Page 191 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes
 V i = 1 to 3
Therefore y = Vy V I = 1 to 3
i i
Therefore y = Vy =  
1 1

y = Vy =  
2 2

y = Vy =  
3 3
We can read the values of the dual variables X X and X for (Z – C) row of slack variables in
1 2 3 j j
Table 4 which are respectively.

Min. =    

Therefore V =

Hence, x =  
1

x = Vx =   
2 2
x = Vx =  
3 3

Therefore the optimal strategy for A is and for B is 2, 3, and and the

value of the game is B =

Self Assessment

State true or false:

6. Two-person-zero-sum game without saddle point is called pure strategy games.
7. One of the important assumptions in a two person zero sum game is that each player has
a finite number of strategies.

8. Two-person-zero-sum game with saddle point is called mixed strategy games.

9.3 Pure Strategies: Game with Saddle Point

The aim of the game is to determine how the players must select their respective strategies such
that the payoff is optimized. This decision-making is referred to as the minimax-maximin
principle to obtain the best possible selection of a strategy for the players.
In a payoff matrix, the minimum value in each row represents the minimum gain for player A.
Player A will select the strategy that gives him the maximum gain among the row minimum

186 LOVELY PROFESSIONAL UNIVERSITY