Chicken vs prisoner's dilemma
The two games share the temptation to slack but differ in one swap, whether acting alone is worse or better than nobody acting, and that swap changes the equilibria, the failure and the fix.
Chicken vs prisoner's dilemma
Two neighbors and a job. Payoffs ordinal, 4 best to 1 worst, (row, column).
Prisoner's Dilemma: draining a shared field. Each ditch helps the whole field, but less than it costs the person who digs it. A lone digger's effort is mostly wasted: they end up worse off than if nobody had dug.
| Neighbor digs | Neighbor doesn't | |
|---|---|---|
| I dig | 3, 3 | 1, 4 |
| I don't | 4, 1 | 2, 2 |
Chicken (game): a snowdrift across a shared lane. Either of them alone can clear it. A lone shoveller is better off than if both stay indoors and nobody gets out.
| Neighbor shovels | Neighbor doesn't | |
|---|---|---|
| I shovel | 3, 3 | 2, 4 |
| I don't | 4, 2 | 1, 1 |
Where the neighbor works (left column), the two games are the same: I'd rather not (4 > 3, greed). The difference is in the right column, where the neighbor doesn't: acting alone is worse than nobody acting in the drainage case (1 < 2) and better in the snowdrift (2 > 1).
a PD is transformed into a chicken game.
— Douglas Heckathorn, "The Dynamics and Dilemmas of Collective Action" (1996), p. 258, of what happens when the sucker's payoff rises above mutual defection
What the swap changes
| Drainage (prisoner's dilemma) | Snowdrift (chicken) | |
|---|---|---|
| Equilibria | One: nobody digs. Not digging is best whatever the neighbor does. | Two: one shovels, the other doesn't. If I'm sure you won't, I will. Plus a mixed one where nobody does it some of the time. |
| Typical outcome | The field stays wet | The lane usually gets cleared, by someone |
| Failure | Universal shirking | The wrong person pays; waiting; standoffs; in big groups, nobody acts (Volunteer's dilemma) |
| Conflict | Me against the group | Me against you: who pays |
| Fix | Change payoffs for everyone: sanctions, rewards, repetition | Allocate: name someone, take turns, split the cost (when one person is enough) |
| Assurance | Doesn't help: if you dig, not digging still pays more | Backfires: if I know you'll shovel, I wait |
Allocation is the distinctive fix only when one actor is enough. When everyone acting is best, chicken is fixed much like a prisoner's dilemma (Dixit, Skeath and Reiley, Games of Strategy, 4th ed., 2015, p. 449). Taylor (The Possibility of Cooperation, 1987, p. 43) judges the prospects for cooperation "a little more promising" in chicken than in the prisoner's dilemma.
Where they blur
- The symptom can look the same: nothing gets done. The pattern is in the payoffs, not the outcome.
- Small changes move a case across the line. Heckathorn's game space (p. 257) puts the two in neighboring regions; chicken appears when the first contribution produces most of the good (p. 258).
- Repetition: Taylor (p. 40) notes that the n-person prisoner's dilemma supergame can itself be a chicken game.
See also Stag hunt vs chicken, Prisoner's dilemma vs stag hunt, Patterns of collective action.
