# Difference between revisions of "Sharing"

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

 [a1] A. Rapoport, "$N$-person game theory: Concepts and applications" , Univ. Michigan Press (1970) pp. 92; 97–100