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Difference between revisions of "Sharing"

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''imputation (in the theory of games)''
 
''imputation (in the theory of games)''
  
A distribution of the overall gain of all players in a [[Cooperative game|cooperative game]] which satisfies the rationality condition. Formally, if for a game with a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084800/s0848001.png" /> of players a characteristic function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084800/s0848002.png" /> is defined, a sharing is a vector <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084800/s0848003.png" /> such that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084800/s0848004.png" />; <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084800/s0848005.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s084/s084800/s0848006.png" />.
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A distribution of the overall gain of all players in a [[Cooperative game|cooperative game]] which satisfies the rationality condition. Formally, if for a game with a set $J=\{1,\ldots,n\}$ of players a characteristic function $v(J)$ is defined, a sharing is a vector $x=(x_1,\ldots,x_n)$ such that $\sum_{i=1}^n$; $x_i\geq v(i)$, $i=1,\ldots,n$.
  
  

Revision as of 13:27, 9 August 2014

imputation (in the theory of games)

A distribution of the overall gain of all players in a cooperative game which satisfies the rationality condition. Formally, if for a game with a set $J=\{1,\ldots,n\}$ of players a characteristic function $v(J)$ is defined, a sharing is a vector $x=(x_1,\ldots,x_n)$ such that $\sum_{i=1}^n$; $x_i\geq v(i)$, $i=1,\ldots,n$.


Comments

References

[a1] A. Rapoport, "-person game theory: Concepts and applications" , Univ. Michigan Press (1970) pp. 92; 97–100
How to Cite This Entry:
Sharing. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Sharing&oldid=32780
This article was adapted from an original article by G.N. Dyubin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article