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?
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 (
an MBA are $14M; 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
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?
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