Homework Help: Game Theory Question

1. Dec 3, 2005

dglee

In the game with payoff Matrix

[4,2,0,-1,5,-2]
[-2,-3,2,5,0,4]
[5,-3,4,0,4,7]
[1,3,3,2,-6,5]

Columngirl's strategy of [1/2,0,0,1/2,0,0] is optimal. Describe all the optimal strategies for Rowboy. Find the value of the game and show that this game is not fair.

Thing is i can't find any optimal value for Rowboy

here is his strategie Rowboy's strategy

Min{W}
-4y1+2y2-5y3-y4+w>=0
-2y1+3y2+3y3-3y4+w>=0
-5y2-2y4+w>=0
-5y1-4y3+6y4+w>=0
2y1-4y2-7y3-5y4+w>=0
y1+y2+y3+y4=1
y1,y2,y3,y4>=0

L(x,y)=w=5/2

2. Dec 3, 2005

HallsofIvy

You are given that the optimal column strategy is [1/2, 0, 0, 1/2, 0, 0]. Any optimal row strategy must be optimal against that so you really only need to consider the first and fourth columns. (I get, as optimal row strategy, [1/2, 1/2, 0, 0].

3. Dec 3, 2005

dglee

I tried that but then i can't show that L(x,y)=w=5/2 which makes the game unfair. If i use Rowboy's strategie as [1/2,1/2,0,0] i get the game is at w=3/2 which doesn't equal to 5/2. I know that is a feasiable strategy but its not optimal.