Page 195 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Step 3: All the entries of III row are higher or equal to I row. Hence eliminate I row.
 
  
 
Step 4: All the entries of III column are lower than that of I column. Hence, eliminate I column.

B Row Min.
A 2 4 2
5 2 2
Col. Max. 5 4

Minimax = 4
Maximin = 2

Therefore Minimax is not equal to Maximin. Hence, no saddle point exists. Hence, we use
algebraic method to find the value of the game.
Let x and (1 – x) and y and (1 – y) denote the probabilities of selecting the first and second
strategies by the players A and B respectively.

x =

=


=
  


= =

Therefore x = and (1 – x) =

y =

=


=
  

= =


y = and (1 – y) =

Value of the game =

=

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