Prisoner's dilemma vs stag hunt
Both games punish the lone cooperator, but only the prisoner's dilemma tempts you to defect when others cooperate, so one is an incentive problem and the other a trust problem.
Prisoner's dilemma vs stag hunt
Payoffs ordinal, 4 best to 1 worst, (row, column).
| Column C | Column D | |
|---|---|---|
| Row C | 3, 3 | 1, 4 |
| Row D | 4, 1 | 2, 2 |
| Column stag | Column hare | |
|---|---|---|
| Row stag | 4, 4 | 1, 3 |
| Row hare | 3, 1 | 2, 2 |
The right column matches: if the other defects, cooperating alone is the worst outcome (1 < 2, fear). The difference is in the left column. In the prisoner's dilemma, defecting while the other cooperates beats mutual cooperation (greed). In the stag hunt, mutual cooperation is the best outcome there is. Heckathorn gets the assurance game from the prisoner's dilemma by reversing exactly these two payoffs, the top two in the ranking ("The Dynamics and Dilemmas of Collective Action", 1996, pp. 258–259).
What that changes
| Prisoner's dilemma | Stag hunt | |
|---|---|---|
| Equilibria | One: both defect | Two: both stag, both hare; the first is better for both |
| The problem | Incentive: breaking ranks pays whatever others do | Trust: I'll cooperate if I'm sure you will |
| Fix | Change the payoffs: sanctions, rewards, repetition | Assurance: make commitment visible or guaranteed |
| Assurance | Doesn't help: defecting still pays more | Is the fix |
A stag hunt can still fail. Players who are unsure of each other settle on hare, and that is an equilibrium too. Taylor counts assurance as not a collective action problem at all, on his assumption that rational players pick the better equilibrium (The Possibility of Cooperation, 1987, pp. 19, 39). He also warns against treating every collective action problem as a prisoner's dilemma:
we should not equate 'the problem of collective action' with the Prisoners' Dilemma
— Michael Taylor, The Possibility of Cooperation (1987), p. 18
How cases move between them
- A moderate penalty for defecting removes greed and turns a prisoner's dilemma into a stag hunt.
- Thresholds: if the good only appears once enough people contribute, a lone contributor's effort is wasted and a defector breaks it, which looks like a stag hunt below the threshold (Aggregation technologies).
- Several cases fit both, depending on the payoffs: the hoplite battle line, arms races, herds turning on a predator.
See also Chicken vs prisoner's dilemma, Stag hunt vs chicken, Patterns of collective action.
