Game theory
Prisoner's dilemma
Why two rational actors betray each other even when cooperation would help them both.
The prisoner's dilemma is a game in which two players, each acting rationally in their own self-interest, betray one another — reaching an outcome that is worse for both than if they had cooperated.
TL;DR
- Two players each choose to cooperate or defect, without communicating.
- Defecting is each player's dominant strategy — better regardless of what the other does.
- So both defect and land on the only Nash equilibrium: mutual defection.
- That equilibrium is worse for both than mutual cooperation would have been.
- Repetition (tit-for-tat), binding contracts, or reputation can rescue cooperation.
When to use it
- Explaining why competitors, nations, or teammates fail to cooperate despite shared gains.
- Spotting situations where individual incentives quietly sabotage the collective outcome.
- Designing contracts, penalties, or repeated interactions that make cooperation rational.
When it fails
- When players can communicate and make binding commitments — that changes the payoffs.
- When the game repeats indefinitely — cooperation can become the rational equilibrium.
- When the real payoffs aren't a dilemma at all — don't force the frame where defection isn't dominant.
Worked example
Two suspects are arrested and held separately, unable to communicate. Each is offered the same deal: betray the other and go free while your partner serves 3 years. If you both betray, you each serve 2 years. If you both stay silent, the police can only convict you of a minor charge — 1 year each.
Look at it from Prisoner A's side. If B stays silent, A goes free (0 years) by confessing instead of serving 1. If B confesses, A serves 2 years by confessing instead of 3 by staying silent. Either way confessing is better for A — and by symmetry, for B.
So both confess and serve 2 years each, even though mutual silence would have cost them only 1 year each. Individually rational choices produce a collectively worse result. That gap — between the stable outcome and the better-but-unstable one — is the whole point of the dilemma.
| Prisoner B | ||
|---|---|---|
| Prisoner A | B stays silent | B confesses |
| A stays silent | −1 / −1 | −3 / 0 |
| A confesses | 0 / −3 | −2 / −2 |
Related concepts
- Dominant strategy — why each prisoner confesses no matter what the other does
- Nash equilibrium — the solution concept the dilemma settles into
- Tit-for-tat — how repetition can rescue cooperation
- Tragedy of the commons — the multiplayer, repeated version of the same trap
FAQ
What is the prisoner's dilemma in simple terms?
It is a situation where two people, each acting in their own self-interest, both end up worse off than if they had cooperated. Betraying the other is better for you no matter what they do, so both betray — even though mutual cooperation would have helped them both.
Why do both prisoners confess if staying silent is better for both?
Because confessing is each prisoner's dominant strategy: whatever the other does, confessing gives you a lighter individual sentence. Both reason identically and defect, landing on mutual confession — the game's only Nash equilibrium — even though mutual silence would have been better for both.
What is a real-life example of the prisoner's dilemma?
Arms races, price wars between competitors, doping in sports, and climate-change inaction. In each, every party gains individually by defecting — building weapons, cutting prices, doping, polluting — so all defect and collectively lose, exactly like the two prisoners.
How is the prisoner's dilemma solved?
In a one-shot game it isn't — mutual defection is rational. But when the game repeats, strategies like tit-for-tat make cooperation stable, because today's betrayal is punished tomorrow. Enforceable contracts, reputation, and communication also reshape the payoffs enough to sustain cooperation.
Prisoner's dilemma vs tragedy of the commons — what's the difference?
Both are cooperation failures driven by individual incentives. The prisoner’s dilemma is usually two players making one decision; the tragedy of the commons is many players repeatedly overusing a shared resource. The commons is essentially a multiplayer, repeated prisoner’s dilemma.