# Difference between revisions of "Sharing"

From Encyclopedia of Mathematics

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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 [[ | + | 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, " | + | <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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+ | [[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=19146

This article was adapted from an original article by G.N. Dyubin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article