MAT 3172 Minot State University Probability Mathematics Presentation

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Hello!I am looking for help with this assignment please! I tried to figure it
out but my assignment failed and I can only resubmit once! The
instructor didn’t tell me what failed-or if it all did, but I attached
my attempt as well as the worksheet and rubric for the assignment. Thank
you so much!!!! I truly appreciate it!
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. You are to put together a PowerPoint presentation that explains all of the key components that you feel will factor into why you should get the position. What to Submit To complete this assignment, you must first download the word document. Use the questions on the worksheet as your guide for the contents of your presentation. Your step-by-step breakdown of the problems, including explanations and all work shown, should be present within the PowerPoint you create. Use excel for your calculations as that file must also be included in the drop box. Do not submit the Word document with instructions.

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GAME THEORY
APPLICATIONS
PART 1
• The first item you want to highlight is your customer satisfaction record. Over the past 18 months of employment you have
worked with 25 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 at least 85% or higher of customers giving you high customer satisfaction
ratings. 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.
Based on the prior work history 22 people have rated highest level of
customer satisfaction out of the already 25 people. To calculate the
probability of getting a satisfied client I will divide 22 people by the total
25 people.
22
highly rated customer satisfaction
Total probability =
=
= 0.88
25
total number of clients
The probability of getting a satisfied client based on previous work
history is 0.88
The probability of getting 85% of the clients giving a high customer satisfaction rating
will be
85% * 60= 51 clients
Number of success = 51
Number of Trials (n)=60
Probability of success (p)=0.88
Formula: =1-binom.dist(k-1,n,p,true) Actual Formula: =1-binom.dist(511,60,0.88,true)
Probability of getting at least 85% of clients= 0.27
The probability of the clients giving a high satisfactory rating
is 0.27 showing that new clients will also give a high
satisfactory rating making me good for the position.
PART II
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.
Manufacturer
Competitor
Sue
Don’t Sue
Sue
(5, -5)
(20, -20)
Don’t Sue
(-15, 15)
(-10, 10)
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:
This coworker concluded that the manufacturer should always do the opposite of the competitor chooses making this a strictly competitive game.
Dominant Strategy
Competitor
Manufacturer
Sue
Don’t sue
Sue
(5,-5)
(20,-20)
Don’t sue
(-15,15)
(-10,10)
The dominant strategy for manufacture is sue since 5 is greater than -15
and 20 is greater than -10.
Competitor
Manufacturer
Sue
Don’t sue
Sue
(5,-15)
(20,-20)
Don’t sue
(-15,15)
(-10,10)
The competitor also has a dominant strategy which is sue since -5 is less than 15
and -20 is less than 10
-both manufacturer and competitor have a dominant strategy for this game.
Nash Equilibrium point. (Sue, Sue)
Nash Equilibrium Point
Competitor
Manufacturer
Sue
Don’t sue
Sue
(5,-15)
(20,-20)
Don’t sue
(-15,15)
(-10,10)
Both the companies choose sue (5,5)as the outcome and therefore the Nash
equilibrium.
Competitor would not deviate from considering litigation since if he chooses don’t sue
and the manufacturer still sues, the manufacturer will increase the costs by $5million.
The best thing for both manufacturer and competitor is to sue therefore (sue, sue) is
the Nash equilibrium point.
The Optimum Strategy
The expected value of either choice is the same
ES=ED
ES=-5p+15(1-p)=15-20p
ED=-20p+10(1-p)=10-30p
15-20p=10-30p
P=1/2
The Manufacturer choice to sue is 50% as well as the competitor.
I do not agree with the co-workers results that the manufacturer will
enjoy the profits solely. This is because neither of the firms would want
to change opinion as they are already getting same profits from the
litigation and it’s not only the manufacturer will benefit since the
outcome is (sue, sue)
.
PART III
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.
Manufacturer
Competitor
Sue
Don’t Sue
Sue
(5, -5)
(20, 10)
Don’t Sue
(10, 20)
(15, 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.
Competitor
Manufacturer
Sue
Don’t sue
Sue
(5,-5)
(20,10)
Don’t sue
(10,20)
(15,15)
The competitor sues the manufacturer will not sue
If the manufacturer sues the competitor will not sue
This means that both firms’ decisions are dependent on
each other and therefore neither of the firms has
dominant strategy.
The optimum strategy for manufacturer
The expected value of either choice is the same
ES=ED
ES=-5p+20(1-p)=20-25p
ED=10p+15(1-p)=15-15p
20-25p=15-5p
P=1/4
The Manufacturer should sue 25% and don’t sue 75%
Optimum strategy for competitor
Expected value of either choice is again the same:
ES=ED
EA=5q+20(1-q) = 20-15q
EB=10q+15(1-q) = 15-5q
Next set the two expected values and solve for q to find competitor optimal strategy.
20-15q= 15-5q
5=10q
1/2=q
The Competitor should sue 50% of the time and don’t sue 50% of the time
I disagree with the co-workers recommendation in accordance
with the results. As it is only the Competitor that should sue 50%
of the time and don’t sue 50% of the time while the
Manufacturer should only sue 25% of the time and don’t sue
75% of the time.
PART IV
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
Manufacturer
Sue
Sue
Don’t Sue
Competitor
Competitor
Sue
Don’t Due
In this scenario the non credible threat will be don’t sue this is because
both outcome for the clients is same and if the manufacturer sues the
competitor will also sue.
Manufacturer
Sue
Sue
Don’t Sue
Competitor
Competitor
Sue
Don’t Due
The first step will be eliminating the don’t sue by the competitor since it is dependent
on the manufacturer choice to sue.
Manufacturer
Sue
Sue
Don’t Sue
Competitor
Competitor
Sue
Don’t Due
After the competitor choice to sue , the manufacturer can maximize its payoff . the result is an
equilibrium found by backward induction of manufacturer choice to sue and the competitor
also to sue.
The optimal strategy would be the competitor sue and the manufacture sues.
Deliverable 07 – Worksheet
Part 1
The first item you want to highlight is your customer satisfaction record. Over the past 18
months of employment you have worked with 25 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 at least 85% or higher of customers giving you high customer satisfaction
ratings. 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.
Slide 1
•
•
Calculate the probability of getting a satisfied client based off of your prior work
history at G& B Consulting. Show all work.
Explain how you found your solution.
Slide 2
•
•
Using your prior work history, calculate the probability of getting at least 85% of
clients giving you high customer satisfaction ratings.
Explain how you found your solution.
Slide 3
•
Interpret your results from slide 2 and use them to make an argument on why
you would be good for the position.
Part 2
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
Manufacturer
Competitor
Sue
Don’t Sue
Sue
(5, -5)
(20, -20)
Don’t Sue
(-15, 15)
(-10, 10)
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:
This coworker concluded that the manufacturer should always do the opposite of the
competitor chooses making this a strictly competitive game.
Slide 4
•
•
Using the payoff matrix shown above, determine if the manufacturer has a
dominant strategy. Show and explain all steps.
Using the payoff matrix shown above, determine if the competitor has a
dominant strategy. Show and explain all steps.
Slide 5
•
•
Find all Nash equilibrium points. Show and explain all steps.
Identify the optimum strategy of the game.
Slide 6
•
Do your results match those of your coworkers? Explain why you agree or
disagree
Part 3
Competitor
Manufacturer
The
Sue
Don’t Sue
Sue
(5, -5)
(20, 10)
Don’t Sue
(10, 20)
(15, 15)
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.
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.
Slide 7
•
Use the mixed strategy algorithm to find the optimum strategy for the
manufacturer. Show all of your steps.
Slide 8
•
Use the mixed strategy algorithm to find the optimum strategy for the
competitor. Show all of your steps.
Slide 9
•
Do your results match those of your coworker’s? Explain why you agree or
disagree.
Part 4
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
Slide 10
•
•
Create the game tree for this scenario, exclude any non-credible threats.
Explain how you identified the non-credible threat.
Slide 10
•
Perform the first step of backwards induction. Shown and explain your work.
Slide 11
•
Perform the second step of backwards induction. Show and explain all your
work.
Slide 12
•
Identify the optimum strategy for the game.
Grading Rubric
F.
F
с
B
A
0
1
2
3
4
No
No Pass
Competence
Proficiency
Mastery
Pass
Not
Did not correctly solve a
Correctly solved a majority of the
Correctly solved almost all
All problems are
Submitted majority of the problems or
problems.
the problems.
solved correctly.
at least one problem not
completed.
Not
Very few steps are
Fairly complete and detailed
Mostly complete and
Complete and detailed
Submitted provided to explain how to
steps are provided to explain
detailed steps are provided
steps are provided to
solve the problem OR the
how to solve the problem OR the to explain how to solve the
explain how to solve
steps provided have
steps provided have some
problem.
the problem.
several errors.
errors.
Not
Explanations generally lack
Explanations demonstrate a
Explanations demonstrate
Explanations
Submitted
a basic understanding of
basic understanding of most of
a proficient understanding
demonstrate a mastery
the concepts or lack of
the concepts and terminology,
of most of the concepts
of understanding of the
proper terminology
but some explanations may be
and terminology, but with
concepts and
incomplete or incorrect.
small errors.
terminology
Not
The majority of
The majority of mathematical
Almost all mathematical
All mathematical
Submitted
mathematical expressions
expressions and any graphs or
expressions and any
expressions and any
and any graphs or tables
tables are properly formatted.
graphs or tables are
graphs or tables are
are not properly formatted
properly formatted.
properly formatted.
OR some are not present.

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Customer satisfaction ratings

customer satisfaction rate

Probability Mathematics

highest level of satisfaction

total number of clients

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