Prisoner's Dilemma

- May 22, 2025
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Explore the classic Prisoner's Dilemma game theory scenario. Adjust payoff values, simulate different strategies, and analyse outcomes to understand cooperation and competition dynamics.

Payoff Matrix Setup

Prisoner A / Prisoner B
Cooperate
Defect
Cooperate
Defect

Payoff Presets

Strategy Simulation

Display Options

About the Prisoner's Dilemma

The Prisoner's Dilemma is a classic scenario in game theory that illustrates why two completely rational individuals might not cooperate, even if it is in their best interest to do so.

The Classic Scenario

Two prisoners are offered a deal: betray your accomplice or stay silent (cooperate). If both stay silent, they each get a light sentence. If both betray each other, they get a moderate sentence. If one betrays and the other stays silent, the betrayer goes free while the silent one gets a heavy sentence.

Key Strategies
  • Always Cooperate: Always stay silent, regardless of what the other prisoner does.
  • Always Defect: Always betray, regardless of what the other prisoner does.
  • Tit for Tat: Start by cooperating, then do whatever the other prisoner did in the previous round.
  • Random: Cooperate or defect with equal probability.
  • Grudger: Start by cooperating, but once the other prisoner defects, always defect thereafter.
  • Pavlov: Start by cooperating. If the last move yielded a positive payoff, repeat it; otherwise, change strategy.
Nash Equilibrium

A Nash Equilibrium is a situation where no player can benefit by changing their strategy while the other players keep theirs unchanged. In the classic Prisoner's Dilemma, mutual defection is the only Nash Equilibrium, even though mutual cooperation would yield a better outcome for both players.

Real-World Applications

The Prisoner's Dilemma applies to many real-world situations:

  • Arms races between countries
  • Environmental protection and climate agreements
  • Advertising competition between companies
  • Price-fixing and cartels
  • Public goods contribution

Understanding the Prisoner's Dilemma

The Prisoner's Dilemma is a famous example in Game-theory/">Game Theory. It shows how two people might not work together, even if it’s the best choice. Each person must decide whether to cooperate or betray the Other. Their choices lead to different outcomes, which can be confusing but exciting to explore.

What Does the Prisoner’s Dilemma Calculator Do?

This calculator helps you simulate the Prisoner’s Dilemma. You can set different payoff values for each prisoner and see how their choices affect the results. It makes it easier to understand the complex ideas behind cooperation and competition in real-life situations.

Setting Up the payoff matrix

  • Enter values for different outcomes when both prisoners cooperate or defect.
  • Choose from classic scenarios or create a custom setup to see how scores change.
  • Adjust the values to reflect different situations that may occur in the real world.

This flexible setup allows you to experiment with various strategies and understand their impacts on the game.

Simulating Different Strategies

You can choose strategies for both Prisoner A and Prisoner B. Options include always cooperating or always defecting. There's also "Tit for Tat," which adjusts based on the other player’s previous move. This feature allows you to see how different approaches affect the game over multiple rounds.

Viewing the Results

After running the simulation, the calculator shows the final scores for each prisoner. It also displays the cooperation rate, which tells you how often both players chose to cooperate. You’ll see a detailed breakdown of each round, making it easy to analyze the game flow and strategy effectiveness.

Payoff Matrix Analysis

  • Examine how the payoff matrix influences decision-making.
  • Visualize the outcomes with charts to see trends in cooperation and defection.
  • Understand the Nash equilibrium, where neither player has anything to gain by changing their strategy.

This detailed analysis helps clarify the strategic implications of the choices made during the simulation.

Real-Life Applications of the Dilemma

The Prisoner's Dilemma isn't just a theory; it has real-world applications. It appears in various situations like climate agreements, business competition, and even personal relationships. By using the calculator, you can see how these dynamics unfold and learn how cooperation can be beneficial in various areas of life.

Why Use the Prisoner’s Dilemma Calculator?

This calculator is not only a learning tool but also a fun way to engage with important concepts in game theory. Whether you’re a student, teacher, or just curious, it helps illustrate complex ideas in a simple and interactive way. Plus, it allows for endless experimentation, making the learning process enjoyable!