Weakly dominant strategy

Definition

A weakly dominant strategy is an action that results in a player achieving at least the same payoff as any other strategy, regardless of what the other players choose, and sometimes provides a better payoff. This concept is important because it helps to identify strategies that are preferable for a player in a game, contributing to their decision-making process. Understanding weakly dominant strategies can also highlight the existence of Nash equilibria in games where players choose strategies based on their payoffs.

5 Must Know Facts For Your Next Test

1. Weakly dominant strategies allow for flexibility in decision-making since they can provide equal or better outcomes depending on opponents' choices.
2. In some games, players may have multiple weakly dominant strategies, which complicates the decision-making process.
3. Identifying weakly dominant strategies can simplify strategic interactions by reducing the number of viable options for players.
4. Weakly dominant strategies may lead to situations where multiple Nash equilibria exist, as players settle on various strategies that meet the criteria.
5. Players are often encouraged to choose weakly dominant strategies when they are uncertain about their opponents' actions to ensure at least an acceptable outcome.

Review Questions

• How does a weakly dominant strategy differ from a strictly dominant strategy in terms of player choices?
  • A weakly dominant strategy allows a player to achieve at least the same payoff as any other strategy, while a strictly dominant strategy guarantees a better payoff regardless of what others do. This means that with a weakly dominant strategy, there might be scenarios where other strategies yield the same payoff, leading to less certainty in decision-making. In contrast, strictly dominant strategies eliminate doubts because they are always superior.
• In what ways can recognizing weakly dominant strategies influence players' approach to reaching Nash equilibria?
  • Recognizing weakly dominant strategies can significantly influence how players approach Nash equilibria since these strategies provide options that ensure at least satisfactory outcomes. When players identify weakly dominant strategies, they may gravitate toward them, leading to stability within the game. This awareness can reduce the complexity of their choices and guide them towards equilibria where no player has an incentive to deviate from their chosen strategy.
• Evaluate the implications of using weakly dominant strategies in games with multiple players and varying preferences.
  • Using weakly dominant strategies in games with multiple players can create complex dynamics due to varying preferences and potential for multiple equilibria. Players might have different interpretations of what constitutes a 'weakly better' outcome, leading to strategic uncertainty. This situation can make predicting outcomes more difficult as players adapt their strategies based on perceived advantages or their opponents’ decisions, ultimately affecting overall game stability and outcomes in unpredictable ways.

Related terms

dominant strategy: A dominant strategy is an action that always results in a higher payoff for a player, no matter what the other players do.

Nash equilibrium: A Nash equilibrium occurs when players choose strategies such that no player can benefit by unilaterally changing their strategy, given the strategies chosen by others.

best response: A best response is a strategy that yields the highest possible payoff for a player, given the strategies chosen by other players.