Weakly dominated strategy

Definition

A weakly dominated strategy is a choice in a game that is never better and sometimes worse than another strategy. In simpler terms, if a player has an alternative strategy that provides equal or better payoffs regardless of what opponents choose, the weakly dominated strategy can be disregarded. This concept plays an essential role in refining strategic choices and helps players identify strategies that are less effective, thereby simplifying decision-making.

5 Must Know Facts For Your Next Test

1. A weakly dominated strategy can be ignored in decision-making since it does not provide any advantage over the alternative options.
2. Unlike strictly dominated strategies, weakly dominated strategies may have situations where they provide equal payoffs, making them less clear-cut to eliminate.
3. Identifying weakly dominated strategies is crucial for simplifying complex games and helping players focus on stronger options.
4. In games with multiple players, a weakly dominated strategy can still be part of a Nash equilibrium, depending on the context and the choices of other players.
5. Eliminating weakly dominated strategies can lead to a more efficient analysis of strategic interactions and improve overall outcomes.

Review Questions

• How does identifying weakly dominated strategies impact the decision-making process in strategic games?
  • Identifying weakly dominated strategies simplifies the decision-making process by allowing players to eliminate options that are not competitive. This helps focus attention on strategies that offer better payoffs or equal outcomes, ultimately guiding players toward more effective choices. By reducing the set of strategies under consideration, players can better analyze potential outcomes and make informed decisions based on their opponents' likely responses.
• Discuss the differences between weakly dominated strategies and strictly dominated strategies in game theory.
  • Weakly dominated strategies differ from strictly dominated strategies in that they may yield equal payoffs under certain circumstances. A strictly dominated strategy is always outperformed by another option, while a weakly dominated strategy may sometimes match or fall short of its alternatives. This distinction affects how players evaluate their choices; weakly dominated strategies might still be considered in specific scenarios where they offer equal benefits, leading to more nuanced strategic planning.
• Evaluate the role of weakly dominated strategies in reaching Nash equilibrium within a multi-player game.
  • In multi-player games, weakly dominated strategies can influence the dynamics leading to Nash equilibrium. While eliminating such strategies may streamline player choices, they can still exist in equilibria under particular conditions. Players might maintain these strategies if they do not incur significant penalties or if their opponents also adopt similar strategies. Analyzing these interactions can reveal how player behavior affects overall outcomes and stability within the game.

Related terms

dominant strategy:

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

strictly dominated strategy: A strictly dominated strategy is one where there is another strategy that always provides a better outcome regardless of what opponents choose.

Nash equilibrium: Nash equilibrium is a situation in which each player's strategy is optimal given the strategies chosen by other players, meaning no player can benefit by changing their strategy unilaterally.