 Solution

Put $c(\varnothing )=0$. For nonempty coalitions, the runway required by a union is the longer of the two required runways, soThe inequality uses nonnegative costs and also holds when either coalition is empty. Thus 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 $v=-c$.