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{{for|United States navy captain|Lloyd Stowell Shapley}}
{{for|Lloyd Stowell Shapley's grand-uncle, the United States navy captain|Lloyd Stowell Shapley}}
{{short description|American mathematician}}
{{Short description|American mathematician (1923–2016)}}
{{Use mdy dates|date=March 2016}}
{{Use mdy dates|date=March 2016}}
{{Infobox scientist
{{Infobox scientist
| image = Shapley, Lloyd (1923).jpeg{{!}}border
| image = Shapley, Lloyd (1923).jpeg{{!}}border
| caption = Shapley in 1980
| caption = Shapley in 1980
| birth_name = Lloyd Stowell Shapley
| birth_name = Lloyd Stowell Shapley
| birth_date = {{Birth date|1923|6|2}}
| birth_date = {{Birth date|1923|6|2}}
| birth_place = [[Cambridge, Massachusetts]], U.S.
| birth_place = [[Cambridge, Massachusetts]], U.S.
| death_date = {{death date and age|2016|3|12|1923|6|2}}
| death_date = {{death date and age|2016|3|12|1923|6|2}}
| death_place = [[Tucson, Arizona]], U.S.
| death_place = [[Tucson, Arizona]], U.S.
⚫
| alma_mater = [[Harvard University]] ([[B. A.|BA]])<br>[[Princeton University]] ([[PhD]])
| nationality = [[United States|American]]
| spouse = Marian Louise Shapley (since 1955)<ref>{{cite news |last1=Jain |first1=C |title=Spouse - source from NYTimes |work=The New York Times |date=March 15, 2016 |url=https://www.nytimes.com/2016/03/15/business/economy/lloyd-s-shapley-92-nobel-laureate-and-a-father-of-game-theory-is-dead.html }}</ref>
⚫
| alma_mater = [[Princeton University]]<br />[[Harvard University]]
| doctoral_advisor = [[Albert W. Tucker]]
| doctoral_advisor = [[Albert W. Tucker]]<ref name=AWT_LSShapley>{{mathgenealogy|id=46053}}</ref>
| doctoral_students =
| doctoral_students =
| thesis_title = Additive and non-additive set functions
⚫
| known_for = [[Shapley value]]<br />[[Shapley–Shubik power index]]<br />[[stochastic games]]<br />[[Bondareva–Shapley theorem]]<br />[[Shapley–Folkman lemma|Shapley–Folkman lemma
| thesis_url = https://www.proquest.com/docview/302034176/
⚫
& theorem]]<br />[[Gale–Shapley algorithm]]<br />[[potential game]]<br />[[Core (game theory)|core]], kernel and nucleolus <br />[[market games]]<br />[[authority distribution]]<br />multi-person utility<br />non-atomic games
| thesis_year = 1953
| influences = [[John von Neumann]]<br />[[Martin Shubik]]<br />[[Jon Folkman]]
⚫
| known_for = [[Shapley value]]<br />[[Shapley–Shubik power index]]<br />[[stochastic games]]<br />[[Bondareva–Shapley theorem]]<br />[[Shapley–Folkman lemma|Shapley–Folkman lemma
| influenced = [[Martin Shubik]]<br />[[Jon Folkman]]
⚫
& theorem]]<br />[[Gale–Shapley algorithm]]<br />[[potential game]]<br />[[Core (game theory)|core]], kernel, and nucleolus <br />[[market games]]<br />[[authority distribution]]<br />multi-person utility<br />non-atomic games
| awards = [[Nobel Memorial Prize in Economic Sciences]] (2012)<br>[[Golden Goose Award]] (2013)<br>[[John von Neumann Theory Prize]] (1981)
| awards = [[Nobel Memorial Prize in Economic Sciences]] (2012)<br>[[File:Bronze Star medal.jpg|10px]] [[Bronze Star Medal]](1944)<br> [[Golden Goose Award]] (2013)<br>[[John von Neumann Theory Prize]] (1981)
| field = [[Mathematics]], [[economics]]
| work_institution = {{nowrap|[[University of California, Los Angeles]]}}<br />[[RAND Corporation]]<br />[[Princeton University]]
| field = [[Mathematics]], [[economics]]
| work_institution = {{nowrap|[[University of California, Los Angeles]]}}<br />[[RAND Corporation]]<br />[[Princeton University]]
| website = {{URL|http://www.econ.ucla.edu/shapley/}}
}}
}}

'''Lloyd Stowell Shapley''' ({{IPAc-en|ˈ|ʃ|æ|p|l|i}}; 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]]. Shapley is generally considered one of the most important contributors to the development of game theory since the work of [[John von Neumann|von Neumann]] and [[Oskar Morgenstern|Morgenstern]].<ref>Roth, A.E., Introduction to the Shapley Value, in "The Shapley Value: Essays in Honor of Lloys S. Shapley", Cambridge University Press, 1988.</ref> 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]]."<ref name=":0">{{Cite news|url=https://www.economist.com/blogs/freeexchange/2016/03/matchmaker-heaven|title=Lloyd Shapley, a Nobel laureate in economics, has died|newspaper=The Economist|issn=0013-0613|access-date=March 13, 2016}}</ref><ref>{{cite journal|url=http://marketdesigner.blogspot.com/2016/03/lloyd-s-shapley-1923-2016.html|title=Lloyd S. Shapley 1923– 2016|last=Roth|first=Al|date=March 12, 2016|website=Market Design|pmid=27075091|access-date=March 13, 2016}}</ref>
'''Lloyd Stowell Shapley''' ({{IPAc-en|ˈ|ʃ|æ|p|l|i}}; June 2, 1923 – March 12, 2016) was an American [[mathematician]] and [[Nobel Memorial Prize]]-winning [[economist]]. He contributed to the fields of [[mathematical economics]] and especially [[game theory]]. Shapley is generally considered one of the most important contributors to the development of game theory since the work of [[John von Neumann|von Neumann]] and [[Oskar Morgenstern|Morgenstern]].<ref>Roth, A.E., Introduction to the Shapley Value, in "The Shapley Value: Essays in Honor of Lloyd S. Shapley", Cambridge University Press, 1988.</ref> 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]]."<ref name=":0">{{Cite news|url=https://www.economist.com/blogs/freeexchange/2016/03/matchmaker-heaven|title=Lloyd Shapley, a Nobel laureate in economics, has died|newspaper=The Economist|issn=0013-0613|access-date=March 13, 2016}}</ref><ref>{{cite journal|url=http://marketdesigner.blogspot.com/2016/03/lloyd-s-shapley-1923-2016.html|title=Lloyd S. Shapley 1923– 2016|last=Roth|first=Al|date=March 12, 2016|journal=Nature|volume=532|issue=7598|page=178|doi=10.1038/532178a|pmid=27075091|bibcode=2016Natur.532..178R|s2cid=4469185|access-date=March 13, 2016|doi-access=free}}</ref>


== Life and career ==
== Life and career ==


Lloyd Shapley was born on June 2, 1923, in [[Cambridge, Massachusetts]], one of the sons of astronomers [[Harlow Shapley]] and [[Martha Betz Shapley]], both from Missouri.<ref>{{cite news|url=https://www.nytimes.com/1981/01/27/obituaries/martha-betz-shapley.html|title=MARTHA BETZ SHAPLEY|date=January 27, 1981|work=The New York Times}}</ref> He attended [[Phillips Exeter Academy]] and was a student at Harvard when he was drafted in 1943. He served in the [[United States Army Air Corps]] in [[Chengdu, China]] and received the [[Bronze Star Medal|Bronze Star]] decoration for breaking the Soviet weather code.<ref name=int>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2012/shapley-interview.html|title=Lloyd S. Shapley – Interview|publisher=Nobel Media AB| accessdate = March 13, 2016}}</ref>
Lloyd Shapley was born on June 2, 1923, in [[Cambridge, Massachusetts]], one of the sons of astronomers [[Harlow Shapley]] and [[Martha Betz Shapley]], both from Missouri.<ref>{{cite news|url=https://www.nytimes.com/1981/01/27/obituaries/martha-betz-shapley.html|title=MARTHA BETZ SHAPLEY|date=January 27, 1981|work=The New York Times}}</ref> He attended [[Phillips Exeter Academy]] and was a student at Harvard when he was drafted in 1943. He served in the [[United States Army Air Corps]] in [[Chengdu, China]] and received the [[Bronze Star Medal|Bronze Star]] decoration for breaking the Soviet weather code.<ref name=int>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2012/shapley-interview.html|title=Lloyd S. Shapley – Interview|publisher=Nobel Media AB| access-date = March 13, 2016}}</ref>


After the war, Shapley returned to Harvard and graduated with an [[Bachelor of Arts|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.<ref name=princ>{{cite web | url = https://www.princeton.edu/main/news/archive/S35/03/02E57/index.xml | title = Princeton alumnus Shapley wins Nobel Prize | date= October 15, 2012 | accessdate = March 13, 2016|publisher = [[Princeton University]]}}</ref> His thesis and post-doctoral work introduced the [[Shapley value]] and the [[core (game theory)|core]] solution in [[game theory]]. 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]]'', along with [[Mel Hausner]], [[John Forbes Nash]], and [[Martin Shubik]].<ref>Hausner, M., Nash, J. F., Shapley, L. S. & Shubik, M., (1964), "So Long Sucker, A Four-Person Game", ''Game Theory and Related Approaches to Social Behavior'', John Wiley & Sons, Inc., New York.</ref> Israeli economist [[Robert Aumann]] said Shapley was "the greatest game theorist of all time."<ref name="Hagerty, James 2016">Hagerty, James, Lloyd Shapley: 1923-2016, Wall Street Journal, March 19–20, 2016, p. A7.</ref>
After the war, Shapley returned to Harvard and graduated with an [[Bachelor of Arts|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<ref name=princ>{{cite web | url = https://www.princeton.edu/main/news/archive/S35/03/02E57/index.xml | title = Princeton alumnus Shapley wins Nobel Prize | date= October 15, 2012 | access-date = March 13, 2016|publisher = [[Princeton University]]}}</ref> based on the thesis "Additive and non-additive set functions".{{r|AWT_LSShapley}}<ref name=PhDLink>{{cite web
|url=https://perso.uclouvain.be/pierre.dehez/Shapley/Shapley-Thesis.pdf
|title=Additive and non-additive set functions
| author=L.S. Shapley|year=1953| access-date = May 13, 2021
}}</ref> His thesis and post-doctoral work introduced the [[Shapley value]] and the [[core (game theory)|core]] solution in [[game theory]]. 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]]'', along with [[Mel Hausner]], [[John Forbes Nash]], and [[Martin Shubik]].<ref>Hausner, M., Nash, J. F., Shapley, L. S. & Shubik, M., (1964), "So Long Sucker, A Four-Person Game", ''Game Theory and Related Approaches to Social Behavior'', John Wiley & Sons, Inc., New York.</ref> Israeli economist and Nobel Laureate [[Robert Aumann]] considered Shapley to be "the greatest game theorist of all time."<ref name="Hagerty, James 2016">Hagerty, James, Lloyd Shapley: 1923–2016, Wall Street Journal, March 19–20, 2016, p. A7.</ref>


[[File:Lloyd Shapley 2 2012.jpg|left|thumb|upright=.85|Lloyd Shapley in Stockholm 2012]]
[[File:Lloyd Shapley 2 2012.jpg|left|thumb|upright=.85|Lloyd Shapley in Stockholm 2012]]
From 1981 until his death, Shapley was a professor 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, in [[Tucson, Arizona]], after suffering from a [[broken hip]], at the age of 92.<ref name=":0" />
From 1981 until his death, Shapley was a professor at the [[University of California, Los Angeles]] (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]], after suffering from a [[broken hip]], at the age of 92.<ref name=":0" />


Shapley was an expert [[Kriegspiel (chess)|Kriegspiel]] player, and an avid baseball fan.<ref name="Hagerty, James 2016"/>
Shapley was an expert [[Kriegspiel (chess)|Kriegspiel]] player, and an avid baseball fan.<ref name="Hagerty, James 2016"/>
Line 37: Line 44:
== Contribution ==
== 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 voting|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 value|Aumann–Shapley]] pricing, the [[John Harsanyi|Harsanyi]]–Shapley solution, the [[Snow–Shapley theorem]] for matrix games, and the [[Shapley–Folkman lemma|Shapley–Folkman lemma & theorem]] bear his name.<ref name=aea/> 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".<ref name=econ>{{cite news | url = https://www.economist.com/blogs/freeexchange/2016/03/matchmaker-heaven | title = Matchmaker in heaven – Lloyd Shapley, a Nobel laureate in economics, has died | work = [[The Economist]] | accessdate = March 13, 2016 | date = March 13, 2016}}</ref> The [[American Economic Association]] noted that Shapley was "one of the giants of game theory and economic theory".<ref name=aea>{{cite web | url = https://www.aeaweb.org/PDF_files/Bios/Shapley_bio.pdf | accessdate = March 13, 2016 | publisher = [[American Economic Association]] | title = Lloyd Shapley | url-status = dead | archiveurl = https://web.archive.org/web/20160316223210/https://www.aeaweb.org/PDF_files/Bios/Shapley_bio.pdf | archivedate = March 16, 2016 | df = mdy-all }}</ref>
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 voting|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 value|Aumann–Shapley]] pricing, the [[John Harsanyi|Harsanyi]]–Shapley solution, the [[Snow–Shapley theorem]] for matrix games, and the [[Shapley–Folkman lemma|Shapley–Folkman lemma & theorem]] bear his name.<ref name=aea/> 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".<ref name=econ>{{cite news | url = https://www.economist.com/blogs/freeexchange/2016/03/matchmaker-heaven | title = Matchmaker in heaven – Lloyd Shapley, a Nobel laureate in economics, has died | newspaper = [[The Economist]] | access-date = March 13, 2016 | date = March 13, 2016}}</ref> The [[American Economic Association]] noted that Shapley was "one of the giants of game theory and economic theory".<ref name=aea>{{cite web | url = https://www.aeaweb.org/PDF_files/Bios/Shapley_bio.pdf | access-date = March 13, 2016 | publisher = [[American Economic Association]] | title = Lloyd Shapley | url-status = dead | archive-url = https://web.archive.org/web/20160316223210/https://www.aeaweb.org/PDF_files/Bios/Shapley_bio.pdf | archive-date = March 16, 2016 | df = mdy-all }}</ref>


Besides, his early work with R. N. Snow and [[Samuel Karlin]] on [[matrix game]]s 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 solution|Von Neumann–Morgenstern stable sets]]. His work with [[Michael Maschler|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.<ref>{{Cite book | url = https://books.google.com/books?id=qWyjAQAAQBAJ&pg=PA385&lpg=PA385&dq=shapley+%22utility+theory%22#v=onepage | title = Economic Thinkers: A Biographical Encyclopedia | page = 385 | last = Diertele | first = David A. | accessdate = 2016-03-13| isbn = 9780313397479 | date = 2013-08-08 }}</ref>
Besides, his early work with R. N. Snow and [[Samuel Karlin]] on [[matrix game]]s 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 solution|Von Neumann–Morgenstern stable sets]]. His work with [[Michael Maschler|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.<ref>{{Cite book | url = https://books.google.com/books?id=qWyjAQAAQBAJ&q=shapley+%22utility+theory%22&pg=PA385 | title = Economic Thinkers: A Biographical Encyclopedia | page = 385 | last = Diertele | first = David A. | access-date = 2016-03-13| isbn = 9780313397479 | date = 2013-08-08 | publisher = Abc-Clio }}</ref>


Shapley argued with his sons about whether he should accept the Nobel Prize at all. He opined that his father, the astronomer [[Harlow Shapley]], deserved it more. His sons persuaded him to accept it and accompanied him to [[Stockholm, Sweden|Stockholm]].<ref>Hagerty, James, Lloyd Shapley: 1923-2016, Wall Street Journal, March 19–20, 2016, p.A7</ref>
Shapley argued with his sons about whether he should accept the Nobel Prize at all. He opined that his father, the astronomer [[Harlow Shapley]], deserved it more. His sons persuaded him to accept it and accompanied him to [[Stockholm, Sweden|Stockholm]].<ref>Hagerty, James, Lloyd Shapley: 1923–2016, Wall Street Journal, March 19–20, 2016, p.A7</ref>


== Awards and honors ==
== Awards and honors ==
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* [[Bronze Star Medal|Bronze Star]], U.S. Army Air Corps, 1944<ref name=int/>
* [[Bronze Star Medal|Bronze Star]], U.S. Army Air Corps, 1944<ref name=int/>
* Procter Fellow, [[Princeton University]], 1951–52<ref name=econometric/>
* Procter Fellow, [[Princeton University]], 1951–52<ref name=econometric/>
* Fellow, [[Econometric Society]], 1967<ref name=econometric>{{cite web | url = http://www.econ.ucla.edu/shapley/ShapleyBio.1.html | title = Lloyd Stowell Shapley – Vita | accessdate = March 13, 2016 | publisher = [[UCLA]]}}</ref>
* Fellow, [[Econometric Society]], 1967<ref name=econometric>{{cite web | url = http://www.econ.ucla.edu/shapley/ShapleyBio.1.html | title = Lloyd Stowell Shapley – Vita | access-date = March 13, 2016 | publisher = [[UCLA]]}}</ref>
* Fellow, [[American Academy of Arts and Sciences]], 1974<ref name=econometric/>
* Fellow, [[American Academy of Arts and Sciences]], 1974<ref name=econometric/>
* Member, [[National Academy of Sciences]], 1978<ref name=econometric/>
* Member, [[National Academy of Sciences]], 1978<ref name=econometric/>
* [[John von Neumann Theory Prize]], 1981<ref name=econometric/>
* [[John von Neumann Theory Prize]], 1981<ref name=econometric/>
* Honorary Ph.D., [[Hebrew University of Jerusalem]], 1986<ref name=econometric/>
* Honorary Ph.D., [[Hebrew University of Jerusalem]], 1986<ref name=econometric/>
* Fellow, INFORMS ([[Institute for Operations Research and the Management Sciences]]), 2002<ref>{{cite web | url = https://www.informs.org/Connect-with-People/Fellows/INFORMS-Fellows-Class-of-2002 | title = INFORMS – Fellows Class of 2002 | publisher = [[Institute for Operations Research and the Management Sciences]] | accessdate = March 13, 2016 | url-status = dead | archiveurl = https://web.archive.org/web/20160314012641/https://www.informs.org/Connect-with-People/Fellows/INFORMS-Fellows-Class-of-2002 | archivedate = March 14, 2016 | df = mdy-all }}</ref>
* Fellow, INFORMS ([[Institute for Operations Research and the Management Sciences]]), 2002<ref>{{cite web | url = https://www.informs.org/Connect-with-People/Fellows/INFORMS-Fellows-Class-of-2002 | title = INFORMS – Fellows Class of 2002 | publisher = [[Institute for Operations Research and the Management Sciences]] | access-date = March 13, 2016 | url-status = dead | archive-url = https://web.archive.org/web/20160314012641/https://www.informs.org/Connect-with-People/Fellows/INFORMS-Fellows-Class-of-2002 | archive-date = March 14, 2016 | df = mdy-all }}</ref>
* Distinguished Fellow, [[American Economic Association]], 2007<ref>{{cite web | url = https://www.aeaweb.org/honors_awards/disting_fellows.php | title = Distinguished Fellows | publisher = [[American Economic Association]] | accessdate = March 13, 2016}}</ref>
* Distinguished Fellow, [[American Economic Association]], 2007<ref>{{cite web | url = https://www.aeaweb.org/honors_awards/disting_fellows.php | title = Distinguished Fellows | publisher = [[American Economic Association]] | access-date = March 13, 2016}}</ref>
* Fellow, [[American Mathematical Society]], 2012<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved July 18, 2013.</ref>
* Fellow, [[American Mathematical Society]], 2012<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved July 18, 2013.</ref>
* Sveriges Riksbank [[Nobel Memorial Prize in Economic Sciences]], 2012<ref name=princ/>
* Sveriges Riksbank [[Nobel Memorial Prize in Economic Sciences]], 2012<ref name=princ/>
* [[Golden Goose Award]], 2013<ref>{{cite web | title=Market Design | url=http://www.goldengooseaward.org/awardees/zfh0utmzft7uewzc3lscuvdp21ogw2 | publisher=The Golden Goose Award | accessdate=May 27, 2015}}</ref>
* [[Golden Goose Award]], 2013<ref>{{cite web | title=Market Design | url=http://www.goldengooseaward.org/awardees/zfh0utmzft7uewzc3lscuvdp21ogw2 | publisher=The Golden Goose Award | access-date=May 27, 2015}}</ref>


== Selected publications ==
== Selected publications ==
Line 78: Line 85:


== See also ==
== See also ==
⚫
{{Portal|Economics|Biography}}


⚫
{{Portal|Economics|Biography}}
* [[Matching theory (economics)]]
* [[Matching theory (economics)]]


== References ==
== References ==

{{reflist|30em}}
{{reflist|30em}}


==Further reading==
==Further reading==

''Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms'', Donald E. Knuth, American Mathematical Society, 1997 (English Translation.)
''Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms'', Donald E. Knuth, American Mathematical Society, 1997 (English Translation.)


== External links ==
== External links ==
* [http://www.econ.ucla.edu/shapley/ Home Page]
<!--* [http://www.econ.ucla.edu/shapley/ Home Page]
* {{MathGenealogy|id=46053}}
* {{MathGenealogy}}-->
* [https://web.archive.org/web/20061001143028/http://www.ma.huji.ac.il/~mseyal/shapley4to95.pdf The Shapley Value]
* [https://web.archive.org/web/20061001143028/http://www.ma.huji.ac.il/~mseyal/shapley4to95.pdf The Shapley Value]
* [https://web.archive.org/web/20121203072321/http://www.informs.org/Recognize-Excellence/Award-Recipients/Lloyd-S.-Shapley 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''."
* [https://web.archive.org/web/20121203072321/http://www.informs.org/Recognize-Excellence/Award-Recipients/Lloyd-S.-Shapley 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''."
* [https://www.informs.org/About-INFORMS/History-and-Traditions/Biographical-Profiles/Wolfe-Philip Albert Tucker's comment on L.S.Shapley's work]. In 1995, [[Albert W. Tucker]] 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.
* [https://www.informs.org/About-INFORMS/History-and-Traditions/Biographical-Profiles/Wolfe-Philip Albert Tucker's comment on L.S.Shapley's work]. In 1995, [[Albert W. Tucker]] 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.
* {{Nobelprize|name=Lloyd S. Shapley}} including the Nobel Lecture
* [https://web.archive.org/web/20110719104159/http://ratio.huji.ac.il/dp/dp428.pdf Robert Aumann's Nobel lecture], also see here [http://www.huji.ac.il/dovrut/nobel_lecture.doc].
* [https://web.archive.org/web/20110719104159/http://ratio.huji.ac.il/dp/dp428.pdf Robert Aumann's Nobel lecture], also see here [http://www.huji.ac.il/dovrut/nobel_lecture.doc].
* [http://newsroom.ucla.edu/releases/ucla-mourns-the-passing-of-nobel-laureate-lloyd-shapley-92 UCLA - In Memoriam]
* [http://newsroom.ucla.edu/releases/ucla-mourns-the-passing-of-nobel-laureate-lloyd-shapley-92 UCLA – In Memoriam]
* [https://www.informs.org/content/view/full/271822 Biography of Lloyd S. Shapley] from the Institute for Operations Research and the Management Sciences
* [https://www.informs.org/content/view/full/271822 Biography of Lloyd S. Shapley] from the Institute for Operations Research and the Management Sciences
*{{Google Scholar id|dbF9HlQAAAAJ}}
* {{Google Scholar id|dbF9HlQAAAAJ}}
*{{cite web|title=Lloyd S. Shapley|url=https://econpapers.repec.org/RAS/psh559.htm|publisher=[[EconPapers]]}}
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Latest revision as of 11:52, 29 September 2024

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

Lloyd Shapley
Shapley in 1980
Born
Lloyd Stowell Shapley

(1923-06-02)June 2, 1923
Cambridge, Massachusetts, U.S.
DiedMarch 12, 2016(2016-03-12) (aged 92)
Tucson, Arizona, U.S.
Alma materHarvard University (BA)
Princeton University (PhD)
Known forShapley 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
SpouseMarian Louise Shapley (since 1955)[2]
AwardsNobel Memorial Prize in Economic Sciences (2012)
Bronze Star Medal(1944)
Golden Goose Award (2013)
John von Neumann Theory Prize (1981)
Scientific career
FieldsMathematics, economics
InstitutionsUniversity of California, Los Angeles
RAND Corporation
Princeton University
ThesisAdditive and non-additive set functions (1953)
Doctoral advisorAlbert W. Tucker[1]
Websitewww.econ.ucla.edu/shapley/

Lloyd Stowell Shapley (/ˈʃæpli/; June 2, 1923 – March 12, 2016) was an American mathematician and Nobel Memorial Prize-winning economist. He contributed to the fields of mathematical economics and especially game theory. Shapley is generally considered one of the most important contributors to the development of game theory since the work of von Neumann and Morgenstern.[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][5]

Life and career

[edit]

Lloyd Shapley was born on June 2, 1923, in Cambridge, Massachusetts, one of the sons of astronomers Harlow Shapley and Martha Betz Shapley, both from Missouri.[6] He attended Phillips Exeter Academy and was a student at Harvard when he was drafted in 1943. He served in the United States Army Air Corps in Chengdu, China and received the Bronze Star decoration for breaking the Soviet weather code.[7]

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[8] based on the thesis "Additive and non-additive set functions".[1][9] His thesis and post-doctoral work introduced the Shapley value and the core solution in game theory. 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, along with Mel Hausner, John Forbes Nash, and Martin Shubik.[10] Israeli economist and Nobel Laureate Robert Aumann considered Shapley to be "the greatest game theorist of all time."[11]

Lloyd Shapley in Stockholm 2012

From 1981 until his death, Shapley was a professor at the University of California, Los Angeles (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, after suffering from a broken hip, at the age of 92.[4]

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

Contribution

[edit]

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.[12] 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".[13] The American Economic Association noted that Shapley was "one of the giants of game theory and economic theory".[12]

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.[14]

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

Awards and honors

[edit]

Selected publications

[edit]
  • 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. doi:10.1073/pnas.39.10.1095
  • 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.

See also

[edit]

References

[edit]
  1. ^ a b Lloyd Shapley at the Mathematics Genealogy Project
  2. ^ Jain, C (March 15, 2016). "Spouse - source from NYTimes". The New York Times.
  3. ^ Roth, A.E., Introduction to the Shapley Value, in "The Shapley Value: Essays in Honor of Lloyd S. Shapley", Cambridge University Press, 1988.
  4. ^ a b "Lloyd Shapley, a Nobel laureate in economics, has died". The Economist. ISSN 0013-0613. Retrieved March 13, 2016.
  5. ^ Roth, Al (March 12, 2016). "Lloyd S. Shapley 1923– 2016". Nature. 532 (7598): 178. Bibcode:2016Natur.532..178R. doi:10.1038/532178a. PMID 27075091. S2CID 4469185. Retrieved March 13, 2016.
  6. ^ "MARTHA BETZ SHAPLEY". The New York Times. January 27, 1981.
  7. ^ a b "Lloyd S. Shapley – Interview". Nobel Media AB. Retrieved March 13, 2016.
  8. ^ a b "Princeton alumnus Shapley wins Nobel Prize". Princeton University. October 15, 2012. Retrieved March 13, 2016.
  9. ^ Hausner, M., Nash, J. F., Shapley, L. S. & Shubik, M., (1964), "So Long Sucker, A Four-Person Game", Game Theory and Related Approaches to Social Behavior, John Wiley & Sons, Inc., New York.
  10. ^ a b Hagerty, James, Lloyd Shapley: 1923–2016, Wall Street Journal, March 19–20, 2016, p. A7.
  11. ^ a b "Lloyd Shapley" (PDF). American Economic Association. Archived from the original (PDF) on March 16, 2016. Retrieved March 13, 2016.
  12. ^ "Matchmaker in heaven – Lloyd Shapley, a Nobel laureate in economics, has died". The Economist. March 13, 2016. Retrieved March 13, 2016.
  13. ^ Diertele, David A. (August 8, 2013). Economic Thinkers: A Biographical Encyclopedia. Abc-Clio. p. 385. ISBN 9780313397479. Retrieved March 13, 2016.
  14. ^ Hagerty, James, Lloyd Shapley: 1923–2016, Wall Street Journal, March 19–20, 2016, p.A7
  15. ^ a b c d e f "Lloyd Stowell Shapley – Vita". UCLA. Retrieved March 13, 2016.
  16. ^ "INFORMS – Fellows Class of 2002". Institute for Operations Research and the Management Sciences. Archived from the original on March 14, 2016. Retrieved March 13, 2016.
  17. ^ "Distinguished Fellows". American Economic Association. Retrieved March 13, 2016.
  18. ^ List of Fellows of the American Mathematical Society, retrieved July 18, 2013.
  19. ^ "Market Design". The Golden Goose Award. Retrieved May 27, 2015.

Further reading

[edit]

Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms, Donald E. Knuth, American Mathematical Society, 1997 (English Translation.)

[edit]
Awards
Preceded by Laureate of the Nobel Memorial Prize in Economics
2012
Served alongside: Alvin E. Roth 		Succeeded by
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