GRAPHICAL METHOD FOR GAME THEORY

Q1.Solve the following 2 x 3 game graphically

                               Player B
Player A    [ 1          3         11
                    8          5          2]



STEP I :
 A's expected pay off against B's pure move is given by:


B's PURE MOVE                     A's EXPECTED PAY OFF E(P)
     B1                                              E1(P)=8-7P1
     B2                                              E2(P)=5-2P1
     B3                                              E3(P)=2P1+2

STEP II:
Now for the graph consider Axis 1 as  A2 and Axis 2 as A1

STEP III:
The reduced Pay off matrix is given by

          B2           B3    --------> the intersection point
A1 [   3              11       3
A2      5               2]      2     maxmin=3

           5               11
minimax=5

maxmin != minmax
Therefore  there exists no saddle point

P1=9/11          p2=2/11

q1=3/11           q2=8/11


Value of game = 49/11

The optimal Strategy is given by
            [  A1          A2
SA  =      9/11       2/11]

           [  B1          B2       B3
SB =      0             3/11     8/11]


NOTE:
The left out matrix value is given as '0'
For 2 x n matrix find lower envelope, find maximin (maximum values)
For m x 2 matrix find upper envelope, find minimax (minimum values)