Weakly dominant strategy

Definition

A weakly dominant strategy is a choice in game theory that provides a player with outcomes that are at least as good as any other strategy, regardless of what the opponents choose, and sometimes even better. This concept is crucial in understanding decision-making within Nash equilibria, where players choose strategies that lead to stable outcomes. It highlights situations where one strategy may not always outperform others but does not perform worse in any scenario.

5 Must Know Facts For Your Next Test

1. A weakly dominant strategy may lead to the same outcome as another strategy but is never worse, which can simplify decision-making for players.
2. In games with multiple players, identifying weakly dominant strategies can help predict which strategies players are likely to adopt.
3. While weakly dominant strategies do not guarantee the best outcome, they can still provide a sense of security for players in uncertain environments.
4. The existence of weakly dominant strategies can influence the stability of Nash equilibria, as players may gravitate towards these safer choices.
5. In some games, players may have both strongly dominant and weakly dominant strategies, where the strongly dominant choice is preferred when available.

Review Questions

• How does a weakly dominant strategy differ from a strongly dominant strategy, and why is this distinction important in game theory?
  • A weakly dominant strategy is one that provides outcomes at least as good as any other strategy but not necessarily better in every scenario. In contrast, a strongly dominant strategy always results in a better outcome regardless of opponents' choices. This distinction matters because it affects how players make decisions; while strongly dominant strategies lead to clear choices, weakly dominant strategies require more consideration of potential outcomes, influencing predictions about behavior in strategic interactions.
• Analyze how the presence of weakly dominant strategies can affect the stability of Nash equilibria in a game.
  • The presence of weakly dominant strategies can enhance the stability of Nash equilibria because players may choose these strategies to avoid worse outcomes. When multiple players adopt their weakly dominant strategies, it creates a stable state where no one has an incentive to deviate since doing so could lead to an equal or worse payoff. This can solidify certain equilibria and provide insights into how rational players behave under uncertainty, ensuring that certain outcomes are maintained even when players are faced with mixed choices.
• Evaluate the implications of weakly dominant strategies on real-world strategic decision-making among firms competing in an oligopoly.
  • In oligopoly markets, firms often face complex competitive dynamics where weakly dominant strategies play a crucial role. For instance, if one firm adopts a pricing strategy that guarantees it won't lose market share regardless of competitors' actions, other firms might follow suit to avoid being at a disadvantage. This behavior leads to price rigidity and can stabilize market conditions despite fluctuations. Understanding how weakly dominant strategies shape firms' decisions helps explain phenomena like collusion and price wars while highlighting the strategic interdependencies that exist in competitive markets.

Related terms

dominant strategy: A strategy that always results in a better outcome for a player, no matter what the other players do.

Nash equilibrium: A situation in a game where no player can benefit from changing their strategy while the other players keep theirs unchanged.

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