18.7 : Equilibrium in Dominant Strategies

In game theory, equilibrium in dominant strategies arises when each player selects their optimal strategy independently of others' choices. This simplifies analysis since each player's best decision is predictable without considering opponents' actions.

Understanding Dominant Strategy Equilibrium

A dominant strategy consistently offers the best outcome for a player, regardless of the choices of other players. When all players adopt their dominant strategies, the game reaches a stable equilibrium, as no player gains from changing their strategy.

Illustrative Example: Advertising Choices

Consider two competing coffee brands, X and Y, deciding whether to invest in a high-budget advertising campaign or a low-budget campaign to attract more customers.

1. If Brand X opts for high-budget advertising, Brand Y's profits for choosing high- and low-budget options are $200,000 and $150,000, respectively, making high-budget advertising the better choice for Brand Y.
2. If Brand X chooses low-budget advertising, Brand Y's profits are again $200,000 for high-budget and $150,000 for low-budget advertising, confirming that high-budget advertising remains the optimal choice for Brand Y.

Because high-budget advertising yields higher profits for Brand Y regardless of what Brand X decides, it becomes the dominant strategy for Brand Y. Similarly, high-budget advertising is the dominant strategy for Brand X. This leads to an equilibrium in dominant strategies, where both brands choose high-budget campaigns, resulting in predictable and stable outcomes.

Absence of Dominant Strategies

Not all strategic games result in dominant strategies. For instance, in a modified version of the coffee brands' scenario, fluctuating market trends might mean neither brand has a clear advantage with a single strategy. In such cases, each brand's optimal decision depends on the other's choice, adding complexity to the analysis. Games without dominant strategies often require approaches like the Nash equilibrium to assess possible outcomes.