Iterated Elimination of Dominated Strategies

Definition

Iterated elimination of dominated strategies is a process in game theory where players systematically remove strategies that are dominated by other strategies, ultimately simplifying the analysis of strategic interactions. This method involves repeatedly identifying and eliminating dominated strategies until no further eliminations can be made, leading to a smaller set of strategies for each player. This technique helps players to focus on more viable strategies and can lead to clearer predictions about equilibrium outcomes.

5 Must Know Facts For Your Next Test

1. The process of iterated elimination can lead to a unique outcome in some games, but not all games guarantee this.
2. Players need to have complete knowledge of their own and others' strategies to effectively apply iterated elimination.
3. This method can significantly reduce the complexity of the game, allowing players to focus on fewer strategies.
4. It can be applied in both finite and infinite games, although the outcomes might differ.
5. Iterated elimination helps in identifying potential Nash equilibria by narrowing down the strategy options.

Review Questions

• How does the iterated elimination of dominated strategies affect the decision-making process for players in a game?
  • The iterated elimination of dominated strategies streamlines the decision-making process for players by removing less viable options from consideration. As players eliminate dominated strategies, they focus only on those strategies that have potential merit based on their opponents' possible actions. This simplification aids in predicting outcomes and facilitates more strategic thinking, as players can hone in on a smaller set of effective responses.
• Evaluate the limitations of using iterated elimination of dominated strategies in predicting game outcomes.
  • While iterated elimination can simplify strategy choices, it has limitations as it does not always lead to a unique outcome or Nash equilibrium. Some games may still present multiple equilibria or not converge to an outcome at all, even after eliminations. Additionally, if players are not fully aware of all available strategies or have incomplete information about opponents, the process may yield misleading conclusions regarding optimal play.
• Synthesize how the concept of iterated elimination of dominated strategies relates to finding Nash equilibria in complex strategic scenarios.
  • The iterated elimination of dominated strategies serves as a foundational tool for identifying Nash equilibria in complex strategic scenarios by systematically reducing the strategy space. As dominated strategies are removed, players are left with more credible choices that can lead to stable outcomes where no player has an incentive to deviate. This process not only clarifies potential equilibria but also highlights how rational decision-making hinges on understanding both one's own preferences and those of others within the strategic landscape.

Related terms

Dominant Strategy: A strategy that results in a better outcome for a player, regardless of what the other players choose.

Nash Equilibrium: A situation in which no player can benefit from changing their strategy while the other players keep theirs unchanged.

Strictly Dominated Strategy: A strategy that is always worse than another strategy, regardless of what the opponents do.