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Term 3 : Chapter 6 : Game Theory

Notes1. Two-person zero-sum game: 1 gain - 1

loss2. Pure-strategy game:

o Row player : min ma

o Column player: ma min

3. !ie"-strategy game:o #se pro$a$ility "istri$ution

%. Pay-o& matri : gain 'or the row resulting

'rom mi strategy.(. )ominate" strategy:

1. * two-person zero-sum game is "e+ne"

$y the 'ollow pay-o& matri.

Player *

,

1

,

2

,

3Play

er*

*

1

1

2*

2

/ 1

1

1

)etermine the optimal strategy 'or ea0h

player an" the alue o' the game. 3

mars4

2. * two- person zero- sum game is "e+ne"

$y the pay-o& matri. 5plain that the

game is sta$le. s it a 'air game7

(4

(1 3 23 5 42 2 5

)3. n a presi"ential 0ampaign8 there are two

0an"i"ates8 a )emo0rat 9) an" a

Repu$li0an 9R8 an" two types o' issues8

"omesti0 issues an" 'oreign issues. The

units assigne" to ea0h 0an"i"ate;s

strategy are gien in the ta$le where it

shows the strength o' the )emo0rat

0an"i"ate 0on0erning the issues in

relation to the Repu$li0an 0an"i"ate.

Repu$li0an)omest

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Term 3 : Chapter 6 : Game Theory

(1 2 33 5 61 2 4

)a. ?how that the game has a sta$le solution.

34$. ?tate the alue o' the game.

140. )etermine the optimal strategy 'or ea0h

player. 24".. Two players Rowan 9Row player an"

Cologne 90olumn player play a zero sum

game $ase" on the Pay-o& matri $elow

C1 C2 C3R1 -2 -1

R2 2 -%R3 % -1

a