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The market research team working on this project creates this payoff matrix that
represents the scaled values that customers give to the different levels of service and the
corresponding payoffs for the telecom company:
Telecom
Company
Customer
(2, 2)
(0, 1)
(3, 0)
(1, 1)
You recognize that the payoff matrix is not the best way to analyze this scenario. You
will construct a game tree to model the scenario and perform backwards induction to find the
optimum strategy, explaining all of your reasoning along the way.
Slide 1

Explain why a game tree must be used in this scenario instead of a payoff
matrix.
Identify who will go first in the game
Slide 2

Draw the game tree that represents the scenario using the payoff matrix given
above.
Identify and explain any non-credible threats.
Slide 3

Redraw the game tree with any non-credible threats removed.
Identify and explain where the first step of backwards induction will occur.
Slide 4

Using the game tree from slide 3, perform the first step of backwards induction.
Explain your reasoning behind the step you took.
Slide 5

Redraw the game tree after the first step of backwards induction.
Identify where the next step of backwards induction occurs.
Slide 6

Slide 7
Using the game tree from slide 5, perform the next step of backwards induction.
Explain your reasoning behind the step you took.

Redraw the game tree after the step you took in slide 6.
Identify the optimum strategy of the game.
Contruct & Analyze
A Game Tree
Joni Filibeck
Rasmussen College
Mathematics of Games
Submitted on 15June2020
Scenario
The market research team working on this project creates this payoff matrix that represents the
scaled values that customers give to the different levels of service and the corresponding
payoffs for the telecom company
You recognize that the payoff matrix is not the best way to analyze this scenario. You will
construct a game tree to model the scenario and perform backwards induction to find the
optimum strategy, explaining all of your reasoning along the way
Step 1
In this scenario a game tree has to be used because the
information has a finite extension form and also sequential
The customer is this will go first because he determines
whether or not he will buy or not buy; therefore the decision
Step 2
Game Tree representing scenario in above matrix
Telecom
Company
Customer
Customer
(2,2)
(0,1)
(3,0)
(1,1)
The non credible threats in this scenario is don’t buy for the customer who is
the don’t buy customer will not be affected and both parties stand to gain nothing.
Step 3
Game Tree with Non Credible Threats Removed
Telecom
Company
Customer
Customer
(2,2)
(3,0)
(1,1)
The first backward induction will start at the customer deciding to buy the
product because either way the customers have to buy for the company to gain.
Step 4
Telecom
Company
Customer
Customer
(2,2)
(3,0)
(1,1)
The red lines are marked to indicate that the customer who will not buy is
eliminated to narrow down the tree and maximize the customers payoff with the
given information set.
Step 5
Telecom
Company
Customer
Customer
(2,2)
(3,0)
(1,1)
After the first reduction the next step of backwards induction will occur at
upgrade since the customers who buy the product would like it when it’s
Step
The customers who buy have remained after eliminating
those who don’t buy, the next step is determining whether to
product will be in high demand; eliminating the don’t
Step 6
Telecom
Company
Customer
Customer
(2,2)
(3,0)
(1,1)
The optimum strategy of the telecom company will choose to upgrade while the
Contruct & Analyze
A Game Tree
Scenario
The market research team working on this project creates this payoff matrix that represents the
scaled values that customers give to the different levels of service and the corresponding
payoffs for the telecom company
You recognize that the payoff matrix is not the best way to analyze this scenario. You will
construct a game tree to model the scenario and perform backwards induction to find the
optimum strategy, explaining all of your reasoning along the way
Step 1
In this scenario a game tree has to be used because the
information has a finite extension form and also sequential
The customer is this will go first because he determines
whether or not he will buy or not buy; therefore the decision
Step 2
Game Tree representing scenario in above matrix
Telecom
Company
Customer
Customer
(2,2)
(0,1)
(3,0)
(1,1)
The non credible threats in this scenario is don’t buy for the customer who is
the don’t buy customer will not be affected and both parties stand to gain nothing.
Step 3
Game Tree with Non Credible Threats Removed
Telecom
Company
Customer
Customer
(2,2)
(3,0)
(1,1)
The first backward induction will start at the customer deciding to buy the
product because either way the customers have to buy for the company to gain.
Step 4
Telecom
Company
Customer
Customer
(2,2)
(3,0)
(1,1)
The red lines are marked to indicate that the customer who will not buy is
eliminated to narrow down the tree and maximize the customers payoff with the
given information set.
Step 5
Telecom
Company
Customer
Customer
(2,2)
(3,0)
(1,1)
After the first reduction the next step of backwards induction will occur at
upgrade since the customers who buy the product would like it when it’s
Step
The customers who buy have remained after eliminating
those who don’t buy, the next step is determining whether to
product will be in high demand; eliminating the don’t
Step 6
Telecom
Company
Customer
Customer
(2,2)
(3,0)
(1,1)
The optimum strategy of the telecom company will choose to upgrade while the
F
F
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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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