Editing Shapley value (section)

{{short description|Concept in game theory}}
In [[cooperative game theory]], the '''Shapley value''' is a method ([[solution concept]]) for fairly distributing the total gains or costs among a group of players who have collaborated. For example, in a team project where each member contributed differently, the Shapley value provides a way to determine how much credit or blame each member deserves. 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.<ref>{{cite web |last=Shapley |first=Lloyd S. |date=August 21, 1951 |title=Notes on the n-Person Game -- II: The Value of an n-Person Game |url=https://www.rand.org/content/dam/rand/pubs/research_memoranda/2008/RM670.pdf |publisher=RAND Corporation |location=Santa Monica, Calif. |number=RM-670}}</ref><ref>{{cite book |title=The Shapley Value: Essays in Honor of Lloyd S. Shapley |publisher=Cambridge University Press |year=1988 |isbn=0-521-36177-X |editor-last=Roth |editor-first=Alvin E. |location=Cambridge |doi=10.1017/CBO9780511528446}}</ref> 

The Shapley value determines each player's contribution by considering how much the overall outcome changes when they join each possible combination of other players, and then averaging those changes. In essence, it calculates each player's average marginal contribution across all possible coalitions.<ref>{{cite book |last=Hart |first=Sergiu |title=The New Palgrave: Game Theory |publisher=Norton |year=1989 |isbn=978-0-333-49537-7 |editor-last=Eatwell |editor-first=J. |pages=210–216 |chapter=Shapley Value |doi=10.1007/978-1-349-20181-5_25 |editor2-last=Milgate |editor2-first=M. |editor3-last=Newman |editor3-first=P.}}</ref><ref>{{cite web |last=Hart |first=Sergiu |date=May 12, 2016 |title=A Bibliography of Cooperative Games: Value Theory |url=http://www.ma.huji.ac.il/~hart/value.html}}</ref> It is the only solution that satisfies four fundamental properties: efficiency, symmetry, additivity, and the dummy player (or null player) property,<ref name=":2" /> which are widely accepted as defining a fair distribution.

This method is used in many fields, from dividing profits in business partnerships to understanding feature importance in [[machine learning]].[[File:Lloyd Shapley 2 2012.jpg|thumb|Lloyd Shapley in 2012]]