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.

Dominant Strategy Rules (Dominance Principle)

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

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.

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

• Algebraic Method
• Calculus Method
• Linear Programming Method

(Try it yourself)