Presentation on Game Theory Applications

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Deliverable 7

By: Kristina Cypser

November 27, 2019

Probability of getting a satisfied client

Over the Past 18 Months of Employment

25 Clients

22 out of 25 clients surveyed scored me with the highest level of satisfaction

Why Would I Make a Great Project Manager?

The probability of getting a satisfied client based off of my prior work history at G& B Consulting is 88%.

Probability of getting at least 85% of clients satisfaction

Customer Satisfaction Record

Based on my previous customer satisfaction record, there is a probability of 88% that I would maintain a consistent overall customer satisfaction record of 85% or higher:

85 % satisfaction

𝑃 = .8224

𝑥 = 60

𝑛 = 51 (60 x .85 = 51)

Calculation

= .8224 (82.24%)

For higher ratings from Better Business Bureau ,G & B Consulting requires a maintenance of high ethical.

Maintaining customer satisfaction rating of 85% and above.

Maintaining this high rating even after serving next 60 clients.

Explanation

The probability of getting at least 85% of clients giving me high customer satisfaction ratings is 82.24%

This is achieved through;

Maintaining customer satisfaction rating of 85% and above.

Maintaining this high rating even after serving next 60 clients

Currently performing most project manager job related responsibilities

Experienced in overseeing other employees, checking their work, and providing insight on improvements

Excellence in client interactions

From my records I would make the company to maintain its standards.

Being the manager will guarantee company success from the high customer satisfaction.

Dominant strategy: Coworker findings

Coworker Zero-Sum Game Solution

Based on the manufacturer’s projections of profits the analysts concluded:

Manufacturer Dominant Strategy: Sue

Competitor Assuming Best Play by Manufacturer: Sue

Pure Strategy: (Sue, Sue)

		Competitor
Manufacturer		Sue	Don’t Sue
	Sue	(5, -5)	(20, -20)
	Don’t Sue	(-10, 10)	(-15, 15)

Based on the information and the work performed,

The conclusion is that the dominant strategy is for the

manufacturer is to choose to sue, and id the competitor

assumed the best play by the manufacturer, they would also sue.

My findings

		Competitor
Manufacturer		Sue	Don’t Sue
	Sue	(5, -5)	(20, -20)
	Don’t Sue	(-10, 10)	(-15, 15)

My Zero-Sum Game Solution

If the Competitor chooses to “Sue”:

Manufacturer chooses to “Sue”

If the Competitor chooses to “Don’t Sue”:

Manufacturer chooses to “Sue”

If the Manufacturer chooses to “Sue”:

Competitor chooses to “Don’t Sue”

If the Manufacturer chooses to “Don’t Sue”:

Competitor chooses to “Don’t Sue”

Manufacturer Dominant Strategy: Sue

(Sue, Sue) 5 > -10 (Sue, Don’t Sue) 20 > -15

Competitor Dominant Strategy: No Dominant Strategy

(Sue, Sue) -5 > -20 (Don’t Sue, Don’t Sue) 15 > 10

Optimum strategy

Coworker Nonzero-Sum Game Solution

Based on independent research to estimate the competitor’s profits, the analysts concluded:

Manufacturer Optimum Strategy: Sue 50%, Don’t Sue 50%

Competitor Optimum Strategy: Sue 50%, Don’t Sue 50%

		Competitor
Manufacturer		Sue	Don’t Sue
	Sue	(5, -5)	(20, 10)
	Don’t Sue	(10, 20)	(15, 15)

Based on the information from the payoff matrix I do agree with my

coworker.

Its true that the dominant strategy for the manufacturer

is “Sue” since those two values when the competitor chooses

to “sue” or “don’t sue” are their highest possible payouts.

The competitor does not have a dominant strategy since they select to “Sue”

if the manufacturer sues and chooses “Don’t Sue” when the manufacturer also chooses to not sue

Manufacturer mixed strategy algorithm

Calculation

Manufacturer Mixed Strategy Algorithm:

= -5p + 20(1-p) = -5p + 20 – 20p = 15p + 20

= 10p + 15(1-p) = 10p + 15 – 15p = 25p +15

15p + 20 = 25p +15

(-15p) = (-15p)

20 = 10p +15

(-15) = (-15)

5 = 10p

𝑃 = 5/10 or 1/2 or .50 or 50%

			Competitor
Manufacturer			Sue	Don’t Sue
		Probability	P	1-P
	Sue	P	(5, -5)	(20, 10)
	Don’t Sue	1-P	(10, 20)	(15, 15)

Competitor mixed strategy algorithm

Calculation

Competitor Mixed Strategy Algorithm:

= 5p + 20(1-p) = 5p + 20 – 20p = 15p + 20

= 10p + 15(1-p) = 10p + 15 -15p = 25p +15

15p + 20 = 25p +15

(-15p) = (-15p)

20 = 10p + 15

(-15) = (-15)

5 = 10p

= 5/10 or 1/2 or .50 or 50%

Optimal Strategy

Manufacturer Optimal Strategy:

Choose to sue 50% (1/2) of the time

Choose to not sue 50% (1/2) of the time

Competitor Optimal Strategy:

Choose to sue 50% (1/2) of the time

Choose to not sue 50% (1/2) of the time

I do agree with my coworker’s conclusion based on the payoff matrix and my results using that data.

Results Comparison

Since both calculations turn out to be the same, I do agree with my coworker’s conclusion.

This means that the optimum strategy for both the manufacturer and competitor is the choose “Sue” half the time, and “Don’t Sue” the other half of the time.

The solution is not realistic as neither company can select a strategy more than once.

Both the manufacturer and the competitor get once chance to choose to either sue the other or not to.

This then means that the optimal strategy shows which company has the bigger advantage or best shot at winning a suit.

In this case, both are split 50/50 in their decision, so neither has the upper hand in the decision they make.

Case Scenario Game Tree

		Competitor
Manufacturer		Sue	Don’t Sue
	Sue	(5, -5)	(20, 10)
	Don’t Sue	(10, 20)	(15, 15)

Manufacturer

Competitor

Sue

Don’t

Sue

Don’t

Sue

Don’t Sue

(20, -10)

(5, -5)

(10, 20)

(15, 15)

There is a non-credible threat in this game tree that must be eliminated before performing backward induction

First step of backwards induction

Manufacturer

Competitor

Sue

Don’t

Sue

Don’t

Sue

Don’t Sue

(20, -10)

(5, -5)

(15, 15)

Competitor

Remove Non-Credible Threat & Start Backward Induction

Second step of backwards induction

Optimum strategy for the game

Once the non-credible threat has been removed, I found the best payout for the competitor relating to both manufacturer’s choices.

Since there is only one remaining option with the client’s choice to not sue, “Don’t Sue,” that is automatically the competitor’s best option relating to that choice.

Based on the choices for the competitor under the manufacturer’s choice to sue, the competitor's best option is to also sue.

Then, in order to find the optimal strategy we must remove the weaker choice(s) branch. Leaving us with just the top portion of the game tree (Sue, Sue) and (Don’t Sue, Don’t Sue), the manufacturer’s best payout will become the optimal strategy. In this scenario, the optimal strategy that is identified is (Don’t Sue, Don’t Sue)