1. Method & Example-1
Method
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dominance method Steps (Rule)
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Step-1:
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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
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Step-2:
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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
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Step-3:
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Again repeat Step-1 & Step-2, if any Row or Column is dominated, otherwise stop the procedure.
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Average dominance method Rule
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1.
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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
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2.
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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
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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
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