Competency
This
competency will allow you to demonstrate your ability and skill in applying
game theory to real world scenarios.
Instructions
After
working for 18 months in your analyst position at G&B Consulting, you are
now being considered for a project manager position that would put you in
charge of several team members. As part of the interview process, you have been
asked to make a presentation to highlight what you think are the most
compelling reasons you should get the position.
The
first item you want to highlight is your customer satisfaction record. Over the
past 18 months of employment you have worked with 24 clients, and according to
the customer satisfaction surveys all clients are asked to take after their
contract is completed, 22 of them rated you with the highest level of
satisfaction. Use this information to find the best predicted probability of
having a new client give the highest level of satisfaction.
However,
having a single satisfied customer is not enough. It is very important to G
& B Consulting that they maintain high ethical standards and continue to
receive the highest rating from the Better Business Bureau consistently. In
order to maintain this rating, the company must maintain a consistent customer
satisfaction rating of 85% or higher. Internal projections predict that G&B
Consulting will serve 60 clients over the next year. If you become the project
manager and use your prior record as an indicator, find the probability that
85% or more of new clients will give the highest level of customer satisfaction
rating. Show all calculations and formulas used. If you use Excel for your
calculations include that along with your submission. Use this information to
make a convincing argument that you are a good choice for the position.
The
other item you wish to highlight comes from some work done for a local
manufacturer. They believed that a competitor was illegally using one of their
patents in their own manufacturing process and were considering litigation.
This competitor’s product were directly cutting into the manufacturer’s profit,
so they wanted to prevent the competitor’s product from being made and recoup
those lost profits. Of course, the litigation process is long and costly, and
the outcome is not guaranteed and would likely result in a countersuit brought
by the competitor. Before continuing with costly legal counsel, the
manufacturer hired G&B Consulting to help them determine their best
strategy.
This
was potentially a very lucrative contract, and a high profile one too since the
manufacturer is one of the biggest employers in the area. Therefore, several
analysts at G&B Consulting, including you, were asked to tackle the problem
independently to help ensure the best possible results. Before compiling a
final report to give to the manufacturer, the results were presented to the
project lead:
The
first solution brought up was given by one of your coworkers. Using the
manufacturer’s projections of profits solely, he was able to create the
following payoff matrix where each entry is in millions of dollars annually:
|
|
Competitor |
||
|
|
Sue |
Don’t |
|
|
Manufacturer |
Sue |
(5, |
(20, |
|
Don’t |
(-10, |
(-15, |
This
coworker concluded that the dominant strategy for the manufacturer is to sue,
and if the competitor assumed best play by the manufacturer, they would also
sue.
Based
only on the above payoff matrix, do you agree with the conclusion made by your
coworker? Show all steps of finding any dominant strategies and Nash
Equilibrium points.
The
second solution was brought by a different coworker. She also created a payoff
matrix for the scenario but did some independent research to estimate the
competitor’s profits in each outcome independent of the manufacturer’s profits
and came up with the following payoff matrix, again, the values represent
millions of dollars in annual profits.
|
|
Competitor |
||
|
|
Sue |
Don’t |
|
|
Manufacturer |
Sue |
(5,-5) |
(20, |
|
Don’t |
(10, |
(15, |
This
coworker concludes that under these circumstances, the manufacturer should sue
50% of the time and not sue the other 50% of the time, and they should expect
their competitor to do the same.
Based
solely on this payoff matrix your coworker provided, do you agree with her
conclusion? Show all steps of the mixed strategy algorithm to find the optimum
strategy and explain if you do or do not agree with your coworker’s results. Do
you think this payoff matrix is a better representation of the scenario than
the first one was? Explain why or why not.
You
present your own solution that is based on a non-simultaneous game where the
manufacturer first has to decide whether or not they wish to pursue litigation.
If they do so choose, then their competitor will also have to decide if the
wish to file a counter-suit. You utilized the same payoff matrix that the
second coworker provided that contains information about both companies’
projected profits, but then you created a game tree that excludes any
non-credible threats. With this game tree, determine the optimum strategy. Show
all steps of backwards induction and include any game trees used.
Create
a PowerPoint presentation that shows all work, explanations, and responses
detailed in the directions above that you will present to your interviewers.
