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THEORY-567: In the donation game, where a cooperator pays c for another to get b, defectors win in a well-mixed population, and each of five mechanisms makes cooperators evolutionarily stable above a benefit-to-cost threshold: kin selection r > c/b, direct reciprocity w > c/b, indirect reciprocity q > c/b, network reciprocity b/c > k and group selection b/c > 1 + n/m; the rules cover altruism only, not mutualism, coordination or conflict

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Properties5
StatusActive
Tagsnatural-sciences, game-theory
SourceLIT-501 — Five Rules for the Evolution of Cooperation
ExtendsTHEORY-408 — In a one-locus model with non-overlapping generations, random mating and weak selection, gene frequencies change as if each individual maximized its inclusive fitness, so a trait that costs its bearer spreads only if its effect on relatives exceeds 1/r times the cost; the increase of mean inclusive fitness is proved only for traits whose total effect on others is not negative, THEORY-672 — In the iterated Prisoner's Dilemma with a probability w of meeting again, no strategy does better against an established TIT FOR TAT than TIT FOR TAT does against itself if and only if w ≥ (T−R)/(T−P) and w ≥ (T−R)/(R−S); always defecting is stable for every w, a cluster of reciprocators can invade it, and a nice stable strategy resists clusters, but the stability is only neutral, since always cooperating ties
Cited as “grounds” byCLAIM-546 — Negative frequency dependence that keeps two types in coexistence does not make their interaction cooperative: in Hawk–Dove with cost C above value V each type increases when rare and they coexist at the interior equilibrium of V/C Hawks, with Hawks still taking the whole resource from Doves, and on the Black Queen account producers of a leaked good and the cells that use it without paying coexist at a frequency set by the community's need; so whether types persist together and whether they cooperate are separate questions, and a coexistence criterion answers only the first, CLAIM-547 — Cooperation within groups and the coexistence of groups are distinct targets that can trade off: in the group-selection rule of Nowak's five, b/c > 1 + n/m, cooperation spreads because a group that grows to size n splits and another group is driven extinct, so the mechanism that stabilizes cooperation inside groups works by removing groups; cooperation local to a group, the persistence of several groups whose interests are opposed, and concern for those outside one's group are three achievements, and none of them secures the next

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Source

Nowak (2006), “Five Rules for the Evolution of Cooperation”, LIT-501 (Science 314: 1560–1563), read in NOTE-409. The main text, figure captions, Table 1 and references were read. Table 1’s matrices and its risk-dominance and advantageousness columns did not survive extraction. The supporting material with the derivations was not read.

What was actually shown

The baseline (Fig. 1). In a well-mixed population of N with i cooperators, f_C = b(i − 1)/(N − 1) − c and f_D = bi/(N − 1). Defectors always do better, and selection lowers mean fitness.

The five rules (eqs. 1–5). Kin selection, r > c/b, by the inclusive- fitness method. Direct reciprocity, w > c/b, with TIT FOR TAT against always-defect over an expected 1/(1 − w) rounds. Indirect reciprocity, q > c/b, where q is the probability of knowing a recipient’s reputation. Network reciprocity, b/c > k, on a regular graph with k neighbours under weak selection. Group selection, b/c > 1 + n/m, with m groups of maximum size n, under weak selection and rare splitting.

Three criteria. With a 2×2 matrix (a, b; g, d), cooperators are an ESS if a > g, risk-dominant if a + b > g + d, and advantageous if a + 2b > g + 2d. For kin selection, network reciprocity and group selection the rule makes cooperators dominate, so it gives all three. For the two reciprocities it gives the ESS condition, and the other two criteria need “slightly more stringent conditions”.

The common thread. Every mechanism makes cooperators meet cooperators more often than chance would, and its rule says how much more is needed per unit of b/c (NOTE-409’s reading).

What could have come out otherwise. A mechanism could have resisted reduction to a single threshold. None of the five does.

What this does not say

  • Anything about mutualism, coordination, contests, division or possession. The donation game has none. Morality-as-cooperation (LIT-503, Table 3) lists this review as incomplete for that reason.
  • That the rules hold outside their models. Several need weak selection, regular graphs or rare splitting.
  • That punishment is ruled out. The claim that punishment “is not a mechanism for the evolution of cooperation” is a survey claim: every model of it so far rests on one of the five.
  • That indirect reciprocity produced morality. One sentence says it “leads to the evolution of morality and social norms”, citing Alexander (LIT-495). That is an assertion, and nothing in the review tests it.
  • That the five are distinct. The closing paragraph allows that all may be expressible as kin selection in a broad, Price-equation sense. The review does not settle it, and Nowak’s later work is among the criticisms of that Price-equation view which Luque answers (LIT-205).

Connections

  • It extends Hamilton’s threshold (THEORY-408; its generalization in Hamilton’s Part II is THEORY-655), restated as r > c/b, and Axelrod & Hamilton’s stability condition (THEORY-672), specialized to the donation game as w > c/b.
  • Network reciprocity and group selection are routes to altruism. They do not map onto morality-as-cooperation’s group domain, which is mutualism and coordination (NOTE-409).
  • Luque’s analysis of the Price equation (LIT-205, NOTE-101) defends the equation against critics who later include Nowak & Highfield (2011). The tension is between Nowak’s later work and this paper.
  • Lloyd’s entry (LIT-160) treats the multilevel-selection debate that the fifth rule enters.

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