This document discusses a game theory case involving two players, A and B, who must choose between multiple options. Player A can choose between options A1, A2, and A3, while Player B can choose between B1 and B2. There is no saddle point, so the optimal strategies are calculated to be Player A choosing A1 with probability 5/19 and A2 with probability 14/19, while Player B chooses B1 with probability 6/19 and B2 with 13/19. The value of the game is determined to be 168/19.

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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
3.2.10 Case 5: 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 5: Games Theory.

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Games Theory
Solve the Following Game:
.
. Player B
Player A
.
.
B1 B2
A1 28 0
A2 2 12
A3 4 7

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Games Theory
Player B
Player A
.
. As Maximin is not equal to Minimax, there is no Saddle Point.
B1 B2 Min
A1 28 0 0
A2 2 12 2
A3 4 7 4 Maximin
Max 28 12
Minimax

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Games Theory
Combining rows A1 & A2 in the proportion ¼ : ¾ (8.5, 9) and
comparing it with Row A3
Player B
Player A
.
.
B1 B2
A1 28 0
A2 2 12

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Games Theory
We have,
𝒑 =
𝒂 𝟐𝟐 − 𝒂 𝟐𝟏
𝒂 𝟏𝟏 + 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 − 𝒂 𝟏𝟐
𝒑 =
𝟏𝟐 − 𝟐
𝟐𝟖 + 𝟏𝟐 − 𝟐 − 𝟎
𝒑 =
𝟓
𝟏𝟗

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Games Theory
We have,
𝒒 =
𝒂 𝟐𝟐 − 𝒂 𝟏𝟐
𝒂 𝟏𝟏 + 𝒂 𝟐𝟐 − 𝒂 𝟐𝟏 − 𝒂 𝟏𝟐
𝒒 =
𝟏𝟐 − 𝟎
𝟐𝟖 + 𝟏𝟐 − 𝟐 − 𝟎
𝒒 =
𝟔
𝟏𝟗

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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 =
𝟐𝟖(𝟏𝟐) − 𝟐(𝟎)
𝟐𝟖 + 𝟏𝟐 − 𝟐 − 𝟎
𝑽𝒂𝒍𝒖𝒆 𝒐𝒇 𝒕𝒉𝒆 𝑮𝒂𝒎𝒆 =
𝟏𝟔𝟖
𝟏𝟗

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GAMES THEORY
Hence,
The Optimal Strategy for player A is (p, 1-p) i.e. (5/19,
14/19,0)
The Optimal Strategy for player B is (q, 1-q) i.e. (6/19,
13/19)
The Value of the Game is 168/19 i.e. Player A will get Rs.
168/19 from Player B.

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EXERCISE
 Solve Case 5: 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