Sharing Costs Suppose that n airlines share the cost of a runway. To serve the planes of company i, the length of the runway must be ci, which is also the cost of a runway of that length. Assume  The...

Sharing Costs

Suppose that n airlines share the cost of a runway. To serve the planes of company i, the length of the runway must be ci, which is also the cost of a runway of that length. Assume
 The cost of coalition S is defined as
 for every nonempty coalition S.

(a) Model this situation as a cost savings game (cf. the three communities game in Chap. 1).

(b) Show that the resulting game is convex, and compute the marginal vectors, the Shapley value, and the core.