Aggregation technologies
How individual contributions add up to a shared good (summation, best shot, weakest link, threshold), and how that decides which collective action pattern a many-player case falls into.
Aggregation technologies
In a many-player building problem, what matters is how contributions combine into the good. Hirshleifer named the main cases ("From Weakest-Link to Best-Shot: The Voluntary Provision of Public Goods", Public Choice, 1983; known here through his abstract and through Sandler). Sandler calls them the "technology of public supply" (Collective Action, 1992, pp. 36–37) and later the "aggregation technology", adding threshold and other cases (Global Collective Action, 2004, pp. 61–68).
| Technology | The good depends on | Sandler's game form (2004, Table 3.2, p. 68) | Our pattern |
|---|---|---|---|
| Summation | The total of contributions | Prisoner's dilemma, or chicken | Prisoner's Dilemma; Chicken (game) if doing nothing is a disaster |
| Best shot | The largest single contribution | "Coordination" game | Volunteer's dilemma (our reading of the payoffs) |
| Weakest link | The smallest contribution | Assurance | Stag hunt |
| Threshold | Whether contributions reach a set level | Assurance | Stag hunt below the level; volunteer's dilemma above it (our reading) |
Why each lands where it does
- Summation. Each contribution adds a bit for everyone. If my share of what I add is smaller than what it costs me, I'm better off not contributing whatever others do. Taylor (The Possibility of Cooperation, 1987, pp. 16–17) shows the n-person game is a prisoner's dilemma when the number of players exceeds the ratio of benefit to cost. If no provision has dire consequences, not contributing stops being dominant and the game is chicken (Sandler 1992, pp. 40–41; 2004, p. 62).
- Best shot. One contribution is enough, so the question is who makes it. Sandler (1992, p. 41; 2004, p. 66) calls this a coordination game, "reminiscent of the Battle of the Sexes" (1992, p. 41). Its payoffs (free ride > contribute alone = both contribute > nobody contributes) are the volunteer's dilemma's order, which is why this wiki files it there. Mirrored archives are an example: one surviving copy suffices.
- Weakest link. Everyone has to do their part. If someone fails, my effort is wasted (fear); if everyone else does theirs, I have no reason to slack (no greed). Sandler gets an assurance game with matching equilibria (1992, pp. 43–44; 2004, pp. 62–64).
- Threshold. Sandler's two-player threshold game is an assurance game (2004, p. 64). With many players, once enough have come, each would rather someone else made up the number, which is volunteer-like. That reading is Taylor's, not Sandler's: his third n-person chicken variant has a sub-game that
is a game of Assurance
— Michael Taylor, The Possibility of Cooperation (1987), p. 42, of the sub-game in his variant G3
The same idea as a curve
Heckathorn draws the same distinction as the shape of the return to joining ("The Dynamics and Dilemmas of Collective Action", 1996, pp. 257–258): a decelerating return (the first contributions do most of the work) gives chicken; an accelerating one gives assurance. Marwell and Oliver's critical mass is a version of the same idea [?], as are Schelling's binary-choice curves (Micromotives and Macrobehavior, 1978, ch. 7).
So what
Sandler (2004, p. 68) notes that technologies other than summation often give a more hopeful prognosis, and that Olson assumed summation. The aggregation technology also explains many cases that fit two patterns. Heartbleed is a battle line if many small users each gain a little (summation) and a volunteer's dilemma if one big firm can fund the fix (best shot). Changing the technology changes the pattern: an assurance contract turns a summation good into a threshold good, and refunds can make contributing dominant (Sandler 2004, p. 64).
