Dominant and Dominated Strategies

A dominant strategy is one that results in the highest payoff for a player, regardless of what the other players decide to do. It ensures the player's outcome is maximized no matter the opponent's choice. For example, if Vendor A earns higher profits by selling high-quality products whether Vendor B chooses high or low quality, then high-quality is Vendor A's dominant strategy.

A dominated strategy consistently leads to worse payoffs than another available strategy, regardless of the opponent's decision. To identify it, compare payoffs across all possible opponent actions. If one strategy yields lower profits in every scenario compared to an alternative, it is dominated. For Vendor A, low-quality is dominated because it produces lower payoffs than high-quality in all cases.

Players should avoid dominated strategies because they guarantee worse outcomes than other available options. By focusing on strategies that maximize payoffs across all opponent scenarios, decision-makers can confidently select options that ensure the highest possible benefit. Avoiding dominated strategies simplifies complex decision-making and prevents players from choosing options that leave them at a disadvantage.

When all players in a game have dominant strategies and each chooses theirs, the result is an equilibrium in dominant strategies. This occurs because no player can improve their payoff by unilaterally changing their choice. Understanding dominant and dominated strategies is foundational to recognizing equilibrium in dominant strategies in competitive situations.

Not all games have dominant strategies for every player. A dominant strategy exists only when one choice yields better payoffs than all alternatives across every possible opponent action. In many competitive situations, players must consider opponent behavior and may lack a universally superior strategy, requiring more complex strategic analysis.

Firms compare payoffs for different production levels given each competitor's possible choices. If high production consistently yields higher profits regardless of competitor output, high production is the dominant strategy. For example, Firm A choosing high production earns 300 or 350 in profit depending on Firm B's choice, making it superior to low production in all scenarios.

A dominant strategy outperforms all alternatives regardless of opponent actions, while a best response is optimal only given a specific opponent choice. A dominant strategy is always a best response to any opponent strategy, but a best response may not be dominant if it performs poorly against other opponent choices. Dominant strategies provide unconditional strategic superiority.