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 $J=\{1,\dots ,n\}$ of players a characteristic function $v(J)$ is defined, a sharing is a vector $x=(x_1,\dots ,x_n)$, with $x_i$ representing the share allocated to player $i$, such that $\sum _{i=1}^n{x}_i=v(J)$ and $x_i\ge v(\{i\})$, $i=1,\dots ,n$.

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