Subgame Perfection

Definition

Subgame perfection is a refinement of Nash equilibrium used in game theory that ensures players' strategies constitute a Nash equilibrium in every subgame of the original game. This concept is crucial in analyzing dynamic games where players make decisions at different points, allowing us to focus on strategies that are credible and rational throughout the entire game, not just in the initial stages. Subgame perfection helps identify outcomes that are stable and can be sustained through the players' choices in subsequent moves.

5 Must Know Facts For Your Next Test

1. Subgame perfection ensures that players' strategies remain optimal not just overall but also when considering any possible future scenarios within the game.
2. It is particularly relevant in games that involve sequential moves, as it addresses how players react to previous actions by others.
3. In a subgame perfect equilibrium, strategies are contingent on the history of play, ensuring rational behavior at every stage.
4. Subgame perfection can eliminate non-credible threats, meaning strategies that could not be rationally executed when a player has to make a choice.
5. The concept is vital for establishing equilibria in extensive-form games, where the structure allows for multiple decision points and potential outcomes.

Review Questions

• How does subgame perfection refine our understanding of Nash equilibrium in dynamic games?
  • Subgame perfection refines Nash equilibrium by ensuring that not only is there mutual best response among players at the game's outset, but also that this condition holds true in every subgame. This means that strategies must be credible and optimal at all possible decision points throughout the game. By focusing on every subgame, we can better analyze situations where players' decisions may change based on prior actions, leading to more stable and predictable outcomes.
• Discuss how backward induction is applied to achieve subgame perfection in extensive-form games.
  • Backward induction is a technique used to find subgame perfect equilibria by analyzing a game from its endpoint back to the beginning. In this method, players consider their best responses at each decision point based on future actions and payoffs. By determining optimal strategies starting from the last move and moving backward, players can identify actions that maintain equilibrium across all subgames. This process helps ensure that strategies are rational and consistent throughout the entire game.
• Evaluate the significance of eliminating non-credible threats through the concept of subgame perfection in strategic interactions.
  • Eliminating non-credible threats is crucial because it strengthens the reliability of strategic interactions among players. When subgame perfection is applied, players can disregard threats that would not be rationally executed if faced with actual choices. This leads to more realistic predictions of behavior in games since players will align their strategies with those that can be credibly enacted. The significance lies in creating a clearer framework for understanding how real-world interactions might unfold, as it filters out unrealistic strategies that could distort outcomes.

Related terms

Nash Equilibrium: A situation in a game where no player can benefit from changing their strategy while the other players keep theirs unchanged, representing a state of mutual best responses.

Backward Induction: A method used to solve dynamic games by analyzing the game from its endpoint backward to determine optimal strategies at earlier stages.

Dynamic Game: A game where players make decisions at various points in time, with the current decisions potentially affecting future choices and payoffs.