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# Game Theory

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1) Explain your reasoning- Consider a vote being taken by a group of friends A, B and C. They are trying to decide which of the three elective courses to take together in this term. (Each one has a different concentration and is taking required courses in her field for the rest of her courses.) Their choices are Economics, Accounting and Finance and their preferences for three courses are as shown.

Player A Player B Player C
Economics Finance Accounting
Accounting Economics Finance
Finance Accounting Economics

They have decided to have a two-round vote: alternative X is first paired with alternative Y, the alternative which gets a majority is then paired against alternative Z - the majority winner in this round is the final choice. Player A won the right to choose the order. How should she proceed? How would your answer change if you would consider 2n+1 friends where n of them are of type B and n are of type C?

2) A professor of game theory recognizes that every hour students devote to his class is an hour lost doing other, perhaps more entertaining things. Further, psychologists have demonstrated that studying for uninteresting subjects takes a heavy emotional toll on a student. Each student foregoes \$200 in outside consulting fees for every hour he or she studies for the class. Further, students who dislike game theory suffer additional costs (of \$800 per hour) in emotional distress while studying game theory. Employers use the grade in game theory courses to screen applicants. An applicant with an MBA degree and a High Pass in game theory signals her quality as a capable worker. Specifically, employers pay a premium for a High Pass in game theory because they have found that the kind of people who enjoy the subject are valuable employees.

The lifetime earnings (net present value) of a worker with an MBA are \$1.4M; for a student with an MBA and a High Pass in game theory, this increases by 5% (by \$70K). This is summarized below:
Lifetime earnings with an MBA degree: \$1,400,000
Lifetime earnings with MBA and a High Pass in game theory: \$1,470,000
Cost per hour of study for a student
who enjoys game theory: \$ 200
who doesn't enjoy game theory: \$ 1,000

a. Over a fourteen week course, what is the minimum number of study hours per week that a game theory class should require in order to earn a High Pass and effectively screen out and award High Pass only to the students who enjoy it? Demonstrate or Explain.
b. What is the maximum number of study hours per week that would still serve as an effective screen? Demonstrate or Explain.

3) (I'm interested only in the numbers, no graphs needed)

You're running ABC Communications a cell-phone provider. Your competitor is XYZ Wireless. Currently XYZ is offering the following plan to all its customers \$65 per month subscription fee 1000 free minutes and 20 cents for all additional minutes. Market research reveals that there are two potential types of customers in the market:
Type 1 consumers' demand per month is Q=300-5P
Type 2 consumers' demand per month is Q=300-6P
(P is expressed in cents and Q is expressed in minutes per month)
Currently your cost of providing airtime is 20 cents/minute.
a) A management consultant tells you that your area contains only Type 1 consumers. What plan should you design to attract all new consumers of Type 1 consumers while maintaining the highest possible profit level?
b) Suppose the consultant tells you that only Type 2 consumers reside in your area. What plan should you design to attract all new consumers of Type 2 consumers while maintaining the highest possible profit level?
c) Suppose your market is composed of both types of consumers but due to a hike in interest rates your per-minute cost went up to 30 cents. What type of plan should you offer?

https://brainmass.com/economics/preferences-choice/game-theory-129189

#### Solution Preview

1) Explain your reasoning- Consider a vote being taken by a group of friends A, B and C. They are trying to decide which of the three elective courses to take together in this term. (Each one has a different concentration and is taking required courses in her field for the rest of her courses.) Their choices are Economics, Accounting and Finance and their preferences for three courses are as shown.

Player A Player B Player C
Economics Finance Accounting
Accounting Economics Finance
Finance Accounting Economics

They have decided to have a two-round vote: alternative X is first paired with alternative Y, the alternative which gets a majority is then paired against alternative Z - the majority winner in this round is the final choice. Player A won the right to choose the order. How should she proceed? How would your answer change if you would consider 2n+1 friends where n of them are of type B and n are of type C?

Player A will choose the order in a manner that would help him to win his first preference. He will select Accounting (X) and Finance (Y) for the first round of voting. Since, Player A prefers Accounting to Finance, he will vote in favor of Accounting. Player B prefers Finance to accounting and will vote for Finance. Player C prefers Accounting to Finance and will vote for Accounting. Thus, accounting will be the majority winner in first round with 2-1. In the second round, we have Accounting (X) and Economics (Z). Since, Player A prefers Economics to Accounting, he will vote in ...

#### Solution Summary

A scenario to attract customers is presented.

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