Lloyd Stowell Shapley (; June 2, 1923 – March 12, 2016) was an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

and

Nobel Prize The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfr ...

-winning

economist An economist is a professional and practitioner in the social sciences, social science discipline of economics. The individual may also study, develop, and apply theories and concepts from economics and write about economic policy. Within this ...

. He contributed to the fields of mathematical economics and especially

game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...

. Shapley is generally considered one of the most important contributors to the development of game theory since the work of

von Neumann Von Neumann may refer to: * John von Neumann (1903–1957), a Hungarian American mathematician * Von Neumann family * Von Neumann (surname), a German surname * Von Neumann (crater), a lunar impact crater See also * Von Neumann algebra * Von Ne ...

and Morgenstern. With

Alvin E. Roth Alvin Eliot Roth (born December 18, 1951) is an American academic. He is the Craig and Susan McCaw professor of economics at Stanford University and the Gund professor of economics and business administration emeritus at Harvard University.

, Shapley won the 2012

Nobel Memorial Prize in Economic Sciences The Nobel Memorial Prize in Economic Sciences, officially the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel ( sv, Sveriges riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne), is an economics award administered ...

"for the theory of stable allocations and the practice of

market design Market design is a practical methodology for creation of markets of certain properties, which is partially based on mechanism design. In some markets, prices may be used to induce the desired outcomes — these markets are the study of auction the ...

Life and career

Lloyd Shapley was born on June 2, 1923, in

Cambridge, Massachusetts Cambridge ( ) is a city in Middlesex County, Massachusetts, United States. As part of the Boston metropolitan area, the cities population of the 2020 U.S. census was 118,403, making it the fourth most populous city in the state, behind Boston, ...

, one of the sons of astronomers

Harlow Shapley Harlow Shapley (November 2, 1885 – October 20, 1972) was an American scientist, head of the Harvard College Observatory (1921–1952), and political activist during the latter New Deal and Fair Deal. Shapley used Cepheid variable stars to estim ...

and Martha Betz Shapley, both from Missouri. He attended

Phillips Exeter Academy (not for oneself) la, Finis Origine Pendet (The End Depends Upon the Beginning) gr, Χάριτι Θεοῦ (By the Grace of God) , location = 20 Main Street , city = Exeter, New Hampshire , zipcode ...

and was a student at Harvard when he was drafted in 1943. He served in the

United States Army Air Corps The United States Army Air Corps (USAAC) was the aerial warfare service component of the United States Army between 1926 and 1941. After World War I, as early aviation became an increasingly important part of modern warfare, a philosophical r ...

in Chengdu, China and received the

Bronze Star The Bronze Star Medal (BSM) is a United States Armed Forces decoration awarded to members of the United States Armed Forces for either heroic achievement, heroic service, meritorious achievement, or meritorious service in a combat zone. Wh ...

decoration for breaking the Soviet weather code. After the war, Shapley returned to Harvard and graduated with an

A.B. Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four yea ...

in mathematics in 1948. After working for one year at the

RAND Corporation The RAND Corporation (from the phrase "research and development") is an American nonprofit global policy think tank created in 1948 by Douglas Aircraft Company to offer research and analysis to the United States Armed Forces. It is financed ...

, he went to

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

where he received a Ph.D. in 1953 based on the thesis "Additive and non-additive set functions". His thesis and post-doctoral work introduced the

Shapley value The Shapley value is a solution concept in cooperative game theory. It was named in honor of Lloyd Shapley, who introduced it in 1951 and won the Nobel Memorial Prize in Economic Sciences for it in 2012. To each cooperative game it assigns a uniq ...

and the

core Core or cores may refer to: Science and technology * Core (anatomy), everything except the appendages * Core (manufacturing), used in casting and molding * Core (optical fiber), the signal-carrying portion of an optical fiber * Core, the centra ...

solution in

. Shapley defined game theory as "a mathematical study of conflict and cooperation." After graduating, he remained at Princeton for a short time before going back to the RAND corporation from 1954 to 1981. In 1950, while a graduate student, Shapley invented the board game ''

So Long Sucker ''So Long Sucker'' is a board game invented in 1950 by Mel Hausner, John Nash, Lloyd Shapley, and Martin Shubik. It is a four-person bargaining/economic strategy game. Each player begins the game with seven chips, and in the course of play, attemp ...

'', along with Mel Hausner,

John Forbes Nash John Forbes Nash Jr. (June 13, 1928 – May 23, 2015) was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow g ...

, and

Martin Shubik Martin Shubik (1926-2018) was an American mathematical economist who specialized in game theory, defense analysis, and the theory of money and financial institutions. The latter was his main research interest and he coined the term "mathematical ...

. Israeli economist

Robert Aumann Robert John Aumann (Hebrew name: , Yisrael Aumann; born June 8, 1930) is an Israeli-American mathematician, and a member of the United States National Academy of Sciences. He is a professor at the Center for the Study of Rationality in the Hebrew ...

said Shapley was "the greatest game theorist of all time."Hagerty, James, Lloyd Shapley: 1923–2016, Wall Street Journal, March 19–20, 2016, p. A7. Lloyd Shapley 2 2012

From 1981 until his death, Shapley was a professor at the

University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...

(UCLA), serving at the time of his death as a professor emeritus there, affiliated with the Mathematics and Economics departments. He died on March 12, 2016, in

Tucson, Arizona , "(at the) base of the black ill , nicknames = "The Old Pueblo", "Optics Valley", "America's biggest small town" , image_map = , mapsize = 260px , map_caption = Interactive map ...

, after suffering from a broken hip, at the age of 92. Shapley was an expert Kriegspiel player, and an avid baseball fan.

Contribution

Along with the

, stochastic games, the

Bondareva–Shapley theorem The Bondareva–Shapley theorem, in game theory, describes a necessary and sufficient condition for the non-emptiness of the core of a cooperative game in characteristic function form. Specifically, the game's core is non-empty if and only if the ...

(which implies that convex games have non-empty cores), the

Shapley–Shubik power index The Shapley–Shubik power index was formulated by Lloyd Shapley and Martin Shubik in 1954 to measure the powers of players in a voting game. The index often reveals surprising power distribution that is not obvious on the surface. The constituent ...

(for

weighted A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is ...

or block voting power), the

Gale–Shapley algorithm In mathematics, economics, and computer science, the Gale–Shapley algorithm (also known as the deferred acceptance algorithm or propose-and-reject algorithm) is an algorithm for finding a solution to the stable matching problem, named for Davi ...

for the

stable marriage problem In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each elem ...

, the concept of a

potential game In game theory, a game is said to be a potential game if the incentive of all players to change their strategy can be expressed using a single global function called the potential function. The concept originated in a 1996 paper by Dov Monderer and ...

(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. According to ''

The Economist ''The Economist'' is a British weekly newspaper printed in demitab format and published digitally. It focuses on current affairs, international business, politics, technology, and culture. Based in London, the newspaper is owned by The Econo ...

'', 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 The American Economic Association (AEA) is a learned society in the field of economics. It publishes several peer-reviewed journals acknowledged in business and academia. There are some 23,000 members. History and Constitution The AEA was esta ...

noted that Shapley was "one of the giants of game theory and economic theory". Besides, his early work with R. N. Snow and

Samuel Karlin Samuel Karlin (June 8, 1924 – December 18, 2007) was an American mathematician at Stanford University in the late 20th century. Biography Karlin was born in Janów, Poland and immigrated to Chicago as a child. Raised in an Orthodox Jewish hous ...

on matrix games was so complete that little has been added since. He has been instrumental in the development of

utility theory As a topic of economics, utility is used to model worth or value. Its usage has evolved significantly over time. The term was introduced initially as a measure of pleasure or happiness as part of the theory of utilitarianism by moral philosopher ...

, 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

on non-atomic games and on long-term competition have all appeared in economic theory. Shapley argued with his sons about whether he should accept the Nobel Prize at all. He opined that his father, the astronomer

, deserved it more. His sons persuaded him to accept it and accompanied him to

Stockholm Stockholm () is the Capital city, capital and List of urban areas in Sweden by population, largest city of Sweden as well as the List of urban areas in the Nordic countries, largest urban area in Scandinavia. Approximately 980,000 people liv ...

Awards and honors

, U.S. Army Air Corps, 1944 * Procter Fellow,

, 1951–52 * Fellow,

Econometric Society The Econometric Society is an international society of academic economists interested in applying statistical tools to their field. It is an independent organization with no connections to societies of professional mathematicians or statisticians. ...

, 1967 * Fellow,

American Academy of Arts and Sciences The American Academy of Arts and Sciences (abbreviation: AAA&S) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and ...

, 1974 * Member,

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

, 1978 *

John von Neumann Theory Prize The John von Neumann Theory Prize of the Institute for Operations Research and the Management Sciences (INFORMS) is awarded annually to an individual (or sometimes a group) who has made fundamental and sustained contributions to theory in operati ...

, 1981 * Honorary Ph.D.,

Hebrew University of Jerusalem The Hebrew University of Jerusalem (HUJI; he, הַאוּנִיבֶרְסִיטָה הַעִבְרִית בִּירוּשָׁלַיִם) is a public research university based in Jerusalem, Israel. Co-founded by Albert Einstein and Dr. Chaim Weiz ...

, 1986 * Fellow, INFORMS (

Institute for Operations Research and the Management Sciences The Institute for Operations Research and the Management Sciences (INFORMS) is an international society for practitioners in the fields of operations research (O.R.), management science, and analytics. It was established in 1995 with the merger of ...

), 2002 * Distinguished Fellow,

, 2007 * Fellow,

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

, 2012 * Sveriges Riksbank

, 2012 *

Golden Goose Award The Golden Goose Award is a United States award in recognition of scientists whose federally funded basic research has led to innovations or inventions with significant impact on humanity or society. Created by Congressman Jim Cooper of Tennessee i ...

, 2013

Selected publications

* A Value for ''n''-person Games

953 Year 953 ( CMLIII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * Battle of Marash: Emir Sayf al-Dawla marches north into the Byzantine Empire an ...

In ''Contributions to the Theory of Games'' volume II, H. W. Kuhn and A. W. Tucker (eds.). * Stochastic Games

''Proceedings of National Academy of Science'' Vol. 39, pp. 1095–1100. * A Method for Evaluating the Distribution of Power in a Committee System

954 Year 954 ( CMLIV) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. Events By place Europe * Spring – A Hungarian army led by Bulcsú crosses the Rhine. He camps at Worms in th ...

(with

), ''

American Political Science Review The ''American Political Science Review'' is a quarterly peer-reviewed academic journal covering all areas of political science. It is an official journal of the American Political Science Association and is published on their behalf by Cambridg ...

'' Vol. 48, pp. 787–792. * College Admissions and the Stability of Marriage

962 Year 962 ( CMLXII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * December – Arab–Byzantine wars – Sack of Aleppo: A Byzantine e ...

(with

David Gale David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". w ...

), ''The

American Mathematical Monthly ''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an e ...

'' Vol. 69, pp. 9–15. * Simple Games : An Outline of the Descriptive Theory

Behavioral Science Behavioral sciences explore the cognitive processes within organisms and the behavioral interactions between organisms in the natural world. It involves the systematic analysis and investigation of human and animal behavior through naturalistic o ...

'' Vol. 7, pp. 59–66. * On Balanced Sets and Cores 967 ''

Naval Research Logistics Quarterly ''Naval Research Logistics'' is a peer-reviewed scientific journal that publishes papers in the field of logistics, especially those in the areas of operations research, applied statistics, and quantitative modeling. It was established in 19 ...

'' Vol. 14, pp. 453–460. * On Market Games

969 Year 969 ( CMLXIX) was a common year starting on Friday (link will display the full calendar) of the Julian calendar, the 969th year of the Common Era (CE) and ''Anno Domini'' (AD) designations, the 969th year of the 1st millennium, the 69th ...

(with

), ''

Journal of Economic Theory The ''Journal of Economic Theory'' is a bimonthly peer-reviewed academic journal covering the field of economic theory. Karl Shell has served as editor-in-chief of the journal since it was established in 1968. Since 2000, he has shared the editor ...

'' Vol. 1, pp. 9–25. * Utility Comparison and the Theory of Games

''La Decision'', pp. 251–263. * Cores of Convex Games

971 Year 971 ( CMLXXI) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * Battle of Dorostolon: A Byzantine expeditionary army (possibly 30–40,000 men) ...

''International Journal of Game Theory'' Vol. 1, pp. 11–26. * The Assignment Game I: The Core

(with

), ''International Journal of Game Theory'' Vol. 1, pp. 111–130. * ''Values of Non-Atomic Games''

974 Year 974 ( CMLXXIV) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar. Events By place Europe * Battle of Danevirke: Emperor Otto II defeats the rebel forces of King Harald I, who ha ...

(with

), Princeton University Press. * Mathematical Properties of the Banzhaf Power Index

979 Year 979 ( CMLXXIX) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * March 24 – Second Battle of Pankaleia: An Ibero-Byzantine expeditionary ...

(with

Pradeep Dubey Pradeep Dubey (born 9 January 1951) is an Indian game theorist. He is Professor of Economics at State University of New York, Stony Brook and a member of the Stony Brook Center for Game Theory. He also holds a visiting position at Cowles Founda ...

), ''

Mathematics of Operations Research ''Mathematics of Operations Research'' is a quarterly peer-reviewed scientific journal established in February 1976. It focuses on areas of mathematics relevant to the field of operations research such as continuous optimization, discrete optimiz ...

'' Vol. 4, pp. 99–132. * Long-Term Competition – A Game-Theoretic Analysis

994 Year 994 ( CMXCIV) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. Events By place Byzantine Empire * September 15 – Battle of the Orontes: Fatimid forces, under Turkish gener ...

(with

), in ''Essays in Game Theory: In Honor of

Michael Maschler Michael Bahir Maschler (Hebrew: ) (July 22, 1927 – July 20, 2008) was an Israeli mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathemat ...

'',

Nimrod Megiddo , birth_date = , birth_place = , death_date = , death_place = , citizenship = , field = Operations researchAlgorithms ComplexityMachine learning Game theory , workplaces = IBM Research ...

(ed.), Springer-Verlag. * Potential Games

996 Year 996 ( CMXCVI) was a leap year starting on Wednesday (link will display the full calendar) of the Julian calendar. Events By place Japan * February - Chotoku Incident: Fujiwara no Korechika and Takaie shoot an arrow at Retired Em ...

(with Dov Monderer), ''

Games and Economic Behavior ''Games and Economic Behavior'' (''GEB'') is a journal of game theory published by Elsevier. Founded in 1989, the journal's stated objective is to communicate game-theoretic ideas across theory and applications. It is considered to be the leadi ...

'' Vol. 14, pp. 124–143. * On Authority Distributions in Organizations

003 003, O03, 0O3, OO3 may refer to: *003, fictional British 00 Agent *003, former emergency telephone number for the Norwegian ambulance service (until 1986) *1990 OO3, the asteroid 6131 Towen * OO3 gauge model railway *''O03 (O2)'' and other related ...

(with Xingwei Hu), ''Games and Economic Behavior'' Vol. 45, pp. 132–152, 153–170. * Multiperson Utility

008 008, OO8, O08, or 0O8 may refer to: * The Streetwear Brand @008us , inspired by Ian Fleming & Virgil Abloh *"030", the fictional 030 Agent of MI6 * '' 038: Operation Exterminate'', a 1965 Italian action film * '' Explosivo 030'' a 1940 Argentine c ...

(with Manel Baucells). ''Games and Economic Behavior'' Vol. 62, pp. 329–347.

References

External links

The Shapley Value

Citation of von Neumann Theory Prize on L.S.Shapley's work
"Lloyd Shapley has dominated game theory for the thirty-seven years since von Neumann and Morgenstern published their path-breaking book, ''The Theory of Games and Economic Behavior''."
Albert Tucker's comment on L.S.Shapley's work
In 1995,

Albert W. Tucker Albert William Tucker (28 November 1905 – 25 January 1995) was a Canadian mathematician who made important contributions in topology, game theory, and non-linear programming. Biography Albert Tucker was born in Oshawa, Ontario, Canada, and ea ...

mentioned in his passing that Shapley was second only to Von Neumann as the most important researcher in theory of games so far. Philip Wolfe Interview by Irv Lustig, May 4, 2001. Video by Irv Lustig, Short Hills, NJ. * including the Nobel Lecture
Robert Aumann's Nobel lecture
also see her

UCLA – In Memoriam

Biography of Lloyd S. Shapley
from the Institute for Operations Research and the Management Sciences * * * {{DEFAULTSORT:Shapley, Lloyd Lloyd Shapley, 1923 births 2016 deaths People from Cambridge, Massachusetts 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 Fellows of the Institute for Operations Research and the Management Sciences Game theorists Mathematical economists RAND Corporation people Probability theorists 20th-century American writers 21st-century American non-fiction writers 20th-century American economists 21st-century American economists 20th-century American mathematicians 21st-century American mathematicians Harvard University alumni Fellows of the American Mathematical Society Distinguished Fellows of the American Economic Association Economists from Massachusetts United States Army Air Forces personnel of World War II American expatriates in China American people of German descent Phillips Exeter Academy alumni

Life and career

Contribution

Awards and honors

Selected publications

See also

References

Further reading

External links