Dominance

Definition

Dominance refers to a situation in game theory where one strategy is better than another for a player, regardless of what the other players decide to do. This concept is crucial as it allows players to simplify their decision-making process by eliminating inferior strategies. By understanding dominance, players can focus on strategies that will yield the highest payoffs, contributing to their overall success in a game.

5 Must Know Facts For Your Next Test

1. In the context of a game, if a player has a strictly dominant strategy, they will always choose that strategy since it guarantees the best outcome.
2. Dominance can simplify complex games by allowing players to eliminate strategies that will never be optimal.
3. Not all games have dominant strategies; some may require mixed strategies to achieve an equilibrium.
4. A strategy can be weakly dominated if there is another strategy that provides at least as good of an outcome in some situations and a strictly better outcome in others.
5. Recognizing dominated strategies is an essential step in calculating Nash Equilibria in both pure and mixed strategies.

Review Questions

• How does the concept of dominance help players make decisions in strategic games?
  • The concept of dominance helps players make decisions by allowing them to identify and eliminate inferior strategies from consideration. By focusing only on strategies that are dominant, players can streamline their decision-making process, leading to more effective outcomes. This understanding is essential for navigating complex interactions in strategic games where multiple players and strategies are involved.
• Discuss the difference between strict dominance and weak dominance, and provide examples of each in a game scenario.
  • Strict dominance occurs when one strategy always provides a better payoff than another for any possible actions of opponents, while weak dominance allows for a strategy to be at least as good as another in some situations but better in others. For example, in a two-player game, if Player A chooses Strategy X and always earns more than Strategy Y regardless of Player B’s choice, X is strictly dominant. Conversely, if Player A earns the same or more with Strategy X depending on Player B's actions but never less, then Strategy Y might be weakly dominated by X.
• Evaluate the role of dominance in identifying Nash Equilibria within games that feature mixed strategies.
  • The role of dominance is crucial in identifying Nash Equilibria in games with mixed strategies because it helps narrow down the options for each player. By eliminating strictly dominated strategies, players can focus on those that are potentially part of a Nash Equilibrium. In mixed strategy contexts, where players randomize their choices, recognizing which strategies remain viable after applying dominance allows for more accurate calculations of expected payoffs and equilibrium strategies.

Related terms

Dominated Strategy: A strategy that results in a worse outcome for a player compared to another strategy, regardless of the actions taken by other players.

Nash Equilibrium: A situation where no player can benefit by changing their strategy while the other players keep theirs unchanged, leading to a stable outcome.

Strict Dominance: When one strategy always yields a better payoff than another strategy for a player, no matter what the opponents do.