View source for Sharing

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''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====
<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>

[[Category:Game theory, economics, social and behavioral sciences]]