Operation research
Unit 3
GAME THEORY
Lesson 27
Learning Objective:
•
•
To learn to apply dominance in game theory.
Generate solutions in functional areas of business and management.
Hello students,
In our last lecture you learned to solve zero sum games having mixed strategies.
But...
Did you observe one thing that it was applicable to only 2 x 2 payoff matrices? So let us implement it to other matrices using dominance and study the importance of DOMINANCE
In a game, sometimes a strategy available to a player might be found to be preferable to some other strategy / strategies. Such a strategy is said to dominate the other one(s). The rules of dominance are used to reduce the size of the payoff matrix. These rules help in deleting certain rows and/or columns of the payoff matrix, which are of lower priority to at least one of the remaining rows, and/or columns in terms of payoffs to both the players. Rows / columns once deleted will never be used for determining the optimal strategy for both the players.
This concept of domination is very usefully employed in simplifying the two – person zero sum games without saddle point. In general the following rules are used to reduce the size of payoff matrix.
The RULES follow are:
( PRINCIPLES OF DOMINANCE )
you will have to
Rule 1: If all the elements in a row ( say i th row ) of a pay off matrix are less than or equal to the corresponding elements of the other row ( say j th row ) then the player A
will never choose the i th strategy then we say i th strategy is dominated by j th strategy and will delete the i th row.
Rule 2: If all the elements in a column ( say r th column ) of a payoff matrix are greater than or equal to the corresponding elements of the other column ( say s th column ) then the player B will never choose the r th strategy or in the other words the r th strategy is dominated by the s th strategy and we delete r th column .
Rule 3: A pure strategy may be dominated
GAME THEORY
Lesson 27
Learning Objective:
•
•
To learn to apply dominance in game theory.
Generate solutions in functional areas of business and management.
Hello students,
In our last lecture you learned to solve zero sum games having mixed strategies.
But...
Did you observe one thing that it was applicable to only 2 x 2 payoff matrices? So let us implement it to other matrices using dominance and study the importance of DOMINANCE
In a game, sometimes a strategy available to a player might be found to be preferable to some other strategy / strategies. Such a strategy is said to dominate the other one(s). The rules of dominance are used to reduce the size of the payoff matrix. These rules help in deleting certain rows and/or columns of the payoff matrix, which are of lower priority to at least one of the remaining rows, and/or columns in terms of payoffs to both the players. Rows / columns once deleted will never be used for determining the optimal strategy for both the players.
This concept of domination is very usefully employed in simplifying the two – person zero sum games without saddle point. In general the following rules are used to reduce the size of payoff matrix.
The RULES follow are:
( PRINCIPLES OF DOMINANCE )
you will have to
Rule 1: If all the elements in a row ( say i th row ) of a pay off matrix are less than or equal to the corresponding elements of the other row ( say j th row ) then the player A
will never choose the i th strategy then we say i th strategy is dominated by j th strategy and will delete the i th row.
Rule 2: If all the elements in a column ( say r th column ) of a payoff matrix are greater than or equal to the corresponding elements of the other column ( say s th column ) then the player B will never choose the r th strategy or in the other words the r th strategy is dominated by the s th strategy and we delete r th column .
Rule 3: A pure strategy may be dominated