SlideShare a Scribd company logo
www.sanjivanimba.org.in
Unit No.3.
DECISION SCIENCE
Presented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Dean, EDP & Associate Professor MBA
1
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in
www.sanjivanimba.org.in
302-DECISION SCIENCE
Unit No.3. Games Theory
3.2.5 Principle of
Dominance
Presented By:
Dr. V. M. Tidake
Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem)
Dean EDP & Associate Professor MBA
2
Sanjivani College of Engineering, Kopargaon
Department of MBA
www.sanjivanimba.org.in
www.sanjivanimba.org.in
GAMES THEORY
 At the End of the Session Student will be able to
understand-
A. Principle of Dominance
www.sanjivanimba.org.in
Games Theory
Principle of Dominance states that, if a strategy of a player dominates over another
strategy in all conditions (i.e. for all counter strategies by the other player), then the
later strategy (being dominated) can be ignored.
Steps in Principle of Dominance:
Step 1: Check if there is a saddle point and if yes then optimal solution is directly
obtained.
Step 2: If the problem does not have Saddle Point, then reduce the table to a 2*2
table using following rules of dominance-
a. If all the elements in a row (say ith row) are less than or equal to the
corresponding elements of any other row (say jth row), then neglect the ith row.
b. If all the elements in a column (say rth column) are greater than or equal to the
corresponding elements of any other column (say sth column), then neglect the
rth column.
www.sanjivanimba.org.in
Games Theory
Solve the Following Game using Principle of Dominance:
Player B
Player A
. Player B
. Player A
B1 B2 B3
A1 1 2 7
A2 6 7 2
A3 6 6 1
B1 B2 B3 Min.
A1 1 2 7 1
A2 6 7 2 2 Max.
A3 6 6 1 1
Max. 6 Min. 7 7
www.sanjivanimba.org.in
Games Theory
Reducing the Table by using Principle of Dominance:
i) We see that all the elements of Row A3 are ≤ the corresponding
elements of Row A2.
Neglecting A3 we get a reduced Matrix like-
. Player B
. Player A
B1 B2 B3
A1 1 2 7
A2 6 7 2
www.sanjivanimba.org.in
Games Theory
Reducing the Table by using Principle of Dominance:
ii) We see that all the elements of Column B2 are ≥ than the
corresponding elements of Column B1.
Neglecting B2 we get a reduced Matrix like-
. Player B
. Player A
B1 B3
A1 1 7
A2 6 2
www.sanjivanimba.org.in
Games Theory
We have,
𝒑 =
𝒂 𝟐𝟐 − 𝒂 𝟐𝟏
𝒂 𝟏𝟏 + 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 − 𝒂 𝟐𝟐
𝒑 =
𝟐 − 𝟔
𝟏 + 𝟐 − 𝟔 − 𝟕
𝒑 =
𝟐
𝟓
www.sanjivanimba.org.in
Games Theory
We have,
𝒒 =
𝒂 𝟐𝟐 − 𝒂 𝟏𝟐
𝒂 𝟏𝟏 + 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 − 𝒂 𝟐𝟐
𝒒 =
𝟐 − 𝟕
𝟏 + 𝟐 − 𝟔 − 𝟕
𝒒 =
𝟏
𝟐
www.sanjivanimba.org.in
Games Theory
We have,
𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑮𝒂𝒎𝒆 =
𝒂 𝟏𝟏 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 𝒂 𝟏𝟐
𝒂 𝟏𝟏 + 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 − 𝒂 𝟏𝟐
𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑮𝒂𝒎𝒆 =
𝟏(𝟐) − 𝟔(𝟕)
𝟏 + 𝟐 − 𝟔 − 𝟕
𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑮𝒂𝒎𝒆 = 4
www.sanjivanimba.org.in
EXERCISE
Hence,
The Optimal Strategy for player A is (2/5, 3/5, 0) or (0.4,
0.6, 0) or (40%, 60%, 0%)
The Optimal Strategy for player B is (1/2, 0, 1/2) or (0.5,
0, 0.5) or (50%, 0%, 50%)
The Value of the Game is 4 i.e. Player A will get Rs. 4
from Player B.
www.sanjivanimba.org.in
EXERCISE
 State and Explain the Principle of Dominance in Games
Theory.
www.sanjivanimba.org.in
For More Details Contact
Dr. V M Tidake
tidkevishal@gmail.com
tidkevishalmba@sanjivani.org.in
www.sanjivanimba.org.in
Thank You

More Related Content

More from Vishal Tidake

Working Capital Management.pptx
Working Capital Management.pptxWorking Capital Management.pptx
Working Capital Management.pptx
Vishal Tidake
 
Cash Flow Statement.pptx
Cash Flow Statement.pptxCash Flow Statement.pptx
Cash Flow Statement.pptx
Vishal Tidake
 
2.9 Fund Flow Statement.pptx
2.9 Fund Flow Statement.pptx2.9 Fund Flow Statement.pptx
2.9 Fund Flow Statement.pptx
Vishal Tidake
 
Ratio Analysis.pptx
Ratio Analysis.pptxRatio Analysis.pptx
Ratio Analysis.pptx
Vishal Tidake
 
Chapter 1- Environment of Business Finance.pptx
Chapter 1- Environment of Business Finance.pptxChapter 1- Environment of Business Finance.pptx
Chapter 1- Environment of Business Finance.pptx
Vishal Tidake
 
1.6 key strategies of financial management
1.6 key strategies of financial management1.6 key strategies of financial management
1.6 key strategies of financial management
Vishal Tidake
 
1.5 a's of financial management
1.5 a's of financial management1.5 a's of financial management
1.5 a's of financial management
Vishal Tidake
 
1.4 functions of financial management
1.4 functions of financial management1.4 functions of financial management
1.4 functions of financial management
Vishal Tidake
 
1.3 approaches to finance
1.3 approaches to finance1.3 approaches to finance
1.3 approaches to finance
Vishal Tidake
 
1.2 introduction to financial management
1.2 introduction to financial management1.2 introduction to financial management
1.2 introduction to financial management
Vishal Tidake
 
1.1 introduction to finance
1.1 introduction to finance1.1 introduction to finance
1.1 introduction to finance
Vishal Tidake
 
Accounting standards notes Dr. V M Tidake
Accounting standards notes Dr. V M TidakeAccounting standards notes Dr. V M Tidake
Accounting standards notes Dr. V M Tidake
Vishal Tidake
 
5.2.9 case 1 probability distribution
5.2.9 case 1 probability distribution5.2.9 case 1 probability distribution
5.2.9 case 1 probability distribution
Vishal Tidake
 
5.2.8 case 2 normal probability distribution
5.2.8 case 2 normal probability distribution5.2.8 case 2 normal probability distribution
5.2.8 case 2 normal probability distribution
Vishal Tidake
 
5.2.7 case 1 normal probability distribution
5.2.7 case 1 normal probability distribution5.2.7 case 1 normal probability distribution
5.2.7 case 1 normal probability distribution
Vishal Tidake
 
5.2.6 case 1 poisson probability distribution
5.2.6 case 1 poisson probability distribution5.2.6 case 1 poisson probability distribution
5.2.6 case 1 poisson probability distribution
Vishal Tidake
 
5.2.5 case 2 binomial probability distribution
5.2.5 case 2 binomial probability distribution5.2.5 case 2 binomial probability distribution
5.2.5 case 2 binomial probability distribution
Vishal Tidake
 
5.2.4 case 1 binomial probability distribution
5.2.4 case 1 binomial probability distribution5.2.4 case 1 binomial probability distribution
5.2.4 case 1 binomial probability distribution
Vishal Tidake
 
5.10 case 7 probability
5.10 case 7 probability5.10 case 7 probability
5.10 case 7 probability
Vishal Tidake
 
5.9 case 6 probability
5.9 case 6 probability5.9 case 6 probability
5.9 case 6 probability
Vishal Tidake
 

More from Vishal Tidake (20)

Working Capital Management.pptx
Working Capital Management.pptxWorking Capital Management.pptx
Working Capital Management.pptx
 
Cash Flow Statement.pptx
Cash Flow Statement.pptxCash Flow Statement.pptx
Cash Flow Statement.pptx
 
2.9 Fund Flow Statement.pptx
2.9 Fund Flow Statement.pptx2.9 Fund Flow Statement.pptx
2.9 Fund Flow Statement.pptx
 
Ratio Analysis.pptx
Ratio Analysis.pptxRatio Analysis.pptx
Ratio Analysis.pptx
 
Chapter 1- Environment of Business Finance.pptx
Chapter 1- Environment of Business Finance.pptxChapter 1- Environment of Business Finance.pptx
Chapter 1- Environment of Business Finance.pptx
 
1.6 key strategies of financial management
1.6 key strategies of financial management1.6 key strategies of financial management
1.6 key strategies of financial management
 
1.5 a's of financial management
1.5 a's of financial management1.5 a's of financial management
1.5 a's of financial management
 
1.4 functions of financial management
1.4 functions of financial management1.4 functions of financial management
1.4 functions of financial management
 
1.3 approaches to finance
1.3 approaches to finance1.3 approaches to finance
1.3 approaches to finance
 
1.2 introduction to financial management
1.2 introduction to financial management1.2 introduction to financial management
1.2 introduction to financial management
 
1.1 introduction to finance
1.1 introduction to finance1.1 introduction to finance
1.1 introduction to finance
 
Accounting standards notes Dr. V M Tidake
Accounting standards notes Dr. V M TidakeAccounting standards notes Dr. V M Tidake
Accounting standards notes Dr. V M Tidake
 
5.2.9 case 1 probability distribution
5.2.9 case 1 probability distribution5.2.9 case 1 probability distribution
5.2.9 case 1 probability distribution
 
5.2.8 case 2 normal probability distribution
5.2.8 case 2 normal probability distribution5.2.8 case 2 normal probability distribution
5.2.8 case 2 normal probability distribution
 
5.2.7 case 1 normal probability distribution
5.2.7 case 1 normal probability distribution5.2.7 case 1 normal probability distribution
5.2.7 case 1 normal probability distribution
 
5.2.6 case 1 poisson probability distribution
5.2.6 case 1 poisson probability distribution5.2.6 case 1 poisson probability distribution
5.2.6 case 1 poisson probability distribution
 
5.2.5 case 2 binomial probability distribution
5.2.5 case 2 binomial probability distribution5.2.5 case 2 binomial probability distribution
5.2.5 case 2 binomial probability distribution
 
5.2.4 case 1 binomial probability distribution
5.2.4 case 1 binomial probability distribution5.2.4 case 1 binomial probability distribution
5.2.4 case 1 binomial probability distribution
 
5.10 case 7 probability
5.10 case 7 probability5.10 case 7 probability
5.10 case 7 probability
 
5.9 case 6 probability
5.9 case 6 probability5.9 case 6 probability
5.9 case 6 probability
 

Recently uploaded

The Building Blocks of QuestDB, a Time Series Database
The Building Blocks of QuestDB, a Time Series DatabaseThe Building Blocks of QuestDB, a Time Series Database
The Building Blocks of QuestDB, a Time Series Database
javier ramirez
 
一比一原版(爱大毕业证书)爱丁堡大学毕业证如何办理
一比一原版(爱大毕业证书)爱丁堡大学毕业证如何办理一比一原版(爱大毕业证书)爱丁堡大学毕业证如何办理
一比一原版(爱大毕业证书)爱丁堡大学毕业证如何办理
g4dpvqap0
 
Population Growth in Bataan: The effects of population growth around rural pl...
Population Growth in Bataan: The effects of population growth around rural pl...Population Growth in Bataan: The effects of population growth around rural pl...
Population Growth in Bataan: The effects of population growth around rural pl...
Bill641377
 
Influence of Marketing Strategy and Market Competition on Business Plan
Influence of Marketing Strategy and Market Competition on Business PlanInfluence of Marketing Strategy and Market Competition on Business Plan
Influence of Marketing Strategy and Market Competition on Business Plan
jerlynmaetalle
 
Enhanced Enterprise Intelligence with your personal AI Data Copilot.pdf
Enhanced Enterprise Intelligence with your personal AI Data Copilot.pdfEnhanced Enterprise Intelligence with your personal AI Data Copilot.pdf
Enhanced Enterprise Intelligence with your personal AI Data Copilot.pdf
GetInData
 
ViewShift: Hassle-free Dynamic Policy Enforcement for Every Data Lake
ViewShift: Hassle-free Dynamic Policy Enforcement for Every Data LakeViewShift: Hassle-free Dynamic Policy Enforcement for Every Data Lake
ViewShift: Hassle-free Dynamic Policy Enforcement for Every Data Lake
Walaa Eldin Moustafa
 
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...
Timothy Spann
 
一比一原版(Harvard毕业证书)哈佛大学毕业证如何办理
一比一原版(Harvard毕业证书)哈佛大学毕业证如何办理一比一原版(Harvard毕业证书)哈佛大学毕业证如何办理
一比一原版(Harvard毕业证书)哈佛大学毕业证如何办理
zsjl4mimo
 
State of Artificial intelligence Report 2023
State of Artificial intelligence Report 2023State of Artificial intelligence Report 2023
State of Artificial intelligence Report 2023
kuntobimo2016
 
一比一原版(UofS毕业证书)萨省大学毕业证如何办理
一比一原版(UofS毕业证书)萨省大学毕业证如何办理一比一原版(UofS毕业证书)萨省大学毕业证如何办理
一比一原版(UofS毕业证书)萨省大学毕业证如何办理
v3tuleee
 
一比一原版(UniSA毕业证书)南澳大学毕业证如何办理
一比一原版(UniSA毕业证书)南澳大学毕业证如何办理一比一原版(UniSA毕业证书)南澳大学毕业证如何办理
一比一原版(UniSA毕业证书)南澳大学毕业证如何办理
slg6lamcq
 
Beyond the Basics of A/B Tests: Highly Innovative Experimentation Tactics You...
Beyond the Basics of A/B Tests: Highly Innovative Experimentation Tactics You...Beyond the Basics of A/B Tests: Highly Innovative Experimentation Tactics You...
Beyond the Basics of A/B Tests: Highly Innovative Experimentation Tactics You...
Aggregage
 
一比一原版(Glasgow毕业证书)格拉斯哥大学毕业证如何办理
一比一原版(Glasgow毕业证书)格拉斯哥大学毕业证如何办理一比一原版(Glasgow毕业证书)格拉斯哥大学毕业证如何办理
一比一原版(Glasgow毕业证书)格拉斯哥大学毕业证如何办理
g4dpvqap0
 
一比一原版(Chester毕业证书)切斯特大学毕业证如何办理
一比一原版(Chester毕业证书)切斯特大学毕业证如何办理一比一原版(Chester毕业证书)切斯特大学毕业证如何办理
一比一原版(Chester毕业证书)切斯特大学毕业证如何办理
74nqk8xf
 
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...
Timothy Spann
 
University of New South Wales degree offer diploma Transcript
University of New South Wales degree offer diploma TranscriptUniversity of New South Wales degree offer diploma Transcript
University of New South Wales degree offer diploma Transcript
soxrziqu
 
原版制作(Deakin毕业证书)迪肯大学毕业证学位证一模一样
原版制作(Deakin毕业证书)迪肯大学毕业证学位证一模一样原版制作(Deakin毕业证书)迪肯大学毕业证学位证一模一样
原版制作(Deakin毕业证书)迪肯大学毕业证学位证一模一样
u86oixdj
 
End-to-end pipeline agility - Berlin Buzzwords 2024
End-to-end pipeline agility - Berlin Buzzwords 2024End-to-end pipeline agility - Berlin Buzzwords 2024
End-to-end pipeline agility - Berlin Buzzwords 2024
Lars Albertsson
 
Global Situational Awareness of A.I. and where its headed
Global Situational Awareness of A.I. and where its headedGlobal Situational Awareness of A.I. and where its headed
Global Situational Awareness of A.I. and where its headed
vikram sood
 
Learn SQL from basic queries to Advance queries
Learn SQL from basic queries to Advance queriesLearn SQL from basic queries to Advance queries
Learn SQL from basic queries to Advance queries
manishkhaire30
 

Recently uploaded (20)

The Building Blocks of QuestDB, a Time Series Database
The Building Blocks of QuestDB, a Time Series DatabaseThe Building Blocks of QuestDB, a Time Series Database
The Building Blocks of QuestDB, a Time Series Database
 
一比一原版(爱大毕业证书)爱丁堡大学毕业证如何办理
一比一原版(爱大毕业证书)爱丁堡大学毕业证如何办理一比一原版(爱大毕业证书)爱丁堡大学毕业证如何办理
一比一原版(爱大毕业证书)爱丁堡大学毕业证如何办理
 
Population Growth in Bataan: The effects of population growth around rural pl...
Population Growth in Bataan: The effects of population growth around rural pl...Population Growth in Bataan: The effects of population growth around rural pl...
Population Growth in Bataan: The effects of population growth around rural pl...
 
Influence of Marketing Strategy and Market Competition on Business Plan
Influence of Marketing Strategy and Market Competition on Business PlanInfluence of Marketing Strategy and Market Competition on Business Plan
Influence of Marketing Strategy and Market Competition on Business Plan
 
Enhanced Enterprise Intelligence with your personal AI Data Copilot.pdf
Enhanced Enterprise Intelligence with your personal AI Data Copilot.pdfEnhanced Enterprise Intelligence with your personal AI Data Copilot.pdf
Enhanced Enterprise Intelligence with your personal AI Data Copilot.pdf
 
ViewShift: Hassle-free Dynamic Policy Enforcement for Every Data Lake
ViewShift: Hassle-free Dynamic Policy Enforcement for Every Data LakeViewShift: Hassle-free Dynamic Policy Enforcement for Every Data Lake
ViewShift: Hassle-free Dynamic Policy Enforcement for Every Data Lake
 
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...
 
一比一原版(Harvard毕业证书)哈佛大学毕业证如何办理
一比一原版(Harvard毕业证书)哈佛大学毕业证如何办理一比一原版(Harvard毕业证书)哈佛大学毕业证如何办理
一比一原版(Harvard毕业证书)哈佛大学毕业证如何办理
 
State of Artificial intelligence Report 2023
State of Artificial intelligence Report 2023State of Artificial intelligence Report 2023
State of Artificial intelligence Report 2023
 
一比一原版(UofS毕业证书)萨省大学毕业证如何办理
一比一原版(UofS毕业证书)萨省大学毕业证如何办理一比一原版(UofS毕业证书)萨省大学毕业证如何办理
一比一原版(UofS毕业证书)萨省大学毕业证如何办理
 
一比一原版(UniSA毕业证书)南澳大学毕业证如何办理
一比一原版(UniSA毕业证书)南澳大学毕业证如何办理一比一原版(UniSA毕业证书)南澳大学毕业证如何办理
一比一原版(UniSA毕业证书)南澳大学毕业证如何办理
 
Beyond the Basics of A/B Tests: Highly Innovative Experimentation Tactics You...
Beyond the Basics of A/B Tests: Highly Innovative Experimentation Tactics You...Beyond the Basics of A/B Tests: Highly Innovative Experimentation Tactics You...
Beyond the Basics of A/B Tests: Highly Innovative Experimentation Tactics You...
 
一比一原版(Glasgow毕业证书)格拉斯哥大学毕业证如何办理
一比一原版(Glasgow毕业证书)格拉斯哥大学毕业证如何办理一比一原版(Glasgow毕业证书)格拉斯哥大学毕业证如何办理
一比一原版(Glasgow毕业证书)格拉斯哥大学毕业证如何办理
 
一比一原版(Chester毕业证书)切斯特大学毕业证如何办理
一比一原版(Chester毕业证书)切斯特大学毕业证如何办理一比一原版(Chester毕业证书)切斯特大学毕业证如何办理
一比一原版(Chester毕业证书)切斯特大学毕业证如何办理
 
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Dat...
 
University of New South Wales degree offer diploma Transcript
University of New South Wales degree offer diploma TranscriptUniversity of New South Wales degree offer diploma Transcript
University of New South Wales degree offer diploma Transcript
 
原版制作(Deakin毕业证书)迪肯大学毕业证学位证一模一样
原版制作(Deakin毕业证书)迪肯大学毕业证学位证一模一样原版制作(Deakin毕业证书)迪肯大学毕业证学位证一模一样
原版制作(Deakin毕业证书)迪肯大学毕业证学位证一模一样
 
End-to-end pipeline agility - Berlin Buzzwords 2024
End-to-end pipeline agility - Berlin Buzzwords 2024End-to-end pipeline agility - Berlin Buzzwords 2024
End-to-end pipeline agility - Berlin Buzzwords 2024
 
Global Situational Awareness of A.I. and where its headed
Global Situational Awareness of A.I. and where its headedGlobal Situational Awareness of A.I. and where its headed
Global Situational Awareness of A.I. and where its headed
 
Learn SQL from basic queries to Advance queries
Learn SQL from basic queries to Advance queriesLearn SQL from basic queries to Advance queries
Learn SQL from basic queries to Advance queries
 

3.2.5 principle of dominance

  • 1. www.sanjivanimba.org.in Unit No.3. DECISION SCIENCE Presented By: Dr. V. M. Tidake Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem) Dean, EDP & Associate Professor MBA 1 Sanjivani College of Engineering, Kopargaon Department of MBA www.sanjivanimba.org.in
  • 2. www.sanjivanimba.org.in 302-DECISION SCIENCE Unit No.3. Games Theory 3.2.5 Principle of Dominance Presented By: Dr. V. M. Tidake Ph. D (Financial Management), MBA(FM), MBA(HRM) BE(Chem) Dean EDP & Associate Professor MBA 2 Sanjivani College of Engineering, Kopargaon Department of MBA www.sanjivanimba.org.in
  • 3. www.sanjivanimba.org.in GAMES THEORY  At the End of the Session Student will be able to understand- A. Principle of Dominance
  • 4. www.sanjivanimba.org.in Games Theory Principle of Dominance states that, if a strategy of a player dominates over another strategy in all conditions (i.e. for all counter strategies by the other player), then the later strategy (being dominated) can be ignored. Steps in Principle of Dominance: Step 1: Check if there is a saddle point and if yes then optimal solution is directly obtained. Step 2: If the problem does not have Saddle Point, then reduce the table to a 2*2 table using following rules of dominance- a. If all the elements in a row (say ith row) are less than or equal to the corresponding elements of any other row (say jth row), then neglect the ith row. b. If all the elements in a column (say rth column) are greater than or equal to the corresponding elements of any other column (say sth column), then neglect the rth column.
  • 5. www.sanjivanimba.org.in Games Theory Solve the Following Game using Principle of Dominance: Player B Player A . Player B . Player A B1 B2 B3 A1 1 2 7 A2 6 7 2 A3 6 6 1 B1 B2 B3 Min. A1 1 2 7 1 A2 6 7 2 2 Max. A3 6 6 1 1 Max. 6 Min. 7 7
  • 6. www.sanjivanimba.org.in Games Theory Reducing the Table by using Principle of Dominance: i) We see that all the elements of Row A3 are ≤ the corresponding elements of Row A2. Neglecting A3 we get a reduced Matrix like- . Player B . Player A B1 B2 B3 A1 1 2 7 A2 6 7 2
  • 7. www.sanjivanimba.org.in Games Theory Reducing the Table by using Principle of Dominance: ii) We see that all the elements of Column B2 are ≥ than the corresponding elements of Column B1. Neglecting B2 we get a reduced Matrix like- . Player B . Player A B1 B3 A1 1 7 A2 6 2
  • 8. www.sanjivanimba.org.in Games Theory We have, 𝒑 = 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 𝒂 𝟏𝟏 + 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 − 𝒂 𝟐𝟐 𝒑 = 𝟐 − 𝟔 𝟏 + 𝟐 − 𝟔 − 𝟕 𝒑 = 𝟐 𝟓
  • 9. www.sanjivanimba.org.in Games Theory We have, 𝒒 = 𝒂 𝟐𝟐 − 𝒂 𝟏𝟐 𝒂 𝟏𝟏 + 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 − 𝒂 𝟐𝟐 𝒒 = 𝟐 − 𝟕 𝟏 + 𝟐 − 𝟔 − 𝟕 𝒒 = 𝟏 𝟐
  • 10. www.sanjivanimba.org.in Games Theory We have, 𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑮𝒂𝒎𝒆 = 𝒂 𝟏𝟏 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 𝒂 𝟏𝟐 𝒂 𝟏𝟏 + 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 − 𝒂 𝟏𝟐 𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑮𝒂𝒎𝒆 = 𝟏(𝟐) − 𝟔(𝟕) 𝟏 + 𝟐 − 𝟔 − 𝟕 𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑮𝒂𝒎𝒆 = 4
  • 11. www.sanjivanimba.org.in EXERCISE Hence, The Optimal Strategy for player A is (2/5, 3/5, 0) or (0.4, 0.6, 0) or (40%, 60%, 0%) The Optimal Strategy for player B is (1/2, 0, 1/2) or (0.5, 0, 0.5) or (50%, 0%, 50%) The Value of the Game is 4 i.e. Player A will get Rs. 4 from Player B.
  • 12. www.sanjivanimba.org.in EXERCISE  State and Explain the Principle of Dominance in Games Theory.
  • 13. www.sanjivanimba.org.in For More Details Contact Dr. V M Tidake tidkevishal@gmail.com tidkevishalmba@sanjivani.org.in