= Cooperative cost game
{title2=$p(N)=c(N),\quad p(S)\leq c(S)$}
A <transferable utility game> formulated as costs $c(S)$ to be shared among members of each <coalition> $S$, with $c(\varnothing)=0$. Its cost <core> consists of payment <vectors> $p$ satisfying the displayed efficiency and coalition inequalities, where $p(S)=\sum_{i\in S}p_i$. A coalition should not be charged more than its standalone cost. Changing signs to $v=-c$ and $x=-p$ converts these conditions to the usual benefit-game <core of a cooperative game>. The <Shapley value> can be applied directly to costs, giving payments whose sum is $c(N)$.
Back to article page
