Solution
= Solution
Put $c(\varnothing)=0$. For nonempty <coalitions>, the runway required by a union is the longer of the two required runways, so
$$
c(S\cup T)=\max(c(S),c(T))\leq c(S)+c(T).
$$
The inequality uses nonnegative costs and also holds when either coalition is empty. Thus \b[the cost function is subadditive], in particular for the stated disjoint <coalitions>. A <subadditive cost game> becomes a <superadditive coalitional game> after changing signs to $v=-c$.