Greed and fear
Two yes/no questions about a two-player game, whether slacking pays when the other cooperates and whether cooperating alone loses, which sort the collective action problems into four patterns.
Greed and fear
Take a symmetric two-player game where both cooperating beats both defecting. Write R for both cooperate, P for both defect, T for the temptation (I defect, you cooperate) and S for the sucker's payoff (I cooperate, you defect). Two questions fix which game it is:
- Greed: if you cooperate, do I do better defecting? (T > R)
- Fear: if you defect, do I do worse cooperating? (P > S)
In plain terms: would I gain by slacking if you pull your weight? Would I lose by pulling my weight alone?
| Fear | No fear | |
|---|---|---|
| Greed | Prisoner's Dilemma (battle line) | Chicken (game), Volunteer's dilemma (chicken) |
| No greed | Stag hunt (assurance) | Harmony (no problem) |
The terms are Macy and Flache's ("Learning Dynamics in Social Dilemmas", PNAS 99 suppl. 3, 2002), who define greed as T > R and fear as P > S. The classification itself is arithmetic. Of the 12 strict orderings with R > P, the four cells hold 1, 3, 3 and 5. So the map covers every strict symmetric case where cooperating together beats defecting together. Orderings where both prefer mutual defection, such as deadlock, are not dilemmas.
Heckathorn gets the same four games by swapping payoffs in the prisoner's dilemma ("The Dynamics and Dilemmas of Collective Action", 1996, pp. 258–259): reverse the top two (R > T) for assurance, the bottom two (S > P) for chicken, both for the "privileged game", and the middle two (P > R) for the "altruist's dilemma", or deadlock. Of the privileged game:
Because individual and collective rationality coincide perfectly, there is no social dilemma.
— Douglas Heckathorn, "The Dynamics and Dilemmas of Collective Action" (1996), p. 259
Why it matters
- The patterns share ingredients. That answers whether chicken and the prisoner's dilemma are "the same": they share greed and differ on fear. See Chicken vs prisoner's dilemma.
- Fixes move a case across the map. Remove greed from a prisoner's dilemma (a penalty for defecting) and it becomes a stag hunt. Remove fear from a stag hunt (a refund if too few contribute) and contributing becomes the dominant strategy, so the problem disappears (Sandler, Global Collective Action, 2004, p. 64, on refunds in threshold games). Most fixes work by moving a case towards "no problem".
- People can answer the questions about their own case without game theory.
The map is for two-player games. Many-player cases add Aggregation technologies and group size; see Patterns of collective action.
