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
| | | Player `B` | | |
| | | `B_3` | `B_4` | | |
Player `A` | `A_1` | | 4 | 2 | |
`A_2` | | 2 | 4 | |
`A_4` | | 5 | 2 | |
Row-1 `<=` Row-3, so remove Row-1
| | | Player `B` | | |
| | | `B_3` | `B_4` | | |
Player `A` | `A_2` | | 2 | 4 | |
`A_4` | | 5 | 2 | |
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then