Prisoner's Dilemma Calculator — Game Theory Payoffs
The prisoner's dilemma is the canonical model of strategic conflict between individual rationality and collective welfare. Enter the four payoffs (T, R, P, S) to see whether a classic dilemma structure holds, identify the Nash equilibrium, and measure the social cost of mutual defection.
Defect (dominant strategy for both players)
How does this calculator work?
In a prisoner's dilemma (T>R>P>S), defecting is each player's dominant strategy, producing a Nash equilibrium of (D,D) with payoff P each — even though both would earn R>P from mutual cooperation. The social cost of defection is 2(R−P). Cooperation can emerge through repetition, reputation, or binding agreements.
Formula
How this is calculated
The prisoner's dilemma has two players, each of whom can either cooperate (C) or defect (D). The payoffs are: T (Temptation — you defect, other cooperates), R (Reward — both cooperate), P (Punishment — both defect), and S (Sucker — you cooperate, other defects). The classic dilemma structure requires T > R > P > S.
Under this ordering, defecting is a dominant strategy for each player regardless of what the other does: if the other cooperates, defecting yields T > R; if the other defects, defecting yields P > S. Because both reason the same way, the unique Nash equilibrium is (Defect, Defect) with each receiving P. Yet both would prefer (Cooperate, Cooperate) with payoff R > P — the Pareto-superior outcome — making this a genuine dilemma.
The social cost of defection is 2(R − P): the total welfare lost by the two players compared to mutual cooperation. Cooperation efficiency R/T measures how large the mutual cooperation reward is relative to the maximum individual gain from defecting. Real-world analogues include arms races, overfishing, climate agreements, and pricing wars — anywhere individual incentives conflict with collective benefit. Repeated games, reputation, and binding agreements are the main mechanisms that sustain cooperation.
Frequently asked questions
The four payoffs must satisfy T > R > P > S. This ensures defecting always pays more regardless of the other player's choice (a dominant strategy), yet the dominant-strategy equilibrium (P, P) is strictly worse for both players than mutual cooperation (R, R). Without this ordering — for instance if R ≥ T — cooperation may be individually rational and no dilemma exists.
Yes. In the infinitely repeated game, cooperation can be sustained as a Nash equilibrium if players are patient enough (the discount factor δ ≥ (T−R)/(T−P)). The 'tit-for-tat' strategy — start cooperative, then mirror the other player's last move — proved highly successful in Axelrod's tournaments. Reputations, communication, and binding contracts achieve similar effects in finite settings.
The Nash equilibrium is the strategy profile where no player can improve their payoff by unilaterally switching — in the classic PD this is (Defect, Defect) with payoff P each. The Pareto-optimal outcome is (Cooperate, Cooperate) with payoff R each; no player can be made better off without making the other worse off. The gap R − P per player measures the tragedy of individually rational behaviour.
Also known as
TG we-Calculate Editorial Team. (2026). Prisoner's Dilemma Calculator — Game Theory Payoffs [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/prisoners-dilemma-calculator
TG we-Calculate Editorial Team. "Prisoner's Dilemma Calculator — Game Theory Payoffs." TG we-Calculate. 2026. https://we-calculate.com/calculator/prisoners-dilemma-calculator.
TG we-Calculate Editorial Team, "Prisoner's Dilemma Calculator — Game Theory Payoffs," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/prisoners-dilemma-calculator
@misc{wecalculate_prisoners_dilemma_calculator, title = {Prisoner's Dilemma Calculator — Game Theory Payoffs}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/prisoners-dilemma-calculator}}, year = {2026}, note = {TG we-Calculate} }
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