Strictly Dominant Strategy

Definition

A strictly dominant strategy is a strategy in a game that yields a higher payoff for a player, regardless of what the other players choose to do. This means that no matter how opponents act, the strictly dominant strategy will always produce better outcomes for the player compared to any other strategies they might consider. Understanding this concept is crucial in analyzing normal form games and payoff matrices, as it helps identify optimal strategies that players can adopt to maximize their benefits.

5 Must Know Facts For Your Next Test

1. In a game with a strictly dominant strategy, a player will always choose this strategy because it guarantees the highest payoff regardless of the opponents' actions.
2. Strictly dominant strategies simplify decision-making for players since they can ignore other strategies without loss of potential payoff.
3. Not all games have strictly dominant strategies; some may have weakly dominant or no dominant strategies at all.
4. When every player in a game has a strictly dominant strategy, the outcome is known as a dominant strategy equilibrium.
5. The existence of strictly dominant strategies can lead to predictable outcomes in games, which helps in strategic planning and decision-making.

Review Questions

• How does the concept of a strictly dominant strategy influence decision-making in normal form games?
  • The concept of a strictly dominant strategy simplifies decision-making in normal form games by providing players with a clear and optimal choice that guarantees higher payoffs. When a player identifies a strictly dominant strategy, they can confidently select it without considering other options, as it will always result in better outcomes. This influences overall game dynamics and helps players predict each other's actions based on their understanding of optimal strategies.
• Discuss the implications of strictly dominant strategies on the outcome of a game involving multiple players.
  • In games where multiple players have strictly dominant strategies, the overall outcome is often predictable, leading to what is known as a dominant strategy equilibrium. Each player will play their strictly dominant strategy, resulting in an outcome that reflects these choices. This can reduce uncertainty and allow for easier predictions about opponents' behavior, but it also raises questions about cooperation and competition among players if everyone follows their self-interested strategies.
• Evaluate the role of strictly dominant strategies in achieving Nash Equilibrium in games with multiple potential outcomes.
  • Strictly dominant strategies play a significant role in achieving Nash Equilibrium by guiding players toward stable outcomes where no one has an incentive to deviate from their chosen strategy. In cases where strictly dominant strategies exist for all players, the equilibrium reached will be stable since every player's choice leads to maximized payoffs based on others' predictable actions. However, when strictly dominant strategies are absent, players may face multiple equilibria, making it more challenging to predict outcomes and potentially leading to less efficient results.

Related terms

Dominant Strategy: A strategy that is the best choice for a player, regardless of what the other players decide to do, but may not necessarily provide strictly higher payoffs than other strategies.

Nash Equilibrium: A situation in a game where no player can gain by changing their strategy while the other players keep theirs unchanged, potentially involving strictly dominant strategies.

Payoff Matrix:

A table that describes the payoffs for each player based on the combination of strategies chosen in a game, used to analyze and determine optimal strategies.