Dominance: Game Theory

The principle of dominance in Game Theory (also known as dominant strategy or dominance method) states that if one strategy of a player dominates over the other strategy in all conditions then the later strategy can be ignored.

A strategy dominates over the other only if it is preferable over other in all conditions. The concept of dominance is especially useful for the evaluation of two-person zero-sum games where a saddle point does not exist.

Generally, the dominance property is used to reduce the size of a large payoff matrix.

Dominant Strategy Rules (Dominance Principle)

• If all the elements of a column (say ith column) are greater than or equal to the corresponding elements of any other column (say jth column), then the ith column is dominated by the jth column and can be deleted from the matrix.
• If all the elements of a row (say ith row) are less than or equal to the corresponding elements of any other row (say jth row), then the ith row is dominated by the jth row and can be deleted from the matrix.

Dominance Example: Game Theory

Use the principle of dominance to solve this problem.

Solution.

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Player B
Player A   I II III IV Minimum
I 3 5 4 2 2
II 5 6 2 4 2
III 2 1 4 0 0
IV 3 3 5 2 2
Maximum   5 6 5 4

There is no saddle point in this game.

Using Dominance Property In Game Theory

If a column is greater than another column (compare corresponding elements), then delete that column.
Here, I and II column are greater than the IV column. So, player B has no incentive in using his I and II course of action.

Player B
Player A   III IV
I 4 2
II 2 4
III 4 0
IV 5 2

If a row is smaller than another row (compare corresponding elements), then delete that row.
Here, I and III row are smaller than IV row. So, player A has no incentive in using his I and III course of action.

Player B
Player A   III IV
II 2 4
IV 5 2

Now you can use any one of the following to determine the value of game

(Try it yourself)

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