Lloyd Stowell Shapley (June 2, 1923 – March 12, 2016) was an American mathematician and Nobel Prize–winning economist. He 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. 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."

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. 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.

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

From 1981 until his death, Shapley was a professor at at University of California, Los Angeles (UCLA), serving at the time of his death as a Professor Emeritus there, affiliated with departments of Mathematics and Economics. He died on March 12, 2016, at the age of 92. According to The Economist, Shapley "may have thought of himself as a mathematician, but he cannot avoid being remembered for his huge contributions to economics". The American Economic Association noted that Shapley was "one of the giants of game theory and economic theory".

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, 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 90s, 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

• 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, 1978
• 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
• Sveriges Riksbank Nobel Memorial Prize in Economic Sciences, 2012
• Golden Goose Award, 2013

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 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.