Centipede Game

- May 11, 2025
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Analyse the classic Centipede Game from game theory. Calculate optimal strategies, payoffs at different nodes, and explore the tension between rational self-interest and cooperation in sequential decision-making.

Game Parameters

(0.1-0.9)

Analysis Options

About the Centipede Game

The Centipede Game is a classic sequential game in game theory that illustrates the tension between rational self-interest and mutual cooperation. Two players take turns choosing whether to "take" (end the game) or "pass" (continue playing). Each time a player passes, the total pot grows larger, but the distribution of payoffs shifts slightly toward the other player.

Game Structure

The Centipede Game has these key features:

  • Sequential Play: Players take alternating turns, starting with Player 1.
  • Growing Pot: With each pass, the total pot grows by a multiplier (typically doubles).
  • Split Ratio: At each node, the player who passes gets a smaller share of the final pot than the other player.
  • Finite Length: The game has a predetermined end point (number of moves).
The Paradox

The Centipede Game presents a fascinating paradox in game theory. Backward induction and rational self-interest suggest that the first player should take immediately at the first node. However, human players often cooperate far longer, passing multiple times to reach mutually beneficial higher payoffs.

This discrepancy between theoretical predictions and observed behaviour has made the Centipede Game an important tool for studying cooperation, trust, and departures from classical equilibrium concepts in experimental economics.

Applications

The Centipede Game has applications in understanding:

  • Negotiations and bargaining behaviour
  • Social dilemmas and public goods provision
  • Trust development in business relationships
  • Political standoffs and brinkmanship
  • Environmental resource management over time

Understanding the Centipede Game

The Centipede Game is a fascinating example of Game Theory. In this game, two players take turns making choices to either "take" or "pass." Each time a player passes, the pot of rewards gets bigger, creating a tension between competing interests and the possibility of cooperation. Players must decide whether to seize the moment or let the game continue for potentially bigger payoffs.

The Centipede Game Calculator

Our Centipede Game calculator helps you analyse this intriguing game. It allows you to input various settings, such as the starting amount, growth factor, and number of moves. The results can show you the outcomes based on your choices, which helps in understanding the dynamics of the game better. This tool is a great way to explore strategies and payoffs for both players.

Key Game Parameters to Explore

When using the calculator, you can adjust several important parameters:

  • Starting Amount: This is how much money is in the pot at the beginning.
  • Growth Factor: This determines how much the pot grows with each pass.
  • Number of Moves: Set how many turns the players will take.
  • Split Ratio: This shows how the pot is divided if a player passes.

These factors influence the potential outcomes and help players devise optimal strategies.

Analysis Options for Detailed Insights

In addition to the basic parameters, the calculator offers advanced options for a more thorough analysis. You can choose the number of decimal places for results and opt to see the calculation steps for clarity. This feature is especially useful for those who want to understand the math behind the game, making the learning process engaging and interactive.

Results You Can Expect

Once you've set your parameters, the calculator will display various results. It shows the Subgame Perfect Equilibrium, which represents the best possible outcome if players act rationally. You can also see payoffs for both players at equilibrium and the cooperative end payoff if both players decide to keep passing. These results make the strategies behind the game clearer.

The Structure of the Game

The Centipede Game has a distinct structure that shapes its outcomes. Key features include:

  • Sequential Play: Players alternate turns, starting with Player 1.
  • Growing Pot: Each pass increases the total rewards.
  • Finite Length: The game ends after a set number of moves, making strategic choices critical.

Understanding these features is vital for making informed decisions during the game.

The Paradox of Rationality

The game presents an interesting paradox. While the theory suggests that the first player should take right away, many players often choose to pass multiple times. This inconsistent behavior contrasts with the idea of rational self-interest. It sparks curiosity about cooperation and decision-making in real-world scenarios, highlighting how people might act against their immediate interests for better long-term gains.

Real-World Applications of the Game

The concepts from the Centipede Game extend beyond theory. They apply to real-world situations like:

  • Negotiation tactics in business settings.
  • Cooperation in public goods provision.
  • Trust-building in personal and professional relationships.
  • Strategies during political negotiations.

Understanding these applications can enrich your perspective on collaboration and competition in various fields.