18.6: Dominant and Dominated Strategies

In strategic decision-making, a dominant strategy is one that always provides the best outcome for a player, no matter what the other players decide. This ensures that the player's payoff is maximized regardless of the choices made by others. On the other hand, a dominated strategy consistently leads to a worse outcome than another available strategy, regardless of the opponent's decision.

For instance, imagine two firms competing in a market by setting production levels—either high or low. Firm A must choose its production level while considering Firm B's choice. If Firm B opts for high production, Firm A compares its outcomes: high production gives Firm A a profit of 300, while low production gives it only 200. In this case, high production is better. If Firm B chooses low production, Firm A again compares the outcomes: high production results in a profit of 350, while low production results in 250. For Firm A, high production is better regardless of what Firm B chooses, making high production a dominant strategy for Firm A. Low production is a dominated strategy for Firm A, as it leads to lower payoffs in every situation compared to high production.

This comparison process is crucial in identifying which strategies offer the best or worst results, helping decision-makers consistently choose options that maximize their own outcomes. By focusing on these consistent patterns of outcomes, players can strategically avoid choices that leave them at a disadvantage. Ultimately, understanding dominant and dominated strategies simplifies complex decision-making and allows players to confidently select strategies that ensure the highest possible benefit, regardless of their opponent's actions.

A dominant strategy is one that results in the highest payoff for a player, no matter what the other players decide to do.

Conversely, a dominated strategy is one that leads to a worse payoff for a player compared to other strategies, regardless of the opponent's actions.

Consider two competing ice cream vendors at a beach. They can choose to sell high-quality or low-quality products.

To determine if Vendor A has a dominant strategy, the payoffs from Vendor A's perspective for each of Vendor B's strategies are compared.

If Vendor B chooses 'high-quality,' Vendor A compares its payoffs between $100 and $50. Here, $100 is better, so the 'high-quality' is a better strategy for Vendor A in this case.

If Vendor B chooses ' low-quality,' Vendor A compares its payoffs between $150 and $80. Here, $150 is better, so the 'high-quality' strategy is better for Vendor A.

Since 'high-quality' yields a better payoff for Vendor A regardless of Vendor B's strategy, it is Vendor A's dominant strategy.

Low-quality' for Vendor A results in a lower payoff in each case compared to 'high-quality,'  low-quality is the dominated strategy for Vendor A.