Centipede Game

Definition

The centipede game is a multi-stage game in game theory where two players alternately decide whether to take a larger share of an increasing pot or pass it to the other player. The game typically unfolds with each player facing a choice to either 'take' the pot at their turn or 'pass' it, leading to a larger potential payoff for both if they continue passing. This game highlights the complexities of strategic decision-making and the importance of backward induction in predicting outcomes in sequential games.

5 Must Know Facts For Your Next Test

1. In the centipede game, players typically reach an outcome that deviates from what is predicted by backward induction, highlighting potential cooperation or trust issues between players.
2. Despite rational choices suggesting that both players should always pass initially, many experiments show that players often take the pot earlier than expected.
3. The game illustrates the tension between short-term incentives and long-term cooperation in strategic decision-making.
4. Different variations of the centipede game can yield different outcomes based on how players perceive risk and reward over time.
5. Understanding the centipede game helps explain behaviors in real-life situations like negotiations and business deals where sequential decision-making is crucial.

Review Questions

• How does backward induction apply to the centipede game and what predictions does it make about player behavior?
  • Backward induction suggests that rational players should take the pot early, as waiting could lead to losing their potential gains if the other player decides to take it instead. In theory, this means that both players would take rather than pass, leading to a quick end to the game. However, actual player behavior often diverges from this prediction, as individuals may choose to pass in hopes of achieving a larger payoff later.
• Analyze how the concept of Nash Equilibrium relates to strategies employed by players in the centipede game.
  • In the context of the centipede game, Nash Equilibrium would imply that if one player chooses to take at a certain point, it is optimal for the other player to also take rather than risk losing out. However, many outcomes observed in experiments reveal that players often choose to cooperate longer than predicted by Nash Equilibrium. This discrepancy highlights how factors like trust and risk perception influence decision-making beyond pure rationality.
• Evaluate how understanding the centipede game and its dynamics can inform real-world business negotiations and strategic interactions.
  • Understanding the centipede game provides insights into how parties might navigate negotiations, as it reveals potential for cooperation despite individual incentives to act early. In business settings, recognizing that both sides may prefer mutual long-term gains can foster collaborative approaches rather than competitive ones. Analyzing past outcomes from similar scenarios allows negotiators to better anticipate behaviors and devise strategies that enhance joint value creation, promoting a more successful negotiation process.

Related terms

Backward Induction: A method used in game theory to solve sequential games by analyzing from the last possible move back to the first, determining optimal strategies at each stage.

Nash Equilibrium: A concept in game theory where no player can benefit by changing their strategy while other players keep theirs unchanged, often used to predict the outcome of strategic interactions.

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