Centipede Game

Definition

The centipede game is a strategic form of game theory involving two players who alternately decide whether to take a larger share of a growing pot of resources or pass it to the other player. The game highlights the tension between cooperation and self-interest in sequential decision-making scenarios, revealing how players can choose different strategies based on their expectations of the other's behavior.

5 Must Know Facts For Your Next Test

1. The centipede game typically features multiple turns where each player can either 'take' or 'pass,' with the pot increasing each turn.
2. If both players act rationally and choose to take at the first opportunity, they will both end up with less than if they had cooperated longer.
3. Backward induction suggests that rational players will take the pot early, contradicting the intuitive cooperative strategy where they should pass to maximize total payoff.
4. The centipede game illustrates how real-world interactions can deviate from theoretical predictions, as players often exhibit cooperative behavior despite rational outcomes suggesting otherwise.
5. Experimental studies show that actual players frequently cooperate longer than predicted by backward induction, indicating that trust and social norms play important roles in decision-making.

Review Questions

• How does the concept of backward induction apply to the centipede game, and what are its implications for player behavior?
  • Backward induction applies to the centipede game by analyzing the best moves starting from the end of the game. If both players follow this reasoning, they would realize that taking early yields better immediate payoffs. However, this leads to a paradox where players might forgo potentially higher rewards from passing in favor of securing lesser rewards sooner. This reveals a conflict between logical reasoning and actual behavior, as players may still choose to cooperate beyond what backward induction predicts.
• Discuss how Nash equilibrium is relevant in understanding outcomes in the centipede game.
  • Nash equilibrium helps us understand that in the centipede game, if both players choose to act rationally and take their immediate payoffs at the earliest opportunity, they reach an equilibrium where neither player benefits from changing their strategy unilaterally. However, this creates a paradox as it fails to recognize the potential for cooperative play that could yield higher payoffs. Thus, while Nash equilibrium provides insight into stable outcomes, it does not account for the dynamic interactions often observed in actual gameplay.
• Evaluate how experimental findings on player behavior in the centipede game challenge traditional economic assumptions about rationality.
  • Experimental findings show that many players in the centipede game tend to cooperate longer than what traditional economic models predict based on rationality. This challenges the assumption that individuals always act purely out of self-interest, revealing that social preferences and trust significantly influence decisions. As players experience interactions over multiple rounds, they often develop expectations about their opponent's behavior that lead to more generous actions. This indicates that real-world decision-making is complex and influenced by factors beyond mere utility maximization.

Related terms

Backward Induction: A method used in game theory to predict outcomes by analyzing the game from the end and reasoning backward to determine optimal strategies.

Nash Equilibrium: A concept in game theory where no player can benefit by changing their strategy while the other players keep theirs unchanged, resulting in a stable outcome.

Sequential Games: Games in which players make decisions one after another, allowing for strategic reasoning based on previous actions.