Answered: Three doctors have banded together to…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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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?

Definition Definition Economic decision-making framework that analyzes how different players optimize their outcomes with given pay-offs corresponding to their available strategies. The assumptions of game theory are: The number of players or competitors are finite/limited; All participants are rational The rules of the game are known to every player; and Each participant has a finite set of actions. A common way in which game theory is presented as an ( m x n ) matrix in which m represents the strategies of row player and n represents the strategies of column player. There are several limitations of game theory: Many businesses have a large number of competitors, and selecting an optimal strategy in these circumstances is difficult; Real-life business operating environments are full of uncertainty and difficult to model as a game theory; and The assumption of rationality and utility maximization isn't always an accurate portrayal of human nature.

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