 Cooperative cost game

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 $c(N)$.