Glossary · Economic ideas
Prisoner’s dilemma
The prisoner’s dilemma is a game in which each player does best by betraying the other, yet if both betray, both end up worse off than if they had cooperated.
Also called: prisoners dilemma, prisoner's dilemma, game theory, tit for tat
In plain words
The police catch two partners in crime, Ann and Bob, and question them in separate rooms. Each gets the same offer: confess and testify against your partner, and you go free while your partner gets 10 years. If both stay silent, there is only enough evidence for 1 year each. If both confess, it is 5 years each. That is the prisoner’s dilemma.
Look at it from Ann’s side. If Bob stays silent, confessing sets her free instead of 1 year. If Bob confesses, confessing gets her 5 years instead of 10. Either way, confessing is better for her. Bob reasons the same way.
So both confess and get 5 years each, when staying silent would have cost them just 1. Each made the smart choice for themselves, and together they made the worst choice for the pair.
Example
Two gas stations on one corner
Two gas stations face each other. If both charge $4.00 a gallon, each earns $1,000 a day.
- If one cuts to $3.80 while the other stays at $4.00, the cheaper one wins most of the customers and earns $1,400; the other earns $300.
- So each owner is tempted to cut, whatever the other does: $1,400 beats $1,000, and $700 beats $300.
- If both cut to $3.80, they split the customers again, but at a lower price: $700 each.
- Both would have earned more at $4.00, but each one fears being undercut.
That is how price wars start, and why drivers gain when sellers can’t trust each other. (Agreeing with a rival to keep prices high is illegal: it is called price fixing.)
One level deeper
The game was worked out in 1950 by Merrill Flood and Melvin Dresher at the RAND Corporation; the mathematician Albert Tucker gave it the prison story. It became the best-known example of game theory, the study of choices that depend on what others choose.
In a game played once, betrayal wins. When the same players meet again and again, cooperation can pay. In Robert Axelrod’s computer tournaments around 1980, the winner was one of the simplest strategies: tit for tat, which cooperates first and then copies whatever the other player did last time.
The dilemma turns up all over economics: arms races, advertising wars, the tragedy of the commons, firms deciding whether to cut prices, countries deciding whether to cut pollution. Contracts, laws, reputation and trust are all ways of escaping it.
Why it matters
It explains why people and firms often fail to cooperate even when cooperating would help all of them.
It shows why rules, contracts and reputation matter: they change the payoffs so that cooperating becomes the smart move.
It explains price wars, and why cartels tend to fall apart: each member gains by quietly breaking the deal.
A common mistake
Myth: Rational players will cooperate, because cooperating is better for both.
In fact: In a single round, rational players betray each other, because each one’s best move doesn’t depend on what the other does. Cooperating becomes rational only when the game repeats, or when promises can be enforced.
Questions people ask
What is the Nash equilibrium of the prisoner’s dilemma?
Both players confess. Neither can do better by changing only their own choice, even though both would be better off if both stayed silent.
What are real-life examples of the prisoner’s dilemma?
Price wars between rival stores, arms races, doping in sports, overfishing, and two companies each spending more on advertising just to cancel out the other’s ads.
How do you win the prisoner’s dilemma?
In a single round, betraying is the best move for each player. In repeated games, strategies that reward cooperation and punish betrayal, like tit for tat, tend to do best.
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About the numbers
- This page explains a term. It is not investment advice.