Centipede Game

Definition

The centipede game is a multi-stage game in game theory where two players alternately choose whether to take a larger share of an increasing payoff or pass the opportunity to the other player, leading to a possible larger future payoff. This game illustrates the concepts of strategic decision-making and subgame perfect equilibrium, as players must consider not only immediate payoffs but also the potential outcomes of future moves. It highlights the complexities of rational decision-making in sequential games, where the optimal strategy may not always be immediately apparent.

5 Must Know Facts For Your Next Test

1. In the centipede game, each player has an incentive to pass the decision to allow for potentially larger payoffs in subsequent rounds.
2. Despite the apparent benefits of passing, backward induction predicts that rational players will choose to take their payoff at the first opportunity, leading to non-cooperative outcomes.
3. The centipede game challenges traditional notions of rationality, as players may behave differently than expected based on simple self-interest.
4. The game can end at various stages depending on the players' decisions, highlighting how cooperation can lead to better overall outcomes if both players are willing to pass.
5. Experimental results show that real players often do not follow backward induction predictions, suggesting that factors like trust and expectation influence decisions.

Review Questions

• How does backward induction apply to the centipede game and what implications does it have for player decision-making?
  • Backward induction applies to the centipede game by analyzing potential outcomes from the last round back to the first. Players must consider that if both choose optimally based on future payoffs, they should take their immediate payoffs instead of passing. This leads to a prediction that both players will end up taking at their first chance rather than cooperating for larger future gains, which can seem counterintuitive given the game's structure.
• Discuss how the centipede game demonstrates concepts of trust and cooperation versus individual rationality in strategic interactions.
  • The centipede game highlights a tension between individual rationality and potential cooperative outcomes. While rational players using backward induction would take their payoff immediately, real-world observations often reveal that players pass multiple times due to trust and an expectation of cooperation. This shows that when players believe their opponent may act cooperatively, they may forgo immediate gains for larger payoffs down the line, indicating that psychology plays a significant role in decision-making.
• Evaluate how experimental findings related to the centipede game challenge traditional theories of rational choice in economics and provide insights into human behavior.
  • Experimental findings from the centipede game challenge traditional theories of rational choice by showing that actual human behavior often deviates from what classical economic models predict. Many participants tend to cooperate by passing even when it would seem more beneficial to take their immediate share based on backward induction logic. This suggests that factors like social norms, trust, and expectations about others' behavior can significantly influence decision-making, prompting economists and theorists to reconsider models of human behavior beyond purely self-interested calculations.

Related terms

Backward Induction: A method used to solve sequential games by analyzing the game from the end to the beginning, determining optimal strategies at each stage.

Nash Equilibrium: A situation in a strategic game where no player can benefit by changing their strategy while the other players keep theirs unchanged.

Subgame Perfect Equilibrium: A refinement of Nash equilibrium that requires players' strategies to be Nash equilibria in every subgame of the original game.