Centipede Game

Category: Statistics
- December 07, 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 well-known example in Game Theory. It’s about two players who alternate turns. Each player can either “take” money and end the game or “pass” to let it grow. The longer they play, the bigger the pot gets, but the rewards shift between players. This creates a tricky balance between wanting to take what you can and hoping for a bigger payout later.

What the Calculator Can Do

The Centipede Game calculator helps players analyze different strategies. You can input various game parameters, like the starting amount and growth factor. It calculates optimal strategies and shows payoffs at each decision point. This makes it easier to understand how decisions change the outcomes of the game.

Setting Up Game Parameters

  • Starting Amount: Choose how much money begins in the pot.
  • Growth Factor: Select how much the pot increases with each pass.
  • Number of Moves: Set how many turns players will take.
  • Split Ratio: Determine how the pot is divided between players.

These inputs help create a clear picture of the game’s dynamics and the players' potential choices.

Analysis Options for Detailed Insights

This calculator offers advanced analysis options. You can select how many decimal places to display in the results. Additionally, you can choose to see the steps taken in calculations. This feature is great for those who want to understand the nitty-gritty of the Math behind the game.

Results from the Centipede Game Calculator

After entering your parameters, the calculator provides results. You'll see the Subgame Perfect Equilibrium, which shows the best strategy for players. It also displays payoffs for both players at the equilibrium point. Plus, you can explore what happens if both players cooperate and keep passing. This insight can reveal surprising outcomes.

The Game Structure Explained

  • Sequential Turns: Players alternate turns, starting with Player 1.
  • Pot Growth: The total pot increases with each pass.
  • Payoff Shifts: The player who passes gets a lesser share of the final pot.
  • Predetermined Moves: The game has a set number of moves.

Understanding these features is key to grasping the game's appeal and strategy.

The Paradox of Cooperation

The Centipede Game highlights a fascinating paradox. The theory suggests that Player 1 should take the money immediately. However, real players often choose to cooperate and pass multiple times. This behavior leads to larger rewards for both players, showing how human nature can differ from theoretical expectations.

Applications of the Centipede Game

Beyond just a game, the Centipede Game has practical applications. It helps us understand negotiations, social dilemmas, and trust in relationships. Players can learn about bargaining strategies and cooperation in various situations, from business deals to managing shared resources. This makes it a valuable tool in both economics and psychology.