Game Theory- Decision Science- Mix Strategy- 4X4 Matrix to be reduced to 2X2 by the principle of dominance and determine value of the game.

1. Question # 1
Newspaper Radio Television Digital Marketing
Newspaper 3 2 4 0
Radio 3 4 2 4
Television 4 2 4 0
Digital Marketing 0 4 0 9
Strategy of Flipkart
StrategyofAmazon
Reduce the game to 2x2 order and obtain strategies for each
player and value of the game.
Prepared by Prof. Sarang 1

2. Step I: Check for saddle point (after every
reduction by dominance repeat this step)
Row Minima
Newspaper Radio Television Digital Marketing
Newspaper 3 2 4 0 0
Radio 3 4 2 4 2
Television 4 2 4 0 0
Digital Marketing 0 4 0 9 0
Column Maxima 4 4 4 9
StrategyofAmazon
Strategy of Flipkart
Prepared by Prof. Sarang 2

3. Newspaper Radio Television Digital Marketing
Newspaper 3 2 4 0
Radio 3 4 2 4
Television 4 2 4 0
Digital Marketing 0 4 0 9
Compare row 1 and 3, first row is dominated by third and hence eliminated
No saddle point after reduction
StrategyofAmazon
Strategy of Flipkart
Step II: Use the principle of dominance
(Delete row having minimum value in compared row and Delete
column having greater value in compared column)
Prepared by Prof. Sarang 3

4. Newspaper Radio Television Digital Marketing
Radio 3 4 2 4
Television 4 2 4 0
Digital Marketing 0 4 0 9
Compare column 1 and 3, by dominance
No Saddle point after reduction
Strategy of Flipkart
StrategyofAmazon
Step III: Use the principle of dominance
(Delete row having minimum value in compared row and Delete
column having greater value in compared column)
Prepared by Prof. Sarang 4

5. Radio Television Digital Marketing
Radio 4 2 4
Television 2 4 0
Digital Marketing 4 0 9
Compare column 1 and combination of 2 and 3 by dominance, remove column 1
No Saddle point after reduction
StrategyofAmazon
Strategy of Flipkart
Step IV: Use the principle of dominance
(Dominance by a convex linear combination of column 2 and 3
{simple average of the values}
Prepared by Prof. Sarang 5

6. Television Digital Marketing
Radio 2 4
Television 4 0
Digital Marketing 0 9
Compare row 1 and combination of 2 and 3 by dominance, remove row 1
No Saddle point after reduction
StrategyofAmazon
Strategy of Flipkart
Step V: Use the principle of dominance
(Delete row having minimum value in compared row and Delete
column having greater value in compared column)
Prepared by Prof. Sarang 6

7. Television Digital Marketing
Television 4 0
Digital Marketing 0 9
x=9-0/(4+9)-(0+0)
x=9/13
y=9-0/(4+9)-(0-0)
y=9/13
Value of the Game
V=4x9 -0x0/(4+9) -(0-0)
V=36/13
StrategyofAmazon
Strategy of Flipkart
Step VI: For mix strategy ,calculate the probability for
every player and value of the game.
Prepared by Prof. Sarang 7