dolution

Three doctors have banded together to form a joint practice: the Port Charles Trio. The overhead for the practice is $40,000 per year. Each doctor brings in annual revenues and incurs annual variable costs as follows: doctor 1— $155,000 in revenue, $40,000 in variable cost; doctor 2— $160,000 in revenue, $35,000 in variable cost; and doctor 3—$140,000 in revenue, $38,000 in variable cost.

The Port Charles Trio wants to use game theory to determine how much each doctor should be paid. Determine the relevant characteristic function and show that the core of the game consists of an infinite number of points. Also determine the Shapley value of the game. Does the Shapley value give a reasonable division of the practice’s profits?