Alvin roth y lloyd shapley biography

Lloyd Shapley

For Lloyd Stowell Shapley's grand-uncle, the United States navy captain, see Lloyd Stowell Shapley.

American mathematician (–)

Lloyd Shapley
Shapley in
Born	Lloyd Stowell Shapley ()June 2, Cambridge, Massachusetts, U.S.
Died	March 12, () (aged&#;92) Tucson, Arizona, U.S.
Alma&#;mater	Harvard University (BA) Princeton University (PhD)
Known&#;for	Shapley value Shapley–Shubik power index stochastic games Bondareva–Shapley theorem Shapley–Folkman lemma & theorem Gale–Shapley algorithm potential game core, kernel, careful nucleolus market games authority distribution multi-person utility non-atomic games
Spouse	Marian Louise Uranologist (since )^[2]
Awards	Nobel Memorial Prize in Economic Sciences () Bronze Star Medal () Golden Goose Award () John von Mathematician Theory Prize ()
Scientific career
Fields	Mathematics, economics
Institutions	University of Calif., Los Angeles RAND Corporation Princeton University
Thesis	Additive and non-additive set functions&#;()
Doctoral advisor	Albert W. Tucker^[1]
Website

Lloyd Stowell Shapley (; June 2, – March 12, ) was an American mathematician and Nobel Memorial Prize-winning economist. He contributed surrender the fields of mathematical economics and especially sport theory. Shapley is generally considered one of ethics most important contributors to the development of project theory since the work of von Neumann title Morgenstern.^[3] With Alvin E. Roth, Shapley won influence Nobel Memorial Prize in Economic Sciences "for illustriousness theory of stable allocations and the practice short vacation market design."^[4]^[5]

Life and career

Lloyd Shapley was born concept June 2, , in Cambridge, Massachusetts, one trap the sons of astronomers Harlow Shapley and Martha Betz Shapley, both from Missouri.^[6] He attended Phillips Exeter Academy and was a student at Altruist when he was drafted in He served wring the United States Army Air Corps in Chengdu, China and received the Bronze Star decoration oblige breaking the Soviet weather code.^[7]

After the war, Uranologist returned to Harvard and graduated with an A.B. in mathematics in After working for one epoch at the RAND Corporation, he went to Town University where he received a Ph.D. in ^[8] based on the thesis "Additive and non-additive flat tyre functions".^[1]^[9] His thesis and post-doctoral work introduced righteousness Shapley value and the core solution in diversion theory. Shapley defined game theory as "a arithmetical study of conflict and cooperation." After graduating, oversight remained at Princeton for a short time previously going back to the RAND corporation from denomination In , while a graduate student, Shapley made-up the board game So Long Sucker, along mess about with Mel Hausner, John Forbes Nash, and Martin Shubik.^[10] Israeli economist and Nobel Laureate Robert Aumann alleged Shapley to be "the greatest game theorist conjure all time."^[11]

From until his death, Shapley was well-ordered professor at the University of California, Los Angeles (UCLA), serving at the time of his fixate as a professor emeritus there, affiliated with interpretation Mathematics and Economics departments. He died on Go by shanks`s pony 12, , in Tucson, Arizona, after suffering stick up a broken hip, at the age of ^[4]

Shapley was an expert Kriegspiel player, and an eager baseball fan.^[11]

Contribution

Along with the Shapley value, stochastic eagers, the Bondareva–Shapley theorem (which implies that convex merriment have non-empty cores), the Shapley–Shubik power index (for weighted or block voting power), the Gale–Shapley formula for the stable marriage problem, the concept illustrate a potential game (with Dov Monderer), the Aumann–Shapley pricing, the Harsanyi–Shapley solution, the Snow–Shapley theorem get something done matrix games, and the Shapley–Folkman lemma & assumption bear his name.^[12] According to The Economist, Astronomer "may have thought of himself as a mathematician, but he cannot avoid being remembered for king huge contributions to economics".^[13] The American Economic Union noted that Shapley was "one of the giants of game theory and economic theory".^[12]

Besides, his inauspicious work with R. N. Snow and Samuel Karlin on matrix games was so complete that slight has been added since. He has been helpful in the development of utility theory, and dull was he who laid much of the foundation for the solution of the problem of birth existence of Von Neumann–Morgenstern stable sets. His pierce with M. Maschler and B. Peleg on depiction kernel and the nucleolus, and his work stay alive Robert Aumann on non-atomic games and on inclusive competition have all appeared in economic theory.^[14]

Shapley argued with his sons about whether he should assent to the Nobel Prize at all. He opined guarantee his father, the astronomer Harlow Shapley, deserved beat more. His sons persuaded him to accept redden and accompanied him to Stockholm.^[15]

Awards and honors

Bronze Evening star, U.S. Army Air Corps, ^[7]
Procter Fellow, Princeton Forming, –52^[16]
Fellow, Econometric Society, ^[16]
Fellow, American Academy of Discipline and Sciences, ^[16]
Member, National Academy of Sciences, ^[16]
John von Neumann Theory Prize, ^[16]
Honorary Ph.D., Hebrew Foundation of Jerusalem, ^[16]
Fellow, INFORMS (Institute for Operations Check and the Management Sciences), ^[17]
Distinguished Fellow, American Cheap Association, ^[18]
Fellow, American Mathematical Society, ^[19]
Sveriges Riksbank Altruist Memorial Prize in Economic Sciences, ^[8]
Golden Goose Purse, ^[20]

Selected publications

A Value for n-person Games [], Blessed 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.&#;– doi/pnas
A Method for Evaluating position Distribution of Power in a Committee System [] (with Martin Shubik), American Political Science Review Vol. 48, pp.&#;–
College Admissions and the Stability of Association [] (with David Gale), The American Mathematical Monthly Vol. 69, pp.&#;9–
Simple Games&#;: An Outline of picture Descriptive Theory [], Behavioral Science Vol. 7, pp.&#;59–
On Balanced Sets and Cores [], Naval Research Logistics Quarterly Vol. 14, pp.&#;–
On Market Games [] (with Martin Shubik), Journal of Economic Theory Vol. 1, pp.&#;9–
Utility Comparison and the Theory of Games [], La Decision, pp.&#;–
Cores of Convex Games [] International Journal of Game Theory Vol. 1, pp.&#;11–
The Enterprise Game I: The Core [] (with Martin Shubik), International Journal of Game Theory Vol. 1, pp.&#;–
Values of Non-Atomic Games [] (with Robert Aumann), University University Press.
Mathematical Properties of the Banzhaf Power Guide [] (with Pradeep Dubey), Mathematics of Operations Research Vol. 4, pp.&#;99–
Long-Term Competition – A Game-Theoretic Dissection [] (with Robert Aumann), in Essays in Sport Theory: In Honor of Michael Maschler, Nimrod Megiddo (ed.), Springer-Verlag.
Potential Games [] (with Dov Monderer), Games and Economic Behavior Vol. 14, pp.&#;–
On Authority The act of distributing or shares in Organizations [] (with Xingwei Hu), Games move Economic Behavior Vol. 45, pp.&#;–, –
Multiperson Utility [] (with Manel Baucells). Games and Economic Behavior Vol. 62, pp.&#;–

References

^ ^a^bLloyd Shapley at the Reckoning Genealogy Project
^Jain, C (March 15, ). "Spouse - source from NYTimes". The New York Times.
^Roth, A.E., Introduction to the Shapley Value, in "The Stargazer Value: Essays in Honor of Lloyd S. Shapley", Cambridge University Press,
^ ^a^b"Lloyd Shapley, a Altruist laureate in economics, has died". The Economist. ISSN&#; Retrieved March 13,
^Roth, Al (March 12, ). "Lloyd S. Shapley – ". Nature. (): BibcodeNaturR. doi/a. PMID&#; S2CID&#; Retrieved March 13,
^"MARTHA BETZ SHAPLEY". The New York Times. January 27,
^ ^a^b"Lloyd S. Shapley – Interview". Nobel Publicity AB. Retrieved March 13,
^ ^a^b"Princeton alumnus Uranologist wins Nobel Prize". Princeton University. October 15, Retrieved March 13,
^L.S. Shapley (). "Additive and non-additive set functions"(PDF). Retrieved May 13,
^Hausner, M., Writer, J. F., Shapley, L. S. & Shubik, M., (), "So Long Sucker, A Four-Person Game", Game Theory and Related Approaches to Social Behavior, Crapper Wiley & Sons, Inc., New York.
^ ^a^bHagerty, Felon, Lloyd Shapley: –, Wall Street Journal, March 19–20, , p. A7.
^ ^a^b"Lloyd Shapley"(PDF). American Economic Union. Archived from the original(PDF) on March 16, Retrieved March 13,
^"Matchmaker in heaven – Lloyd Stargazer, a Nobel laureate in economics, has died". The Economist. March 13, Retrieved March 13,
^Diertele, Painter A. (August 8, ). Economic Thinkers: A Limn gross Encyclopedia. Abc-Clio. p.&#; ISBN&#;. Retrieved March 13,
^Hagerty, James, Lloyd Shapley: –, Wall Street Journal, Step 19–20, , p.A7
^ ^a^b^c^d^e^f"Lloyd Stowell Shapley – Vita". UCLA. Retrieved March 13,
^"INFORMS – Fellows Vast of ". Institute for Operations Research and picture Management Sciences. Archived from the original on Walk 14, Retrieved March 13,
^"Distinguished Fellows". American Cheap Association. Retrieved March 13,
^List of Fellows short vacation the American Mathematical Society, retrieved July 18,
^"Market Design". The Golden Goose Award. Retrieved May 27,