Three doctors have banded together to form a jointpractice: the Port Charles Trio. The overhead for the practiceis $40,000 per year. Each doctor brings in annual revenuesand 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 doctor3—$140,000 in revenue, $38,000 in variable cost.The Port Charles Trio wants to use game theory todetermine how much each doctor should be paid. Determinethe relevant characteristic function and show that the coreof the game consists of an infinite number of points. Alsodetermine the Shapley value of the game. Does the Shapleyvalue give a reasonable division of the practice’s profits?
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
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?
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