and U.S. citizen who teaches at the Hebrew University of Jerusalem.



Schelling, 84, teaches at the University of Maryland.




“Game theory” is a science of strategy, which attempts to determine what actions different “players” - be they trading partners, employers and unions or even crime syndicates - should take to secure the best outcome for themselves.




Schelling has been applying it to global security and the arms race since the 1950s while Aumann has conducted analysis of “Infinitely repeated games” to identify what outcomes can be maintained over time.



“Insights into these issues help explain economic conflicts such as price wars and trade wars, as well as why some communities are more successful than others in managing common-pool resources,” said the Academy citation.

[ProudInfidel]

Robert J. Aumann

Robert J. Aumann's has been one of the leading figures in the mathematical surge that has characterized Neo-Walrasian economics and game theory in the past forty years. Aumann entered into economics via cooperative game theory -

In Neo-Walrasian theory, Robert Aumann is perhaps best known for his theory of core equivalence in a "continuum" economy. Aumann introduced measure theory into the analysis of economies with an infinite number of agents - formalizing the "perfectly competitive" scenario. In his classical 1964 paper, Aumann proved the equivalence of the Edgeworthian core and Walrasian equilibrium allocations when there are an uncountable infinite number of agents - thereby providing the limit case for future work on core convergence. In order to prove this result was not vacuous, Aumann went on to prove the existence of equilibrium (1966) in this "perfectly competitive" scenario. On his way, he contributed to mathematics itself by providing a definition of the "integral" of a correspondence (1965), which was previously absent.

Previously, Aumann (1962) had swung Ockham's razoe and helped remove the axiom of completeness of preferences from the Walrasian theory of choice. In another classical paper with F.J. Anscombe in 1964, Aumann formalized the notion of "subjective probability", a concept that had been earlier forwarded by Leonard Savage, that profoundly changed the theory of choice under uncertainty.

His contributions to game theory have perhaps been no less path-breaking. Aumann entered game theory in 1959 to carefully distinguish between infinitely and finitely repeated games. With Bezalel Peleg in 1960, Aumann formalized the notion of a coalitional game without transferable utility (NTU) - one of the organizing beacons of his later research. With Michael Maschler (1963), he introduced the concept of a "bargaining set". In 1974, Aumann went on to identify "correlated equilibrium" in Bayesian games. In 1975, Aumann went on to prove a convergence theorem for the Shapley value. In 1976, he formally defined the concept of "Common Knowledge". Also in 1976, in an unpublished paper with Lloyd Shapley, Aumann provided the perfect folk theorem using the limit of means criterion.

For Aumann, game theory is clearly the more "general theory". His ruminations on the role of game theory in economic analysis are wonderfully laid out in Aumann (1985).

Game Theory

Game Theory has emerged recently as a powerful challenger to the conventional method of examining economics. Although many illustrious predecessors worked on problems in what can be called "game theory", the fundamental, formal conception of game theory as part and parcel of economic theory were first organized in John von Neumann and Oskar Morgenstern's 1944 classic, Theory of Games and Economic Behavior (1944).

The main purpose of game theory is to consider situations where instead of agents making decisions as reactions to exogenous prices ("dead variables"), their decisions are strategic reactions to other agents actions ("live variables"). An agent is faced with a set of moves he can play and will form a strategy, a best response to his environment, which he will play by. Strategies can be either "pure" (i.e. play a particular move) or "mixed" (random play). A " Nash Equilibrium" will be reached when each agent's actions begets a reaction by all the other agents which, in turn, begets the same initial action. In other words, the best responses of all players are in accordance with each other.

Game Theory can be roughly divided into two broad areas: non-cooperative (or strategic) games and co-operative (or coalitional) games. The meaning of these terms are self evident, although John Nash claimed that one should be able to reduce all co-operative games into some non-cooperative form. This position is what is known as the "Nash Programme". Within the non-cooperative literature, a distinction can also be made between "normal" form games (static) and "extensive" form games (dynamic).

John von Neumann and Oskar Morgenstern (1944) introduced the strategic normal game, strategic extensive game, the concept of pure/mixed strategies, coalitional games as well as the axiomatization of expected utility theory, which was so useful for economics under uncertainty. They employed the "maximin" solution concept derived earlier by John von Neumann (1928) to solve simple strategic, zero-sum normal games.

In 1950, John Nash introduced the concept of a "Nash Equilibrium" (NE), which became the organizing concept under Game Theory -- even though the concept actually stretched as far back as Cournot (1838). Nash followed this up in 1951 with the concept of a "Nash Bargaining Solution" (NBS) for coalitional games." John Nash - the professor in the movie "A Beautiful Mind (2001)

Then the floodgates opened for the refinement of Nash Equilibrium. In the field of non-cooperative games, R. Duncan Luce and Howard Raiffa (1957) provided the first popular textbook on game theory and, in it, they formalized the idea of the Iterated Elimination of Dominated Strategies (IEDS) method for Strategic Normal Games and introduced the concept of "Repeated Game" (static games which are played several times over). H.W. Kuhn (1953) introduced extensive games with "imperfect information" (i.e. where one does not know what moves have already been played by other players). William Vickrey (1961) provided the first formalization of "auctions". Reinhard Selten (1965) developed the concept of a "Subgame Perfect Equilibrium" (SPE) (i.e. elimination by backward induction) as a refined solution for extensive form games. John C. Harsanyi (1967-8) developed the concept of a "Bayesian Nash Equilibrium" (BNE) for Bayesian games (i.e. games with incomplete information - where there is some uncertainty surrounding moves, or where "nature" plays as well.)

In coalitional (co-operative) games further refinements also occurred. Lloyd Shapley (1953) introduced the concept of the "Shapley Value" and the "Core" (which had been originally conceived by F.Y. Edgeworth (1881)) as solutions to Coalitional Games. Throughout the early 1960s, Robert J. Aumann and Martin Shubik began to apply cooperative game theory extensively throughout economics (e.g. industrial organization, general equilibrium, monetary theory, etc.), and, in the process, went on to invent several solution concepts for coalitional games (e.g. Bargaining Set, Strong Equilibrium), "large games" with infinite players and early statements of the "Folk Theorems" (solution concepts for Repeated Games). David Schmeidler (1969) developed the "Nucleolus" solution for coalitional games.

[Mediocrates]

Yes I was going to write yesterday about the similarities to Nash's nonlinear 'disoptimal optimization'. Figured I'd be talking to myself.

[ygalg1]

http://william-king.www.drexel.edu/t.../histf.html#AT
0-500AD

The Babylonian Talmud is the compilation of ancient law and tradition set down during the first five centuries A.D. which serves as the basis of Jewish religious, criminal and civil law. One problem discussed in the Talmud is the socalled marriage contract problem: a man has three wives whose marriage contracts specify that in the case of this death they receive 100, 200 and 300 respectively. The Talmud gives apparently contradictory recommendations. Where the man dies leaving an estate of only 100, the Talmud recommends equal division. However, if the estate is worth 300 it recommends proportional division (50,100,150), while for an estate of 200, its recommendation of (50,75,75) is a complete mystery. This particular Mishna has baffled Talmudic scholars for two millennia. In 1985, it was recognised that the Talmud anticipates the modern theory of cooperative games. Each solution corresponds to the nucleolus of an appropriately defined game.

[Justcurious]

Today's Jerusalem Post has this article about Aumann:

Nobel winner known to speak his mind

• By AVI KRAWITZ




Prof. Robert J. Aumann is not shy about expressing his views, which often conflict with his colleagues in academia, but Israel’s eighth Nobel Laureate is, nevertheless, very well respected and liked by his colleagues.
“His views often conflict with the more left-wing inclined academic community but he’s a great guy, who has suffered tremendous personal loss, and is liked by everyone,” Professor Hershel Farkas, chairman of the Institute of Mathematics at the Hebrew University said in an interview Tuesday.
The 75 year-old great-grandfather of two and grandfather of “18.99,” as he put it (he’s expecting number 19 by the end of the week), who lost a son in Lebanon in 1982, repeated in interviews Tuesday what he said in his first public address after receiving the award Monday -- that he did not foresee an end to the Middle East conflict in the near future.
“Some conflicts you just can’t solve, I don’t see how using my theory or any other can bring this one to an end,” Aumann said in response to a question about whether he felt his work in using game theory in conflict resolution, for which he received the prize, could be effective in bringing an end to the dispute between Israel and the Palestinians.
German-born Aumann, who with his aliya from the US in 1956 was appointed immediately to the department of mathematics at Hebrew University, today serves as Chairman of the university’s Center for Rationality, which he co-founded.
The center works to bring people together from different backgrounds, such as mathematics, biology, psychology, etc. to use their disciplines to attack problems from varying angles and Aumann, who doesn’t stop working, Farkas said was really the driving force behind the center.
Aumann shares the award with Thomas C. Schelling, a retired professor from the University of Maryland. The prize recognizes their work done in the 1960s and 70’s “that helped defense analysts use models to map out options available to an adversary and thus predict what the opponent might do in a confrontation,” the Royal Swedish Academy of Sciences said. It noted Aumann’s work in repeated game theory the study of the emergence of patterns in behavior - in announcing the award.
While the subject of the thesis for his Ph.d, which he received at age 25 from MIT, was centered around Knot theory, Aumann moved to game theory when he came to Israel, working closely on the subject through the years with Israeli born Prof. Michael Mashler at Hebrew University.
“Under the guidance of Aumann and Mashler, our mathematics department became the world center for game theory,” Farkas said.
Today, he added, Aumann’s research has centred around the theory of games with many players, with practical applications in election scenarios, large markets and traffic patterns, by way of example.
The Mathematics department is hoping the Nobel Prize will raise the profile of mathematics amongst the general population and the importance of research in government circles, as the university is less able to support graduate work due to major budget cuts over the past few years.
The government has cut its subsidies to the university by approximately NIS 220 million over the past six years, Farkas said.

http://epaper.jpost.com/Daily/skins/...=1129106047968

[Justcurious]

[/B]

In coalitional (co-operative) games further refinements also occurred. Lloyd Shapley (1953) introduced the concept of the "Shapley Value" and the "Core" (which had been originally conceived by F.Y. Edgeworth (1881)) as solutions to Coalitional Games. Throughout the early 1960s, Robert J. Aumann and Martin Shubik began to apply cooperative game theory extensively throughout economics (e.g. industrial organization, general equilibrium, monetary theory, etc.), and, in the process, went on to invent several solution concepts for coalitional games (e.g. Bargaining Set, Strong Equilibrium), "large games" with infinite players and early statements of the "Folk Theorems" (solution concepts for Repeated Games). David Schmeidler (1969) developed the "Nucleolus" solution for coalitional games.

Co-operatives are taking their first steps in Israel, at least according to the International Co-operative Alliance's newly released list, where the best Israeli firm is only 143th. Together these co-operatives represent more than 800 million people worldwide. Do you have experiences of co-operatives?



http://www.global300.coop/media

[psyops]

The Nobel Prize. Didn't Yasser Arafat get one of those?