Question: Moe, Larry, and Curly have banded together to form a leg, back, and lip waxing business, LBLWax, Inc. The overhead to the business is 40K per year. Each stooge brings in annual business and incurs annual costs as follows: Moe-155K revenue, 40K costs; Larry-160K revenue, 35K costs; Curly-140K revenue, 38K costs. Costs include, wax, flame throwers, antibiotics, and so on. Overhead includes rent, secretaries, insurance, and so on. At the end of each year, they take out all the profit and allocate it to the partners.
(a) Find a characteristic function that can be used to determine how much each waxer should be paid.
(b) Find the nucleolus.
(c) Find the Shapley allocation