Lloyd S. Shapley

June 2, 1923 – March 12, 2016

Brief Biography

The son of noted astronomer Harlow Shapley, Lloyd Stowell Shapley came from a bright and intelligent family. He and his siblings would play mathematical games around the family’s Cambridge, Massachusetts home. Shapley attended the Philips Exeter Academy and attended Harvard as an undergraduate. In the middle of his junior year, he was drafted into the United States Army.

Shapley was sent to the military’s meteorological school and was trained as a weather observer for the US Army Air Corps, plotting and interpreting weather maps. He was taken to a top-secret outpost in China but managed to share his location with his family via an encoded message. In addition to serving as a meteorological outpost, Shapley’s station intercepted encrypted broadcasts from a variety of wartime players including the Japanese, the Soviets, and even the Allied Pacific Fleet. For breaking the Soviet weather code and providing invaluable data to the war effort, Shapley was awarded a Bronze Star. He left the Army immediately after V-J Day and resumed his studies at Harvard the following spring.

Shapley was hired by the RAND Corporation after graduating, starting a decades-long affiliation with the company. RAND was an attractive place for Shapley to work as it was set up by the Air Force to keep in contact with the scientific community. It was there where he was first introduced to game theory. With Robert Snow, another young mathematician, he developed a way to find all solutions to a matrix game. The resulting Shapley-Snow theorem received serious attention from John von Neumann, who encouraged both to further develop this work. With his new found status as a rising game theorist, Shapley started  graduate school at Princeton University.

During his time at Princeton, Shapley spent the summers at RAND and studied under Albert W. Tucker. In 1953, he developed the so-called “Shapley Value”, a possible solution to the important question of finding a fair distribution of payoffs in n-person games. His treatment of the subject is cited as a splendid example of the use of the axiom method. Shapley wrote his dissertation on the topic and received a PhD in mathematics that year.

After completing a year-long research fellowship at the California Institute of Technology, Shapley returned to RAND full-time. He thoroughly enjoyed his research research and considered the RAND community as the best place to pursue it, continuing his award-winning work on game theory. He was rarely pressured to work on traditional military problems and collaborated frequently with Martin Shubik, beginning with a note on solutions on n-person games with ordinal utilities. In 1974, he and Robert Aumann co-authored a book on games with many players who affect an outcome only as members of a coalition rather than as individuals. In 1981, Shapley was awarded the John von Neumann Theory Prize by the Operations Research Society of America (ORSA) and The Institute of Management Sciences (TIMS) for his lifelong contributions to game theory. Thirty-one years later, he was jointly awarded the Nobel Prize in Economics with Alvin E. Roth “for the theory of stable allocations and the practice or market design.”

Shapley left RAND in the fall of 1981 when he realized that he was the only one left at the corporation still doing game theory. He was not drawn to teaching but admired the culture of academic research at universities. After joining the faculty at the University of California, Los Angeles, he found it rewarding to train graduate students and share his knowledge with future generations of game theorists. Shapley retired as a professor of economics having never traditionally practiced or taught the subject. 

Other Biographies

Wikipedia Entry for Lloyd Shapley

American Economic Association. Bios: Llyod Shapley. Accessed July 10, 2018. (link

Nobel Prize Foundation. Nobel Prizes and Laureates: Lloyd Shapley - Biographical. Accessed April 22, 2015. (link

UBS Nobel Perspectives.  Lloyd Shapley - When is a game worth playing?  Accessed April 25, 2019 (link


Harvard University, AB 1948

Princeton University, PhD 1953 (Mathematics Genealogy


Academic Affiliations
Non-Academic Affiliations

Key Interests in OR/MS


Oral Histories

Shapley, February 9, 1994 (restricted). RAND History Project Interviews. Accession No. 1999-0037, Box 10. Cassette tape transcript. National Air and Space Museum, Archives Division. National Air and Space Museum. Smithsonian Institute: Washington D.C. (link)

Memoirs and Autobiographies


University of California Los Angeles Economics Department. Lloyd Stowell Shapley Vita. Accessed April 22, 2015. (link


Los Angeles Times (2016) Nobel laureate economist Lloyd Shapley dies at 92; UCLA Professor won Nobel for game-theory work. March 14 (link)

The New York Times (2016) March 15 (link)

Awards and Honors

U. S. Air Army Corps Bronze Star 1944

Econometric Society Fellow 1976

National Academy of Sciences 1979

John von Neumann Theory Prize 1981

Institute for Operations Research and the Management Sciences Fellow 2002

Selected Publications

Shapley L. S. (1953) A value for n-person games. Kuhn H. & Tucker A. W., eds. in Contributions to the Theory of Games, Vol. 2, 307-317. Princeton University Press: Princeton, NJ.

Shapley L. S. & Shubik M. (1954) A method for evaluation the distribution of power in a committee system. American Political Science Review, 48(3): 787-792.

Shapley L. S. (1964) Some topics in two-person games. Advances in Game Theory, 52: 1-29.

Shapley L. S. & Shubik M. (1969) On the core of an economic system with externalities. The American Economic Review, 59(4):678-684.

Shapley L. S. (1971) Cores of convex games. International Journal of Game Theory, 1(1): 11-26.

Aumann R. J. & Shapley L. S. (1974) Values of Non-Atomic Games. Princeton University Press: Princeton, NJ.

Minor J. W. & Shapley L. S. (1978) Values of large games II: Oceanic games. Mathematics of Operations Research, 3(4): 290-307.

Dudley P. & Shapley L. S. (1984) Totally balanced games arising from controlled programming problems. Mathematical Programming, 29(3): 245-267.

Aumann R. J. & Shapley L. S. (1994) Long-Term Competition – A Game-theoretic Analysis. Springer: New York.

Monderer D. & Shapley L. S. (1996) Potential games. Games and Economic Behavior, 14(1): 124-143. 

Additional Resources

Ferguson S., Parthassarathy T., Raghavan T. E. S., & Vrieze O. J. , eds. (1990) Stochastic Games and Related Topics: In Honor of Professor L. S. Shapley. Kluwer Academic Publishers: Boston, MA. 

New York Times (2012) 2 From U.S. Win Nobel in Economics. October 15. B1. (link

Roth A. E., ed. (1998) The Shapley Value: Essays in Honor of Lloyd S. Shapley. Cambridge University Press: Cambridge, UK.