# Sharing

From Encyclopedia of Mathematics

*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 $x_i\geq v(\{i\})$, $i=1,\ldots,n$.

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#### 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