A simple expression for the nucleolus in a special case

We present a simple algorithm for calculating the nucleolus of a game whenever (a) the characteristic function is non-positive, ie. a “cost” function, and (b) the players can be ordered by “size” in such a way that the cost of any coalition is equal to the cost of the largest player in that coalition. The cumulative nucleolus is approximately equal to the convex envelope of this cost function. A numerical and geometric illustration is given for a game based upon Birmingham airport runway costs, where there are over 13,000 players (aircraft movements) of 11 distinct (aircraft) types.