Prisoner's Dilemma

- May 11, 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 concept in Game-theory/">Game Theory. It shows how two people might not work together, even if it’s better for both. In this classic scenario, two prisoners must decide whether to betray each Other or stay silent. Their choices lead to different outcomes, highlighting the struggle between cooperation and self-interest.

How the Prisoner's Dilemma Calculator Works

Our Prisoner's Dilemma Calculator lets you simulate this scenario easily. You can set up payoff values to see how different decisions impact the results. By adjusting strategies for both prisoners, you can explore various outcomes. It’s a great way to learn about decision-making in competitive situations.

Setting Up Payoff Values

In the calculator, you can define the payoff matrix. This includes the consequences for each prisoner based on their choices. For instance, you can set different penalties or rewards for cooperating or defecting. This flexibility helps you understand how varying situations can change the game's dynamics.

Selecting Strategies to Test

The calculator offers several strategies for both prisoners to choose from. Here’s a quick list of the available options:

  • Always Cooperate: Remain silent no matter what.
  • Always Defect: Always betray.
  • Tit for Tat: Start by cooperating and mimic the opponent's last move.
  • Random: Choose to cooperate or defect with equal chances.
  • Grudger: Start by cooperating, but defect if betrayed.
  • Pavlov: Repeat the last winning move or change if it fails.

Payoff Presets for Quick Analysis

The calculator also includes preset scenarios for quick setup. You can select from classic examples like the Stag Hunt or the Chicken Game. This feature allows you to bypass manual input and dive straight into the analysis. It’s perfect for those who want quick insights without complicated setups.

Viewing Simulation Results

Once you've set up the simulation, you can view the results in detail. The calculator displays the final scores for both prisoners and the cooperation rate. You'll also find information about Nash equilibrium, which shows the stable strategy pairs in this game. This helps in understanding the best strategies in competitive environments.

Visualising the Outcomes

Visual aids enhance your understanding of the results. The calculator offers a cumulative score chart that tracks performance over time. You can also see a payoff matrix analysis, illustrating the impact of different decisions. These visuals make it easier to grasp complex outcomes and strategies in the Prisoner's Dilemma.

Applications Beyond the Game

The concepts from the Prisoner's Dilemma extend far beyond the game theory realm. They apply to real-life situations like:

  • International relations and arms control
  • Environmental negotiations
  • Business competition and pricing
  • Public goods and community cooperation

Understanding these principles can help in making strategic decisions in various fields.