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Lloyd Shapley

Lloyd Shapley
File:Shapley, Lloyd (1923).jpeg
Lloyd Shapley, 1980
Born Lloyd Stowell Shapley
(1923-06-02) June 2, 1923 (age 92)
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 Template:If empty
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
multi-person utility
non-atomic 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)
File:Lloyd Shapley 2 2012.jpg
Lloyd Shapley in Stockholm 2012

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]

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 post-doctoral 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.


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, 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 non-atomic games and on long-term competition have all appeared in economic theory.

In his 80s, Shapley continued publishing in the areas of specialization he created or advanced, such as multi-person utility (with Manel Baucells) and authority distribution (a generalization to the Shapley–Shubik power index and useful in ranking, planning and group decision-making).

Awards and honors

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.
  • Multiperson Utility [2008] (with Manel Baucells). Games and Economic Behavior Vol. 62, pp. 329–347.


In 1950, Shapley invented the board game So Long Sucker, along with Mel Hausner, John Forbes Nash, and Martin Shubik.


  1. ^ The Shapley Value: Essays in honor of Lloyd S. Shapley, A.E. Roth, ed., Cambridge University Press, 1988.
  2. ^ 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.
  3. ^ R. Aumann's Nobel Lecture. R. Aumann considers L.S. Shapley to be the greatest game theorist of all time.
  4. ^ Official announcement at
  5. ^
  6. ^
  7. ^ List of Fellows of the American Mathematical Society, retrieved 2013-07-18.
  8. ^ "Market Design". The Golden Goose Award. Retrieved 2015-05-27. 

External links

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