Q1.Solve the game whose Pay off Matrix is given by
B1 B2 B3 Player B
Player A A1 [ 1 3 1
A2 0 -4 -3
A3 1 5 -1]
Soln:
STEP I:
Find out the Row minima and column maxima.
[1 3 1 1
0 -4 -3 -4 maximin=1
1 5 -1] -1
1 5 1
minimax=1
STEP II:
maximin=minimax=1
There exists a saddle point value of game = 1
The optimal strategy is (A1,B1) --> this value is the intersection of maxima and minima.
The game is strictly determined since maximin=minima is not equal to 0
Q2. Solve:
[ 0 2
-1 4]
Soln:
STEP I:
[ 0 2 0
-1 4] -1 maximin=0
0 4
minimax=0
STEP II:
maximin=minimax=0
there exists a saddle point value of game=0
The optimum strategy is (A1,B1)
The game is fair since maximin=minimax=0
B1 B2 B3 Player B
Player A A1 [ 1 3 1
A2 0 -4 -3
A3 1 5 -1]
Soln:
STEP I:
Find out the Row minima and column maxima.
[1 3 1 1
0 -4 -3 -4 maximin=1
1 5 -1] -1
1 5 1
minimax=1
STEP II:
maximin=minimax=1
There exists a saddle point value of game = 1
The optimal strategy is (A1,B1) --> this value is the intersection of maxima and minima.
The game is strictly determined since maximin=minima is not equal to 0
Q2. Solve:
[ 0 2
-1 4]
Soln:
STEP I:
[ 0 2 0
-1 4] -1 maximin=0
0 4
minimax=0
STEP II:
maximin=minimax=0
there exists a saddle point value of game=0
The optimum strategy is (A1,B1)
The game is fair since maximin=minimax=0
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