The prisoner's dilemma is the one piece of game theory almost every microeconomics course covers, because it explains a puzzle markets keep producing: two parties who could both gain by cooperating instead choose the outcome that leaves them both worse off. This explainer builds the dilemma from a payoff matrix, defines dominant strategy and Nash equilibrium along the way, and shows why it predicts that price-fixing cartels keep falling apart.
The Setup: Two Suspects, One Choice
The classic story: two suspects are arrested and questioned in separate rooms, unable to communicate. Each is offered the same deal — confess (betray the other) or stay silent (cooperate with the other).
The consequences depend on what both do:
- If both stay silent, the police have a weak case; each gets a light sentence — 1 year.
- If both confess, both are convicted on the strong case; each gets 5 years.
- If one confesses and the other stays silent, the confessor goes free (rewarded for cooperating with police) and the silent one gets the full 10 years.
The structure is the point: each prisoner privately prefers to confess, yet if both follow that preference they land in an outcome worse for both than if they'd both stayed silent. To analyze it precisely, economists put it in a grid.
Reading a Payoff Matrix
A payoff matrix lays out every combination of choices and the result for each player. Prisoner A picks a row, Prisoner B picks a column; each cell shows (A's payoff, B's payoff). We'll write sentences as negative numbers, since fewer years is better.
| B stays silent | B confesses | |
|---|---|---|
| A stays silent | A: −1, B: −1 | A: −10, B: 0 |
| A confesses | A: 0, B: −10 | A: −5, B: −5 |
To read it, fix one player's choice and scan the other's options. Suppose B stays silent (left column): A gets −1 by staying silent, or 0 by confessing. A prefers 0 — confessing is better. Now suppose B confesses (right column): A gets −10 by staying silent, or −5 by confessing. A again prefers −5 — confessing is still better.
Dominant Strategy and Nash Equilibrium
That last paragraph found something important. No matter what B does, A is better off confessing. A choice that is best regardless of the other player's move is a dominant strategy. Confessing is a dominant strategy for A.
The matrix is symmetric, so confessing is also B's dominant strategy. Both players, reasoning independently and selfishly, confess — landing on the (confess, confess) cell, where each serves 5 years.
That cell is a Nash equilibrium: an outcome where no player can improve their own payoff by unilaterally changing strategy, given what the other is doing. From (confess, confess), if A switches to silent while B keeps confessing, A's sentence jumps from 5 years to 10. So A won't switch — and neither will B. The outcome is stable.
Here is the dilemma stated sharply: the Nash equilibrium is (confess, confess) with 5 years each, but (silent, silent) would give each only 1 year. Both players would be better off cooperating, yet rational self-interest drives them to the worse outcome. The equilibrium is not the best joint result.
Why It Matters in Economics: Cartels and Oligopoly
The prisoner's dilemma isn't really about prisoners — it's a template for any situation where individual incentives clash with the group's interest. The headline economic application is collusion among firms in an oligopoly.
Imagine two firms that dominate a market and secretly agree to fix a high price — to form a cartel. Replace "stay silent" with "honor the agreement (keep price high)" and "confess" with "cheat (cut price)":
- If both keep the price high, both earn large profits — like both staying silent.
- If both cheat and cut prices, they compete the profit away — like both confessing.
- If one cheats while the other holds the high price, the cheater steals the whole market and earns the most, while the loyal firm earns the least.
The payoff structure is identical to the prisoner's dilemma. Cheating is each firm's dominant strategy — whatever the rival does, undercutting it captures more sales. So the Nash equilibrium is for both to cheat, prices fall, and the cartel collapses. This is why economists predict price-fixing agreements are inherently unstable: the very logic that makes them profitable also gives every member a private incentive to break them. It's also part of why competition among firms tends to benefit consumers — the same forces explored in perfect competition vs. monopoly.
Why Cooperation Sometimes Survives: Repeated Games
If the dilemma is so bleak, why do cartels — and cooperative behavior generally — ever last? The answer is repetition.
The one-shot prisoner's dilemma is played once and ends. But firms interact month after month. In a repeated game, a player who cheats today can be punished by the other tomorrow. A simple strategy called tit-for-tat — cooperate first, then copy whatever the rival did last round — makes cheating costly: a firm that undercuts gets undercut right back, losing future profit. When players value the future enough and the game has no clear final round, the threat of retaliation can sustain the cooperative (high-price) outcome that the one-shot game rules out. Repetition doesn't change the matrix; it changes the stakes by adding consequences that arrive later.
Conclusion
The prisoner's dilemma shows two rational players each picking a dominant strategy and arriving at a Nash equilibrium that's worse for both than the cooperative outcome they could have reached. In economics it explains why cartels and other collusive agreements are fragile — every member has a private incentive to cheat. The escape hatch is repetition: when the same players meet again and again, the threat of future punishment can make cooperation hold.
