Prisoners Dilemma Calculator - 2x2 Payoff Matrix Solver

A prisoners dilemma calculator takes four payoff values (T, R, P, and S) and turns them into a 2x2 payoff matrix so you can read the dominant strategy, the Nash equilibrium, and the best joint outcome.

• • Game theory homework: Work through a textbook payoff matrix and confirm the dominant strategy and Nash equilibrium.
• • Teaching cooperation and defection: Show students why individually rational choices can produce a worse group result, using the 2x2 matrix.
• • Negotiation or pricing analysis: Plug in custom payoffs to model a price-fixing meeting, an arms-race decision, or competitive bidding.
• • Sensitivity checks on payoffs: Test whether changing the sucker or temptation payoff by one unit flips the Nash equilibrium from (D, D) to (C, C).

The classical prisoners dilemma story is short: two suspects are questioned separately and can stay silent (cooperate) or confess (defect). If both stay silent they each get a small sentence. If one confesses and the other does not, the confessor walks free and the silent one gets the longest sentence. If both confess they each get a medium sentence. The dominant strategy is to confess.

The calculator applies that story to the four outcomes (CC, CD, DC, DD) and labels the Nash equilibrium and any cell that Pareto-dominates it. The same machinery works for any two-player symmetric game with the same payoff ordering, which is why economics and political science classes use it to teach non-cooperative game theory.

The payoff matrix is a 2x2 grid where each cell holds the payoffs for a binary strategy choice, and a truth table generator builds the same kind of binary-input to cell-value grid for every strategy combination.

The prisoners dilemma payoff matrix is built directly from your four inputs. Once the four cells are filled in, the calculator checks which cell is a Nash equilibrium, which cells are Pareto-superior to it, and how much welfare the two players gain or lose by switching from mutual defection to mutual cooperation.

• T: The defector's payoff when the other player cooperates. In the classic story this is 0 (the defector walks free).
• R: Both players' payoff when they both cooperate. In the classic story this is 1 year each.
• P: Both players' payoff when they both defect. In the classic story this is 2 years each.
• S: The cooperator's payoff when the other player defects. In the classic story this is 3 years, the worst individual outcome.

Each player compares the two cells in their column (or row) and picks the lower number when payoffs are years in prison. When T < R and P < S, defection dominates cooperation for both players and the unique Nash equilibrium is the (D, D) cell.

The cooperation gain is the welfare at DD minus the welfare at CC. In a valid prisoners dilemma that difference is positive, which means the (D, D) equilibrium wastes more total welfare than the (C, C) cell, and that gap is why the defection equilibrium looks irrational from a social-welfare perspective even though it is the only stable outcome in a single shot.

According to Stanford Encyclopedia of Philosophy, the standard payoff ordering is T > R > P > S in utility terms, or S > P > R > T when payoffs are costs such as years in prison.

These four ideas explain why the matrix looks the way it does and why the equilibrium is so often mutual defection.

Whether defection truly dominates cooperation depends on the relative size of the four payoffs, and a ratio calculator lets you compare the temptation-to-reward and sucker-to-punishment ratios to verify the strict T > R > P > S (or S > P > R > T) ordering.

Set the four payoffs, then read the matrix, the equilibrium flags, and the welfare comparison in that order.

1. 1 Enter the temptation payoff (T): Payoff for the defector when the other player cooperates. Classic years-in-prison value: 0.
2. 2 Enter the reward payoff (R): Payoff for each player when they both cooperate. Classic value: 1 year.
3. 3 Enter the punishment payoff (P): Payoff for each player when they both defect. Classic value: 2 years.
4. 4 Enter the sucker payoff (S): Payoff for the cooperator when the other player defects. Classic value: 3 years.
5. 5 Read the 2x2 payoff matrix: The result panel reproduces the four cells CC, CD, DC, and DD with the row player first and the column player second.
6. 6 Read the equilibrium flags and cooperation gain: The Nash equilibrium and the cells that Pareto-dominate it are flagged, the dominant strategy for each player is printed, and the cooperation gain shows how much welfare the defection equilibrium wastes.

If you want to model a price-fixing meeting where both firms can either hold the cartel (cooperate) or undercut the other (defect), start with T = 0, R = 1, P = 2, S = 3. The calculator will show that defection dominates and both firms end up serving 2 years of profit loss instead of 1 year of cartel profit.

The total social welfare at a cell is just the sum of the two players' payoffs, and a basic addition calculator does that two-number sum the same way the welfare totals in the result panel do.

These are the practical reasons to run the numbers rather than reason them out in your head.

• • Reads the matrix in seconds: The calculator fills the four cells and prints the dominant strategy for each player.
• • Flags the Nash equilibrium and Pareto-superior cells: You see at a glance which cell is the equilibrium and which cells are strictly better for both players.
• • Quantifies the cooperation gain: The welfare comparison shows how many years defection wastes.
• • Accepts custom T, R, P, S values: Plug in any payoff set, not only the classic numbers.
• • Works for classroom and negotiation work: The matrix appears in game theory homework, oligopoly pricing, and arms-control prep.

The cooperation gain is the signed change from CC welfare to DD welfare, and an absolute change calculator gives the same signed-difference with magnitude reading the prisoners dilemma uses to show the welfare gap.

The numbers you type in set the single-shot result, but the real-world outcome often depends on these additional features of the situation.

• • The calculator only models a two-player symmetric game with the four standard payoffs. Larger or asymmetric games need a different matrix and are out of scope here.
• • The numbers are inputs, not estimates. Real-world payoffs are rarely exact, so treat the equilibrium as a directional signal.

According to Robert Axelrod, The Evolution of Cooperation, iterated prisoners dilemma tournaments show that tit-for-tat beats always-defect when the probability of meeting again is high enough.

The defection penalty is often reported as a percent change from CC to DD welfare, and a percentage change calculator gives the (DD welfare - CC welfare) divided by CC welfare times 100 number the prisoners dilemma analysis uses to show how big the welfare loss really is.