Backward induction

Definition

Backward induction is a method used in game theory to determine optimal strategies by analyzing a game from the end to the beginning. It involves looking at the last possible moves of players and determining their best responses, then moving sequentially backward through the game tree to deduce the optimal actions of earlier moves. This technique is particularly relevant in analyzing strategic interactions in sequential games and helps in identifying subgame perfect equilibria.

5 Must Know Facts For Your Next Test

1. Backward induction starts by analyzing the final decision points in a game, allowing players to make informed choices based on anticipated future actions.
2. This method ensures that players' strategies are consistent across all stages of the game, leading to optimal outcomes when each player acts rationally.
3. In extensive form games, backward induction helps establish credible threats and promises by assessing how players will react in response to various actions.
4. It plays a crucial role in establishing subgame perfect equilibria, ensuring that every player's strategy remains optimal not just overall but at every point in the game.
5. The technique can be applied to both finite and infinite horizon games, though it may require more complex reasoning for infinite scenarios due to potential ongoing decisions.

Review Questions

• How does backward induction influence the strategies of players in extensive form games?
  • Backward induction shapes players' strategies by allowing them to anticipate how future actions will affect their current decisions. By starting from the end of the game and working backwards, players can identify optimal responses at each stage. This method helps ensure that their choices align with the overall objective of maximizing their payoffs while considering the likely responses of other players.
• Discuss how backward induction is essential for achieving subgame perfect equilibrium in sequential games.
  • Backward induction is fundamental for achieving subgame perfect equilibrium because it evaluates players' strategies across all subgames. This ensures that even when faced with different choices in subgames, players will continue to act rationally and optimally. By using backward induction, players can identify credible threats and promises, reinforcing their strategies as optimal within any given context of the game.
• Evaluate the implications of applying backward induction to real-world bargaining scenarios, such as the Rubinstein bargaining model.
  • Applying backward induction to real-world bargaining scenarios like the Rubinstein bargaining model demonstrates its power in structuring negotiations. In this model, each player's strategy at any point is influenced by their expectations of future negotiations. Backward induction allows them to predict opponents' responses at various stages, leading to more informed decisions about offers and counteroffers. The resulting equilibrium reflects rational behavior as each party considers how their actions will shape the bargaining process's outcomes over time.

Related terms

Game Tree: A graphical representation of a sequential game that shows the possible moves of players and their outcomes at each decision point.

Subgame Perfect Equilibrium: A refinement of Nash equilibrium applicable in dynamic games, where players' strategies constitute a Nash equilibrium in every subgame.

Sequential Rationality: The concept that players make decisions based on rational choices at every point in a dynamic game, considering future moves and strategies.