Subgame Perfect Equilibrium

Definition

Subgame perfect equilibrium is a refinement of Nash equilibrium applicable to dynamic games, where players' strategies are optimal not only for the entire game but also for every subgame that could be reached. This concept helps ensure that strategies are credible at every point in the game, thus avoiding non-credible threats and promises that could undermine strategic reasoning.

5 Must Know Facts For Your Next Test

1. Subgame perfect equilibrium is particularly useful in extensive-form games, where the structure of the game includes a sequence of moves over time.
2. This concept eliminates non-credible threats, ensuring that players' strategies remain consistent at every stage of the game.
3. To achieve a subgame perfect equilibrium, players often use backward induction to derive optimal strategies from the game's end to its start.
4. In many cases, subgame perfect equilibria lead to more predictable and stable outcomes compared to Nash equilibria, especially in dynamic settings.
5. It can be shown that every finite game has at least one subgame perfect equilibrium, which may not be the case with Nash equilibria.

Review Questions

• How does subgame perfect equilibrium enhance the credibility of strategies compared to Nash equilibrium in dynamic games?
  • Subgame perfect equilibrium enhances credibility by ensuring that players' strategies are optimal for every possible subgame. While Nash equilibrium may allow for non-credible threats that could lead to irrational outcomes, subgame perfect equilibrium requires that all players act rationally at every decision point. This means that if a player threatens an action in a future subgame, it must be a strategy they would actually follow through on if that subgame were reached.
• In what way does backward induction play a crucial role in determining subgame perfect equilibria in extensive-form games?
  • Backward induction is essential for finding subgame perfect equilibria as it involves analyzing the game from its final stages and working backwards to determine optimal strategies at earlier points. By evaluating what actions players would take at the end of the game, backward induction helps identify strategies that will also be optimal in earlier subgames. This method ensures that the strategies chosen are consistent throughout the entire game, meeting the requirements of subgame perfection.
• Evaluate how subgame perfect equilibrium can be applied in economic applications such as oligopoly and market competition, and discuss its implications on strategic interactions between firms.
  • In oligopoly and market competition, firms often engage in strategic decision-making regarding pricing, output levels, and market entry. Subgame perfect equilibrium provides a framework for these firms to determine optimal strategies at each stage of competition. For example, when firms consider retaliatory actions against price cuts or capacity expansions, they must ensure their strategies are credible throughout every potential future scenario. By applying this concept, firms can foster stable outcomes and avoid destructive competitive behavior while anticipating their rivals' reactions.

Related terms

Backward Induction: A method used in game theory to solve dynamic games by analyzing the game's possible outcomes from the end back to the beginning, allowing players to make optimal decisions at each point.

Nash Equilibrium: A situation in a strategic game where no player can benefit by unilaterally changing their strategy, given the strategies of all other players remain unchanged.

Perfect Bayesian Equilibrium: An equilibrium concept that extends Nash equilibrium by incorporating beliefs about the types of players and their strategies in games with incomplete information.