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 Calculator

The Prisoner's Dilemma Calculator is a fun and insightful tool that helps you explore key concepts in Game-theory/">Game Theory. By adjusting the payoff values, you can see how different choices affect the outcomes of two players. This calculator allows you to simulate various strategies, letting you grasp the dynamics of cooperation and competition in a simple and interactive way.

Setting Up Your Payoff Matrix

When using the calculator, you start by setting up a payoff matrix. This matrix represents the potential outcomes based on the choices made by two players, referred to as Prisoner A and Prisoner B. You can enter the values for four possible scenarios:

  • Both cooperate
  • Prisoner A cooperates while Prisoner B defects
  • Prisoner A defects while Prisoner B cooperates
  • Both defect

Choosing Payoff Presets

The calculator comes with several payoff presets to make setup easier. You can select from options like Classic Prisoner's Dilemma or Stag Hunt. Each preset represents different scenarios, allowing you to quickly see how payoffs change the game's dynamics. This feature is especially useful if you want to compare various situations without starting from scratch each time.

Simulating Strategies in the Game

You also have the option to test different strategies for both prisoners. Some strategies you can choose include Always Cooperate, Always Defect, or Tit for Tat. Each strategy leads to unique results and helps illustrate how decisions impact the overall score. By simulating multiple iterations, you can understand which strategies work best in the context of the dilemma.

Visualising the Results

The calculator provides a wealth of information through visualisation tools. For instance, you can view a cumulative score chart that shows how points accumulate over multiple rounds. There's also a matrix analysis section where you can better understand how each choice affects the players and their outcomes. This visual approach makes it easier to grasp complex concepts in game theory.

Exploring Round-by-Round Outcomes

What makes this calculator truly engaging is the round-by-round results feature. You can see detailed outcomes for each round of play, including choices made and payoffs received by each prisoner. This breakdown helps clarify how strategies unfold over time and how cooperation can fluctuate based on previous rounds.

Theoretical Insights on Cooperation and Competition

Using the Prisoner's Dilemma Calculator isn’t just about numbers; it’s also a gateway to understanding essential theories. You’ll learn about concepts like Nash Equilibrium, which reveals why some rational players might end up choosing not to cooperate, even when it benefits them. This insight can apply to real-world situations, from business negotiations to international relations.

Diving into Real-World Applications

The lessons from the Prisoner's Dilemma extend beyond the calculator. Here are some real-world examples:

  • Arms races between countries
  • Environmental policy agreements
  • Business competition and pricing strategies
  • Collaborative projects and resource sharing

Understanding these applications shows how game theory can explain human behaviour in various fields.