Patterns of collective action
A two-level typology of collective action problems. The top level is a greed/fear map of four games plus a taking-or-building axis; the second level is group size, aggregation, the shape of returns, information and repetition; next to it sit principal-agent and second-order problems.
Patterns of collective action
A pattern here is a named strategic structure with a typical way of failing and typical fixes. Two problems are the same pattern if their payoff matrices have the same equilibrium structure, whatever they are called. For the names used in different fields, see Names of collective action problems. For the basic apparatus, see Game theory basics.
Collective action is not one game. Taylor (The Possibility of Cooperation, 1987, p. 18) warns against equating it with the prisoner's dilemma. Ostrom reports the same for common-pool resources, some of which are
better characterized as "assurance" games and as the game known as "chicken"
— Elinor Ostrom, Governing the Commons (1990), p. 46, summarizing Runge and Taylor
Top level
Greed and fear
Two questions sort the games (Greed and fear). Would I gain by slacking if you pull your weight? Would I lose by pulling my weight alone?
| Fear | No fear | |
|---|---|---|
| Greed | Battle line (Prisoner's Dilemma). One equilibrium, and it's bad. | Chicken (Volunteer's dilemma; with two players, Chicken (game)). Someone gives way; the fight is over who. |
| No greed | Stag hunt (assurance game). Two equilibria, one better. | No problem (harmony; the privileged game). Cooperating pays anyway. |
Each pattern has its own fix: change the payoffs (battle line), give assurance (stag hunt), decide who acts (chicken, where one actor is enough; otherwise chicken is fixed like a prisoner's dilemma: Dixit, Skeath and Reiley, Games of Strategy, 4th ed., 2015, p. 449). Fixes work by moving a case across the map towards "no problem".
Off the map, as a baseline: the pure Coordination game (which side of the road), where the only problem is matching. Battle of the sexes, where each prefers a different match, belongs with chicken.
Comparisons:
- Chicken vs prisoner's dilemma — one swap, different failure, different fix.
- Prisoner's dilemma vs stag hunt — incentive problem vs trust problem.
- Stag hunt vs chicken — the fix for one backfires on the other.
Taking and building
The second axis is what cooperating means (Taking and building): restraint (not overfishing, not emitting) or contribution (work, money, code). It is a simplification of Ostrom's appropriation and provision. It doesn't change the equilibria, but it changes the remedies. All three patterns occur on both sides:
| Battle line | Stag hunt | Chicken | |
|---|---|---|---|
| Taking | Open-access fisheries (Newfoundland cod) | Bank runs | Who gets the good spot: the Alanya fishing sites |
| Building | Public goods; open source; the public-goods experiment | Protests and revolutions | A person collapses in the street |
Second level
Finer axes that split or merge cases within the map:
- Number of players. Chicken with two players becomes the volunteer's dilemma with many, and the chance that nobody acts rises with group size (Dixit, Skeath and Reiley pp. 455–457). In large groups, public-good provision "almost always" ends up a prisoner's dilemma (p. 430).
- Aggregation technologies. How contributions add up. In Sandler's mapping summation gives a prisoner's dilemma (or chicken if doing nothing is a disaster), weakest link and threshold give assurance, and best shot a "coordination" game, which has the volunteer's payoff order.
- Shape of the return to joining. Heckathorn ("The Dynamics and Dilemmas of Collective Action", 1996, pp. 257–258): a decelerating return gives chicken, an accelerating one assurance; the value of the good relative to its cost separates the dilemmas from the non-dilemmas.
- Information. Whether defection can be seen; Ostrom's monitoring puzzle (p. 45). Information cascades and pluralistic ignorance sit here rather than in the payoffs.
- Repetition. Indefinite repetition makes cooperation one equilibrium among very many, which turns a battle line into a coordination problem (Folk theorem; Osborne and Rubinstein, A Course in Game Theory, 1994, p. 134).
- Timing and asymmetry. In chicken, committing first gains. A big player who gains enough to act alone turns a case into a privileged group (Olson, The Logic of Collective Action, 1965, pp. 49–50).
Many real cases fit two patterns: the hoplite line, climate, the naval race before 1914, Heartbleed, and the AI race, which fits all three. Almost all are many-player threshold cases or cases whose payoffs shift with a parameter; Heckathorn's game space (p. 257) and Ostrom (pp. 46–47) both note that small changes in parameters change the game. Case by case: Cases on the pattern map.
Second layer
Next to the patterns rather than part of them. Each item is placed as a pattern, a cause, a remedy, or adjacent.
| Item | Placement |
|---|---|
| Principal-agent problem (moral hazard, adverse selection) | Adjacent: two parties, not a group. A cause once a group delegates monitoring |
| Moral hazard in teams | Pattern: a battle line inside an organization |
| Second-order free-rider problem | Pattern, one level up: who punishes, who supplies the rules |
| Hold-up problem, Commitment problem | Causes |
| Folk theorem, Selective incentives, Assurance contracts | Remedies |
| Mechanism design, Clarke–Groves and VCG | Remedy family: design the game |
| Rotation, lotteries, correlated equilibrium | Remedies for chicken and coordination |
| Bargaining | Adjacent: how a who-gives-way conflict gets settled |
Typologies in the literature
- Olson 1965: privileged, intermediate and latent groups, by whether one member gains enough to act alone and whether each contribution is noticeable (pp. 49–51).
- Taylor 1987: prisoner's dilemma, chicken and assurance, in two- and n-person forms (pp. 16–19, 34–45).
- Ostrom 1990: appropriation vs provision (pp. 47–50); common-pool situations take many game forms (pp. 46–48).
- Heckathorn 1996: five games from payoff swaps in the prisoner's dilemma (pp. 258–259).
- Kollock 1998: two-person dilemmas (prisoner's dilemma, assurance, chicken); n-person public goods and commons dilemmas; motivational, strategic and structural solutions (from the abstract).
- Hirshleifer 1983; Sandler 1992, 2004: aggregation technologies and the game forms they give (Sandler 1992, pp. 36–44; 2004, pp. 61–68).
- Dixit, Skeath and Reiley 2015: collective-action games come in three forms, prisoner's dilemma, chicken and assurance, drawn as n-person payoff curves (pp. 418–430).
Full references: Collective action bibliography.
