AP® Microeconomics · Unit 4 · Topic 4.5
The Prisoner's Dilemma and Why Cartels Break
A cartel's cooperative deal is not a Nash equilibrium because each firm earns more by secretly overproducing no matter what its rival does, so the prisoner's dilemma predicts cheating even though everyone would do better by cooperating.
Picture two firms splitting a market. If both hold output low, they act like a monopolist and split the big profit. That is the cooperative outcome. But each firm privately asks: what happens if I produce more while my rival sticks to the deal? Extra output steals customers and raises the cheater's profit, even though total industry profit falls. Since this logic holds for both firms, and holds whether the rival cooperates or defects, defecting is a dominant strategy. Each firm chooses it out of self-interest, and the cooperative outcome collapses even though both firms knew it was better for them jointly.
This is exactly the prisoner's dilemma: a game where the jointly best outcome is not an equilibrium, because individual incentives pull every player toward defection. An oil cartel like OPEC sets output quotas to keep prices high. Every member benefits if all hold their quota. But any single member can pump extra barrels, sell at the still-high price, and pocket extra revenue, as long as others keep restricting output. Since every member reasons this way, the quota deal is fragile. The cooperative outcome is not a Nash equilibrium, because at least one firm always has a profitable reason to deviate from it.
This connects directly to oligopoly pricing and game theory in this unit: firms that could earn monopoly-level profit by colluding instead drift toward the competitive, lower-profit outcome because no enforceable commitment exists. Repeated interaction changes the calculus. When the same firms play month after month, cheating today can trigger punishment tomorrow, so firms may sustain cooperation if future losses from retaliation outweigh today's gain from defecting.
Key terms
- Prisoner's dilemma
- A game where each player has a dominant strategy to defect, leaving both worse off than if they had cooperated.
- Dominant strategy
- An action that gives a player the highest payoff no matter what the other player chooses.
- Nash equilibrium
- A set of strategies where no player can gain by changing their own choice while others hold theirs fixed.
- Cartel
- A group of firms that agree to restrict output or fix prices to earn higher joint profit.
- Defect
- To break a cooperative agreement by producing more or pricing lower than agreed.
Watch it explained
- How it worksHow does the prisoner's dilemma structure show up in an oil cartel's output choice?
- How it worksWalk me through the cooperative outcome and why neither player can hold on to it.
- Worked exampleFind the payment that flips a firm's dominant strategy when defecting pays 12 and cooperating pays 8.
- Going furtherWhat changes when the same two firms play the game every month instead of once?
Check yourself
End of topic.