Lloyd Shapley
Lloyd S. Shapley | |
|---|---|
.jpg) Lloyd Shapley, 1980 | |
| Born | June 2, 1923 |
| Nationality | American |
| Alma mater | Princeton University Harvard University |
| 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 |
| Awards | John von Neumann Theory Prize |
| Scientific career | |
| Fields | Mathematics, Economics |
| Institutions | University of California, Los Angeles, 1981- Rand Corporation, 1948-9, 1954-81 Princeton University, 1953-4 US Army, 1943-5 |
| Doctoral advisor | Albert W. Tucker |
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 of mathematical economics and especially game 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.[1][2][3]
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 to Princeton University where he received a Ph.D. in 1953. His thesis and post-doctoral work continued the ideas of Francis Ysidro Edgeworth introducing the Shapley value and the core solution concept in game 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 at UCLA.
Contribution
Along with the Shapley value, stochastic games, the Bondareva-Shapley theorem (which implies that convex games have non-empty 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, 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, 2007
Selected 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 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.
External links
- Home Page
- Mathematical Genealogy Project
- The Shapley Value
- Citation of von Neumann Theory Prize on L.S.Shapley's work
- 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.