- Lloyd Shapley
Infobox_Scientist
name = Lloyd S. Shapley
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caption = Lloyd S. Shapley in 2002, Los Angeles
birth_date = Birth date and age|1923|6|2|mf=y
birth_place =Cambridge, Massachusetts
death_date =
death_place =
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field =Mathematics ,Economics
work_institution =University of California, Los Angeles , 1981-Rand Corporation , 1948-9, 1954-81
Princeton University , 1953-4
US Army, 1943-5
alma_mater =Princeton University
Harvard University
doctoral_advisor =Albert W. Tucker
doctoral_students =
known_for =Shapley value
Shapley-Shubik power index
stochastic games
Bondareva-Shapley theorem
Gale-Shapley algorithm
potential game
core, kernel and nucleolus
market games
authority distribution
multi-person utility
non-atomic games
prizes =John von Neumann Theory Prize
footnotes =Lloyd Stowell Shapley (born June 2, 1923) is a distinguished American mathematician and economist. He is a Professor Emeritus at
University of California, Los Angeles , affiliated with departments of Mathematics and Economics. He has contributed to the fields ofmathematical economics and especiallygame theory . Since the work of von Neumann and Morgenstern in 1940s, Lloyd Shapley has been regarded by many experts as the very personification of game theory. ["The Shapley Value: Essays in honor of Lloyd S. Shapley," A.E. Roth, ed., Cambridge University Press, 1988.] ["Stochastic Games and Related Topics: In Honor of Professor L. S. Shapley," T. E. S. Raghavan, T. S. Ferguson, T. Parthasarathy and O. J. Vrieze, eds., Kluwer Academic Publishers, 1990.] [ [http://nobelprize.org/nobel_prizes/economics/laureates/2005/aumann-lecture.html R.Aumann's Nobel Lecture] . R. Aumann considers L.S.Shapley to be the greatest game theorist of all time.]Career
Lloyd Shapley was born on June 2, 1923, in Cambridge, Massachusetts, one of the sons of the distinguished astronomer
Harlow Shapley . He was a student at Harvard when he was drafted in 1943, and in the same year, as a sergeant in the Army Air Corps in Chengdu, China, he received the Bronze Star decoration for breaking the Soviet weather code. After the war, he returned to Harvard and graduated with an A.B. in mathematics in 1948. After working for one year at the Rand Corporation, he went toPrinceton University where he received a Ph.D. in 1953. His thesis and post-doctoral work continued the ideas ofFrancis Ysidro Edgeworth introducing theShapley value and the core solution concept ingame theory . After graduating, he remained at Princeton for short time before going back to the RAND corporation from 1954 to 1981. He married Marian Ludolph in 1955 (with whom he has two sons, Peter and Christopher). Since 1981 he has been a professor atUCLA .Contribution
Along with the
Shapley value ,stochastic games , theBondareva-Shapley theorem (which implies that convex games have non-empty cores), theShapley-Shubik power index (for weighted- or block voting power), theGale-Shapley algorithm (for thestable marriage problem ), the concept of apotential game (withDov Monderer ), the Aumann-Shapley pricing, and the Harsanyi-Shapley solution bear his name.Besides, his early work with R.N.Snow and Samuel Karlin on matrix games was so complete that little has been added since. He has been instrumental in the development of utility theory, and it was he who laid much of the groundwork for the solution of the problem of the existence of Von Neumann-Morgenstern stable sets. His work with M.Maschler and B.Peleg on the kernel and the nucleolus, and his work with
Robert Aumann on non-atomic games and on long-term competition have all had a tremendous impact in economic theory.In his 80s, L.S.Shapley continues publishing his old results, such as multi-person utility and authority distribution (a generalization to the
Shapley-Shubik power index and useful in ranking, planning and group decision-making).Awards and Honors
*Bronze Star, U.S. Army Air Corps, 1944
*Procter Fellow,Princeton University , 1951-52
*Fellow,Econometric Society , 1967
*Fellow,American Academy of Arts and Sciences , 1974
*Member, National Academy of Sciences, 1979
*John von Neumann Theory Prize , 1981
*Honorary Ph.D.,Hebrew University of Jerusalem , 1986
*Fellow, INFORMS (Institute for Operations Research and the Management Sciences ), 2002
*Distinguished Fellow,American Economic Association , 2007elected Publications
*A Value for n-person Games [1953] , In "Contributions to the Theory of Games" volume II, H.W. Kuhn and A.W. Tucker (eds.).
*Stochastic Games [1953] , "Proceedings of National Academy of Science" Vol. 39, pp. 1095-1100.
*A Method for Evaluating the Distribution of Power in a Committee System [1954] (with
Martin Shubik ), "American Political Science Review" Vol. 48, pp.787-792.*College Admissions and the Stability of Marriage [1962] (with David Gale), "The American Mathematical Monthly" Vol. 69, pp. 9-15.
*Simple Games : An Outline of the Descriptive Theory [1962] , "Behavioral Science" Vol. 7, pp. 59-66.
*On Balanced Sets and Cores [1967] , "Naval Research Logistics Quarterly" Vol. 14, pp. 453-460.
*On Market Games [1969] (with
Martin Shubik ), "Journal of Economic Theory" Vol. 1, pp. 9-25.*Utility Comparison and the Theory of Games [1969] , "La Decision", pp. 251-263.
*Cores of Convex Games [1971] "International Journal of Game Theory" Vol. 1, pp. 11-26.
*The Assignment Game I: The Core [1971] (with
Martin Shubik ), "International Journal of Game Theory" Vol. 1, pp. 111-130.*"Values of Non-Atomic Games" [1974] (with
Robert Aumann ), Princeton University Press.*Mathematical Properties of the Banzhaf Power Index [1979] (with
Pradeep Dubey ), "Mathematics of Operations Research" Vol. 4, pp. 99-132.*Long-Term Competition – A Game-Theoretic Analysis [1994] (with
Robert Aumann ), In "Essays in Game Theory: In Honor of Michael Maschler" Nimrod Megiddo (ed.), Springer-Verlag.*Potential Games [1996] (with
Dov Monderer ), "Games and Economic Behavior" Vol. 14, pp. 124–143.*On Authority Distributions in Organizations [2003] (with X.Hu), "Games and Economic Behavior" Vol. 45, pp. 132-152, 153-170.
Trivia
In 1950, Lloyd Shapley invented the board game
So Long Sucker , along withMel Hausner ,John Forbes Nash , andMartin Shubik .References
External links
* [http://econweb.sscnet.ucla.edu/shapley/ Home Page]
* [http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=46053 Mathematical Genealogy Project]
* [http://www.ma.huji.ac.il/~mseyal/shapley4to95.pdf The Shapley Value]
* [http://www.informs.org/article.php?id=1014 Citation of von Neumann Theory Prize on L.S.Shapley's work]
* [http://www.e-optimization.com/directory/trailblazers/wolfe/princeton.cfm Albert Tucker's comment on L.S.Shapley's work] . In 1995,
Albert W. Tucker mentioned in his passing that Shapley was second only to Von Neumann as the most important researcher in theory of games so far.* [http://ratio.huji.ac.il/dp/dp428.pdf Robert Aumann's Nobel lecture] , also see [http://www.huji.ac.il/dovrut/nobel_lecture.doc here] .
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