Game Theory problem using Dominance method Method & Example-1

1. Method & Example-1

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Home > Operation Research calculators > Game Theory >> Saddle Point example

2. Dominance method example ( Enter your problem )

( Enter your problem )

Method & Example-1
Example-2

Other related methods

1. Saddle point
(Previous method)

2. Example-2
(Next example)

Player $B$

Player $A$

Method

dominance method Steps (Rule)
Step-1:	If all the elements of Column-i are greater than or equal to the corresponding elements of any other Column-j, then the Column-i is dominated by the Column-j and it is removed from the matrix. eg. If Column-2 $>=$ Column-4, then remove Column-2
Step-2:	If all the elements of a Row-i are less than or equal to the corresponding elements of any other Row-j, then the Row-i is dominated by the Row-j and it is removed from the matrix. eg. If Row-3 $<=$ Row-4, then remove Row-3
Step-3:	Again repeat Step-1 & Step-2, if any Row or Column is dominated, otherwise stop the procedure.

Average dominance method Rule
1.	If Column-i is dominated by the average of Column-j and Column-k then Column-i is removed from the matrix. eg. If Column-1 $>=$ average of Column-2 and Column-3, then Column-1 is removed
2.	If Row-i is dominated by the average of Row-j and Row-k then Row-i is removed from the matrix. eg. If Row-1 $<=$ average of Row-2 and Row-3, then Row-1 is removed

Example-1
1. Find Solution of game theory problem using dominance method
_{Player A}\^{Player B} B1 B2 B3 B4
A1 3 5 4 2
A2 5 6 2 4
A3 2 1 4 0
A4 3 3 5 2

Solution:
2. Dominance rule to reduce the size of the payoff matrix
Using dominance property

		Player $B$
		$B_1$	$B_2$	$B_3$	$B_4$
Player $A$	$A_1$	3	5	4	2
	$A_2$	5	6	2	4
	$A_3$	2	1	4	0
	$A_4$	3	3	5	2

Row-3

$<=$ Row-4, so remove Row-3

		Player $B$
		$B_1$	$B_2$	$B_3$	$B_4$
Player $A$	$A_1$	3	5	4	2
	$A_2$	5	6	2	4
	$A_4$	3	3	5	2

Column-2

$>=$ Column-4, so remove Column-2

		Player $B$
		$B_1$	$B_3$	$B_4$
Player $A$	$A_1$	3	4	2
	$A_2$	5	2	4
	$A_4$	3	5	2

Column-1

$>=$ Column-3, so remove Column-1

Row-1

$<=$ Row-3, so remove Row-1

This material is intended as a summary. Use your textbook for detail explanation.
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