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Difference between revisions of "Sharing"

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(Category:Game theory, economics, social and behavioral sciences)
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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 $J=\{1,\ldots,n\}$ of players a characteristic function $v(J)$ is defined, a sharing is a vector $x=(x_1,\ldots,x_n)$ such that $\sum_{i=1}^n$; $x_i\geq v(i)$, $i=1,\ldots,n$.
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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 $x=(x_1,\ldots,x_n)$, with $x_i$ representing the share allocated to player $i$, such that $\sum_{i=1}^n x_i = v(J)$ and $x_i\geq v(\{i\})$, $i=1,\ldots,n$.
  
  
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====References====
 
====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  A. Rapoport,  "$N$-person game theory: Concepts and applications" , Univ. Michigan Press  (1970)  pp. 92; 97–100</TD></TR></table>
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<table>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  A. Rapoport,  "$N$-person game theory: Concepts and applications" , Univ. Michigan Press  (1970)  pp. 92; 97–100</TD></TR>
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</table>
  
 
[[Category:Game theory, economics, social and behavioral sciences]]
 
[[Category:Game theory, economics, social and behavioral sciences]]

Latest revision as of 18:18, 9 January 2016

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 $x=(x_1,\ldots,x_n)$, with $x_i$ representing the share allocated to player $i$, such that $\sum_{i=1}^n x_i = v(J)$ and $x_i\geq v(\{i\})$, $i=1,\ldots,n$.


Comments

References

[a1] A. Rapoport, "$N$-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=37419
This article was adapted from an original article by G.N. Dyubin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article