Case 4: Games Theory

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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

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302-DECISION SCIENCE
Unit No.3. Games Theory
3.2.9 Case 4: Games
Theory
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

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GAMES THEORY
 At the End of the Session Student will be able to
understand-
A. Case 4: Games Theory.

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Games Theory
Solve the Following 2*2 Game:
Player B
Player A
. Player B
. Player A
As the Game has no Saddle Point its a Mixed Strategy Game
B1 B2
A1 11 7
A2 9 10
B1 B2 Min.
A1 11 7 7
A2 9 10 9 Maximin
Max. 11 10
Minimax

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Games Theory
We have,
𝒑 =
𝒂 𝟐𝟐 − 𝒂 𝟐𝟏
𝒂 𝟏𝟏 + 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 − 𝒂 𝟏𝟐
𝒑 =
𝟏𝟎 − (𝟗)
𝟏𝟏 + 𝟏𝟎 − 𝟗 − 𝟕
𝒑 =
𝟏
𝟓

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Games Theory
We have,
𝒒 =
𝒂 𝟐𝟐 − 𝒂 𝟏𝟐
𝒂 𝟏𝟏 + 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 − 𝒂 𝟏𝟐
𝒒 =
𝟏𝟎 − 𝟕
𝟏𝟏 + 𝟏𝟎 − 𝟗 − 𝟕
𝒒 =
𝟑
𝟓

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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 =
𝟏𝟏(𝟏𝟎) − 𝟗(𝟕)
𝟏𝟏 + 𝟏𝟎 − 𝟗 − 𝟕
𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑮𝒂𝒎𝒆 =
𝟒𝟕
𝟓
= 𝟗. 𝟒

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GAMES THEORY
Hence,
The Optimal Strategy for player A is (p, 1-p) i.e. (1/5, 4/5)
or (0.20, 0.80) or (20%, 80%)
The Optimal Strategy for player B is (q, 1-q) i.e. (3/5, 2/5)
or (0.60, 0.40) or (60%, 40%)
The Value of the Game is 9.4 i.e. Player A will get Rs. 9.4
from Player B.

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EXERCISE
 Solve Case 4: Games Theory

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For More Details Contact
Dr. V M Tidake
tidkevishal@gmail.com
tidkevishalmba@sanjivani.org.in

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Thank You