Prisoner's Dilemma Calculator
Analyze the classic game theory scenario and find Nash equilibria
Payoff when both cooperate
Payoff when both defect
Highest individual payoff
Lowest individual payoff
How to Use This Calculator
Enter Payoff Values
Enter the four payoff values: R (reward for mutual cooperation), P (punishment for mutual defection), T (temptation to defect), and S (sucker's payoff).
Validate Conditions
Ensure the values satisfy Prisoner's Dilemma conditions: T > R > P > S and R > (S + T) / 2.
Analyze Results
Review the payoff matrix, Nash equilibrium, dominant strategy, and game theory analysis.
Formula & Game Structure
Prisoner's Dilemma Conditions: T > R > P > S and R > (S + T) / 2
Payoff Symbols:
- R = Reward for mutual cooperation
- P = Punishment for mutual defection
- T = Temptation (best individual payoff when defecting)
- S = Sucker's payoff (worst individual payoff when cooperating)
Nash Equilibrium:
Both players defect because:
- If B cooperates, A should defect (T > R)
- If B defects, A should defect (P > S)
- Same logic applies to B
About Prisoner's Dilemma Calculator
The Prisoner's Dilemma is one of the most famous scenarios in game theory, illustrating how rational individuals might not cooperate even when it appears to be in their best interest. It demonstrates the conflict between individual rationality and collective benefit.
The Classic Scenario
Two suspects are arrested and interrogated separately. Each has the choice to cooperate (stay silent) or defect (confess and betray the other). The dilemma arises because while mutual cooperation yields a good outcome for both, each player has an incentive to defect regardless of what the other does.
Why It's Called a Dilemma
The paradox is that the rational strategy for each individual (defect) leads to a worse collective outcome than if both cooperated. The Nash equilibrium is mutual defection, even though mutual cooperation would give both players a better payoff.
Real-World Applications
- Economics: Price competition, cartels, trade wars
- Politics: Arms races, environmental agreements
- Evolution: Biological cooperation and competition
- Social Psychology: Trust, reciprocity, social norms
- Business: Competitive strategy, partnership decisions
Solutions to the Dilemma
Ways to promote cooperation:
- Repeated Games: When players interact multiple times, cooperation can emerge
- Reputation: Future interactions encourage cooperation
- Communication: Ability to coordinate can help
- Institutions: Legal frameworks and enforcement mechanisms
- Social Norms: Cultural values that promote cooperation
Frequently Asked Questions
Why do both players defect in the Nash equilibrium?
Because defect is a dominant strategy - it gives a better payoff regardless of what the other player does. If the other cooperates, defecting gives T (better than R). If the other defects, defecting gives P (better than S). So both players rationally choose to defect.
Is mutual cooperation ever the rational choice?
In a one-shot game, no - defection is always better. However, in repeated games (iterated Prisoner's Dilemma), cooperation can emerge as rational because players can use strategies like "tit-for-tat" that reward cooperation and punish defection.
What makes this different from other games?
The key is that the Nash equilibrium (mutual defection) is Pareto inefficient - both players would be better off if they could commit to cooperation, but they can't because each has an incentive to cheat.
Can this calculator handle other game types?
This calculator is specifically designed for the Prisoner's Dilemma structure. For other game types (chicken game, stag hunt, etc.), you'd need different payoff orderings and analysis methods.
What happens if I enter values that don't satisfy PD conditions?
The calculator will alert you. The Prisoner's Dilemma requires specific payoff ordering (T > R > P > S) and a condition on cooperation (R > (S + T) / 2). Different orderings create different types of games with different equilibria.