Prisoner's Dilemma
The Prisoner's Dilemma is a two-player game in which each player is better off defecting whatever the other does, so mutual defection is the only Nash equilibrium, even though both players would be better off if both cooperated. It is the standard model of how individually rational choices can produce a collectively worse outcome.
Payoff matrix
| Row player (rows) / Column player (columns) | Cooperate | Defect |
|---|---|---|
| Cooperate | (3, 3) | (0, 5) |
| Defect | (5, 0) | (1, 1) Nash equilibrium |
Payoffs are ordinal scores from the DecisionPlay engine's template for this game, 0 to 5, higher is better. They rank outcomes and are not dollar values. [MODELED]
Nash equilibria
- Pure: Row player plays Defect, Column player plays Defect. Payoffs (1, 1).
Computed by the DecisionPlay solver from the matrix above. [MODELED]
Where it shows up
Illustrative
- Price competition. Two firms in the same market each gain by undercutting the other's price, yet if both undercut, both earn less than if both had held their prices.
- Arms races. Two rival states each gain security by arming more than the other, yet if both arm, both bear the cost and neither is more secure than if both had held back.
Common misreadings
- The players are irrational. Each player is choosing the best response to the other's choice. The poor joint outcome comes from the incentives, not from a reasoning mistake.
- Cooperation can never happen. The one-shot equilibrium is mutual defection. Repeated interaction, enforceable agreements, or changed payoffs alter the incentives, which is why the one-shot matrix is a starting point and not a forecast.
- The model says defecting is the right thing to do. The model describes which choice each player's incentives favor. It makes no claim about what players ought to do.
Try it
Map your own scenario or edit a payoff matrix in the solver.