7

Click here to load reader

Question on Game Theory

Embed Size (px)

Citation preview

Page 1: Question on Game Theory

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

Stra

tegy

of

Am

azo

n

Reduce the game to 2x2 order and obtain strategies for each player and value of the game.

Prepared by Prof. Sarang 1

Page 2: Question on Game Theory

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

Stra

tegy

of

Am

azo

n Strategy of Flipkart

Prepared by Prof. Sarang 2

Page 3: Question on Game Theory

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

Stra

tegy

of

Am

azo

n Strategy of Flipkart

Step II: Use the principle of dominance(Delete row having minimum value in compared row and Deletecolumn having greater value in compared column)

Prepared by Prof. Sarang 3

Page 4: Question on Game Theory

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

Stra

tegy

of

Am

azo

n

Step III: Use the principle of dominance(Delete row having minimum value in compared row and Deletecolumn having greater value in compared column)

Prepared by Prof. Sarang 4

Page 5: Question on Game Theory

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

Stra

tegy

of

Am

azo

n 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

Page 6: Question on Game Theory

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

Stra

tegy

of

Am

azo

n

Strategy of Flipkart

Step V: Use the principle of dominance(Delete row having minimum value in compared row and Deletecolumn having greater value in compared column)

Prepared by Prof. Sarang 6

Page 7: Question on Game Theory

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

Stra

tegy

of A

maz

on

Strategy of Flipkart

Step VI: For mix strategy ,calculate the probability forevery player and value of the game.

Prepared by Prof. Sarang 7