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 Calculator

The Centipede Game Calculator is a handy tool for anyone interested in Game Theory. This classic game involves two players who must make choices about whether to take a growing pot of money or pass it to the Other player. The calculator helps analyse different strategies and payoffs at each decision point, making it easier to understand the underlying dynamics of the game.

Key Features of the Calculator

This calculator offers several features that enhance your understanding of the Centipede Game. You can define important game parameters, such as:

  • Starting Amount: The initial value of the pot.
  • Growth Factor: How much the pot increases with each move.
  • Number of Moves: The total turns for both players.
  • Split Ratio: The share of the pot for the player who passes.

These variables are crucial for calculating the optimal strategies in the game.

What Is the Subgame Perfect Equilibrium?

A significant concept in the Centipede Game is the Subgame Perfect Equilibrium (SPE). The SPE is an outcome where each player's strategy is optimal at every possible point in the game. This means that a player would not want to change their decision at any node if the game were to continue. The calculator helps find the SPE using backward induction, making it simpler to visualise the players' best moves at each stage.

Exploring Payoffs at Different Nodes

With the Centipede Game Calculator, you can explore the payoffs for both players at each decision point. The tool will display important information like:

  • Player 1's Payoff
  • Player 2's Payoff
  • Cooperative End Payoff (if both players always pass)

By analysing these outcomes, you can see how the choices made by each player affect the final rewards.

The Game Structure Explained

The Centipede Game has distinct features that make it intriguing. Some key aspects include:

  • Sequential Play: Players alternate turns, starting with Player 1.
  • Growing Pot: The total value increases with each pass, usually doubling.
  • Split Ratio: The player who passes earns a smaller share than the other player.

Understanding these components is essential for analysing strategies and outcomes in the game.

The Paradox of Rational Decision-Making

One of the most interesting parts of the Centipede Game is the paradox it presents. While logic suggests that the first player should take the pot right away, many players choose to pass multiple times. This unexpected behaviour often leads to higher rewards for both players. The calculator can help you examine these decisions and what they reveal about human behaviour in competitive settings.

Applications of the Centipede Game

The Centipede Game is not just an academic exercise; it has real-world applications. Its principles can be applied in various scenarios, such as:

  • Negotiations and bargaining situations
  • Social dilemmas in public goods provision
  • Building trust in business relationships
  • Political negotiations and strategies
  • Environmental resource management

By using the calculator to simulate these scenarios, you can better understand the dynamics at play.

Enhancing Your Game Theory Knowledge

The Centipede Game Calculator is an excellent resource for students, educators, or anyone interested in game theory. It simplifies complicated concepts and allows for deeper exploration of strategies and outcomes. Whether you're studying for an exam or just curious about decision-making dynamics, this tool can greatly enhance your understanding.