Lloyd Shapley
Lloyd Shapley  

File:Shapley, Lloyd (1923).jpeg
Lloyd Shapley, 1980


Born  Lloyd Stowell Shapley June 2, 1923 Cambridge, Massachusetts 
Residence  U.S. 
Nationality  American 
Fields  Mathematics, Economics 
Institutions  University of California, Los Angeles, 1981–present (Emeritus 2000–present) Rand Corporation, 1948–49, 1954–81 Princeton University, 1953–54 US Army, 1943–45 
Alma mater  Princeton University Harvard University 
Doctoral advisor  Albert W. Tucker 
Known for  Shapley value Shapley–Shubik power index stochastic games Bondareva–Shapley theorem Shapley–Folkman lemma & theorem Gale–Shapley algorithm potential game core, kernel and nucleolus market games authority distribution multiperson utility nonatomic games 
Influences  John von Neumann Martin Shubik Jon Folkman 
Influenced  Martin Shubik Jon Folkman 
Notable awards  Nobel Memorial Prize in Economic Sciences (2012) Golden Goose Award (2013) John von Neumann Theory Prize (1981) 
Lloyd Stowell Shapley (born June 2, 1923) is a distinguished American mathematician and Nobel Prize–winning economist. He is a Professor Emeritus at University of California, Los Angeles (UCLA), affiliated with departments of Mathematics and Economics. He has contributed to the fields of mathematical economics and especially game theory. Since the work of von Neumann and Morgenstern in 1940s, Shapley has been regarded by many experts as the very personification of game theory.^{[1]}^{[2]}^{[3]} With Alvin E. Roth, Shapley won the 2012 Nobel Memorial Prize in Economic Sciences "for the theory of stable allocations and the practice of market design."^{[4]}
Contents
Life and career
Lloyd Shapley was born on June 2, 1923, in Cambridge, Massachusetts, one of the sons of Martha (Betz) and the distinguished astronomer Harlow Shapley, both from Missouri.^{[5]} He attended Phillips Exeter Academy and was a student at Harvard when he was drafted in 1943. He served in the Army Air Corps in Chengdu, China and received the Bronze Star decoration for breaking the Soviet weather code.^{[6]} 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 to Princeton University where he received a Ph.D. in 1953. His thesis and postdoctoral work introduced the Shapley value and the core solution in game theory. After graduating, he remained at Princeton for a short time before going back to the RAND corporation from 1954 to 1981. Since 1981 he has been a professor at UCLA.
Contribution
Along with the Shapley value, stochastic games, the Bondareva–Shapley theorem (which implies that convex games have nonempty cores), the Shapley–Shubik power index (for weighted or block voting power), the Gale–Shapley algorithm (for the stable marriage problem), the concept of a potential game (with Dov Monderer), the Aumann–Shapley pricing, the Harsanyi–Shapley solution, the Snow–Shapley theorem for matrix games, and the Shapley–Folkman lemma & theorem 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 nonatomic games and on longterm competition have all appeared in economic theory.
In his 80s, Shapley continued publishing in the areas of specialization he created or advanced, such as multiperson utility (with Manel Baucells) and authority distribution (a generalization to the Shapley–Shubik power index and useful in ranking, planning and group decisionmaking).
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, 2007
 Fellow, American Mathematical Society, 2012^{[7]}
 Sveriges Riksbank Nobel Memorial Prize in Economic Sciences, 2012
 Golden Goose Award, 2013^{[8]}
Selected publications
 A Value for nperson 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 NonAtomic 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.
 LongTerm Competition – A GameTheoretic Analysis [1994] (with Robert Aumann), In Essays in Game Theory: In Honor of Michael Maschler Nimrod Megiddo (ed.), SpringerVerlag.
 Potential Games [1996] (with Dov Monderer), Games and Economic Behavior Vol. 14, pp. 124–143.
 On Authority Distributions in Organizations [2003] (with Xingwei Hu), Games and Economic Behavior Vol. 45, pp. 132–152, 153–170.
 Multiperson Utility [2008] (with Manel Baucells). Games and Economic Behavior Vol. 62, pp. 329–347.
Trivia
In 1950, Shapley invented the board game So Long Sucker, along with Mel Hausner, John Forbes Nash, and Martin Shubik.
References
 ↑ 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.
 ↑ R. Aumann's Nobel Lecture. R. Aumann considers L.S. Shapley to be the greatest game theorist of all time.
 ↑ Official announcement at Nobelprize.org
 ↑ http://www.nytimes.com/1981/01/27/obituaries/marthabetzshapley.html
 ↑ http://www.nobelprize.org/nobel_prizes/economicsciences/laureates/2012/shapleyinterview.html
 ↑ List of Fellows of the American Mathematical Society, retrieved 20130718.
 ↑ "Market Design". The Golden Goose Award. Retrieved 20150527.<templatestyles src="Module:Citation/CS1/styles.css"></templatestyles>
External links
 Home Page
 Lloyd Shapley at the Mathematics Genealogy Project
 The Shapley Value
 Citation of von Neumann Theory Prize on L.S.Shapley's work: "Lloyd Shapley has dominated game theory for the thirtyseven years since von Neumann and Morgenstern published their pathbreaking book, The Theory of Games and Economic Behavior."
 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.
 Robert Aumann's Nobel lecture, also see here.
 Pages with broken file links
 1923 births
 Living people
 John von Neumann Theory Prize winners
 American Nobel laureates
 Nobel laureates in Economics
 Members of the United States National Academy of Sciences
 Fellows of the Econometric Society
 Game theorists
 Mathematical economists
 RAND Corporation people
 American economists
 Researchers in stochastics
 20thcentury American writers
 21stcentury American writers
 20thcentury economists
 21stcentury economists
 20thcentury American mathematicians
 21stcentury American mathematicians
 Harvard University alumni
 Recipients of the Bronze Star Medal
 Fellows of the American Mathematical Society