Prisoner’s Dilemma Payoff Calculator
Enter a 2×2 payoff matrix to find each player’s dominant strategy, the Nash equilibrium, and whether it is a true prisoner’s dilemma.
Result
- Payoff orderingT=5, R=3, P=1, S=0
- Dominant strategyDefect
- Nash equilibriumBoth defect (D, D)
- Pareto-efficient outcomeBoth cooperate (each gets 3)
- True prisoner’s dilemma?Yes (T > R > P > S, 2R > T+S)
Step-by-step
- Compare strategies: defecting beats cooperating if T > R (when other cooperates) and P > S (when other defects).
- Here T=5 > R=3 and P=1 > S=0, so defection is dominant → Nash equilibrium is mutual defection.
- Because T > R > P > S, both defect and earn 1 each, though mutual cooperation (3 each) is better — the dilemma.
How to use this calculator
- Enter the Reward payoff for mutual cooperation (R).
- Enter the Temptation (T), Sucker (S), and Punishment (P) payoffs.
- Read the dominant strategy and the Nash equilibrium.
- Check whether the ordering T > R > P > S makes it a true dilemma.
About this calculator
The prisoner’s dilemma is the most famous game in game theory: two players each choose to cooperate or defect, and the payoffs are arranged so that defecting is individually rational yet leaves both worse off than if they had cooperated. The four payoffs are conventionally labeled Temptation (T, defect while the other cooperates), Reward (R, both cooperate), Punishment (P, both defect), and Sucker (S, cooperate while the other defects). The game is a true prisoner’s dilemma when T > R > P > S. This calculator takes your four payoff values, determines whether defection or cooperation is the dominant strategy, identifies the Nash equilibrium, and tells you whether the matrix forms a genuine dilemma. It illustrates why self-interested players reach a mutually poor outcome even when a better one exists.
How it works — the formula
Defect dominates ⇔ T > R AND P > S
True dilemma ⇔ T > R > P > S
(efficiency check: 2R > T + S)Each player compares their two strategies against both of the opponent’s choices. When defecting wins in both cases, it is dominant and mutual defection is the Nash equilibrium.
Worked examples
- Inputs:
- T=5, R=3, P=1, S=0
- Output:
- Defect dominant; Nash (D,D); true dilemma
- Inputs:
- T=3, R=5, P=1, S=0
- Output:
- Cooperate dominant; Nash (C,C); not a PD
- Inputs:
- T=10, R=6, P=2, S=0
- Output:
- Defect dominant; true dilemma (2R=12>T+S=10)
Limitations
- Models a symmetric, one-shot game with standard payoff labels.
- Does not analyze mixed-strategy or asymmetric games in depth.
- Iterated-game dynamics (tit-for-tat etc.) are out of scope.
Educational game-theory model; real strategic situations may add communication, repetition, or asymmetry.