The rule of dominance

The rule of dominance is a decision-making principle in game theory that suggests that a strategy can be eliminated from consideration if it is always dominated by another strategy, meaning that it always yields a worse outcome regardless of the other player’s strategy.

To apply the rule of dominance, a player evaluates each of their strategies based on the payoffs that they would receive for all possible strategies that the other player could play. If one strategy always yields a worse outcome than another strategy, it can be eliminated from consideration as it is dominated.

For example, consider a game between two players, Alice and Bob, in which Alice can choose between two pure strategies, A1 and A2, and Bob can choose between two pure strategies, B1 and B2. The game matrix is as follows:

To apply the rule of dominance, Alice evaluates her strategies based on Bob’s possible strategies:

• If Bob plays B1, Alice’s payoffs for each of her strategies are 3 for A1 and 2 for A2. Therefore, A2 is dominated by A1 and can be eliminated from consideration.
• If Bob plays B2, Alice’s payoffs for each of her strategies are 1 for A1 and 2 for A2. Therefore, A1 is dominated by A2 and can be eliminated from consideration.

Thus, applying the rule of dominance results in the elimination of A2 and the conclusion that Alice should choose A1 if Bob plays B1 and A2 if Bob plays B2.

The rule of dominance is a useful tool in game theory as it can simplify the analysis of a game by reducing the number of strategies that need to be considered. However, it should be used with caution as it may not always identify the correct equilibrium outcome.