Prisoner's Dilemma
What is Prisoner's Dilemma?
The prisoner's dilemma is a game theory scenario where two rational individuals acting in their own self-interest do not produce the optimal outcome for either.
In oligopoly, it explains why firms may fail to collude even when mutual cooperation would lead to higher joint profits, because each has an incentive to cheat on the agreement to gain a short-term advantage.
Prisoner's Dilemma: a worked example
Two gas stations on the same corner each pick a High price or a Low price. Daily profits work out like this: both High gives each $800; both Low gives each $500; and if one goes Low while the other stays High, the low one takes $1,000 and the other keeps $300. Look at station A's choices. If B prices High, A earns $1,000 by undercutting against $800 by matching. If B prices Low, A earns $500 by matching against $300 by holding out. Low wins in both columns, and B faces the identical arithmetic, so both price Low and take $500, which is $800 - $500 = $300 less each than cooperating would have paid.
The mistake students make with prisoner's dilemma
Students often label the cooperate-cooperate cell the Nash equilibrium, reasoning that it gives the largest combined payoff so rational players should land there. Combined payoff never decides a Nash equilibrium. The equilibrium is the cell each player reaches by following their own dominant strategy, which in this game is the mutually worse defect-defect outcome. The pull toward the wrong answer comes from equilibrium sounding like the sensible destination rather than simply the cell nobody can improve on alone.
Prisoner's Dilemma questions
Why do both players pick the worse outcome in a prisoner's dilemma?
Both players pick the worse outcome in a prisoner's dilemma because defecting is a dominant strategy for each of them. Whatever the other player does, defecting pays more, so neither needs to guess to know what to do. They cannot make binding promises, and cooperating while the other defects is the worst result of all, so both defect and land in the outcome each of them dislikes.
How can you tell a payoff matrix is a prisoner's dilemma?
A payoff matrix is a prisoner's dilemma when two conditions hold together. First, each player has a dominant strategy to defect, meaning defecting beats cooperating in both of the other player's columns. Second, the cell where both defect pays each player less than the cell where both cooperate. If either condition fails, the game is some other kind of game.
How do firms escape the prisoner's dilemma?
Firms escape the prisoner's dilemma mainly through repetition. When the same rivals meet day after day, a credible threat to answer any price cut with a lasting price war makes the one-off gain from cheating look small next to the losses that follow. Small numbers of firms, easily observed prices and no fixed end date all make that threat more believable and cooperation easier to sustain.
Related terms
Common comparisons
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated