Question: In the figure, three locations are connected as in the network. The numbers on the branches represent the cost to move one unit along that branch. The goal is to connect each location to the main trunk and to each other in the most economical way possible. The benefit of being connected to the main trunk is shown next to each location. Branches can be traversed in both directions. Take the minimal cost path to the main trunk in all cases.
(a) Find an appropriate characteristic function and be sure it is superadditive.
(b) Find the nucleolus.
(c) Find the Shapley value.