Source
Maynard Smith & Price (1973), “The Logic of Animal Conflict”, LIT-505 (Nature 246: 15–18), read in full in NOTE-404. Table 1 digits misread by OCR were checked against values the prose quotes.
What was actually shown
The ESS (p. 17). A strategy I is evolutionarily stable if, for all J, E_I(I) > E_I(J); or if E_I(I) = E_I(J), then E_J(I) > E_J(J).
The contest model. Contestants have “identical fighting prowess” and no memory across contests. Moves are conventional, dangerous or retreat. One dangerous blow injures seriously with probability 0.10. Payoffs: +60 for a win, −100 for serious injury, −2 per non-injuring blow received, up to +20 for a short contest. Losing uninjured scores 0, so future breeding remains.
Table 1. Mouse and Bully each beat Hawk in a Hawk population, so Hawk is not an ESS. Mouse scores 29.0 against Retaliator, as Retaliator does against itself, and Retaliator scores 29.0 against Mouse, as Mouse does against itself. The paper: “Retaliator is an ESS since no other strategy does better, though Mouse does equally well.” By its own second condition that tie makes Retaliator at most neutrally stable. Prober-Retaliator “is almost an ESS”.
Sensitivity. Hawk becomes the ESS if a dangerous blow injures with probability 0.90, or if retreating uninjured costs as much as serious injury. The qualitative result is said to survive “moderate changes”; those runs are not shown.
War of attrition (p. 17). If the contestant willing to pay more wins and both pay the smaller cost, no pure strategy is stable: a little more persistence beats any fixed m. The mixture p(x) = (1/v)exp(−x/v) is an ESS. The derivation is deferred to later work.
What could have come out otherwise. Escalation could have paid in a population of retaliators. It does not under the stated payoffs, though it does under the high-injury and costly-retreat variants.
What this does not say
- That Retaliator is strictly stable. Mouse can drift in. Gale & Eaves (1975) commented on the analysis; that comment was not read.
- A Hawk–Dove game. The word “dove” does not occur, and the strategies are Mouse, Hawk, Bully, Retaliator and Prober-Retaliator. The record holds no source for the two-strategy game.
- Display and deference. Contestants are identical, so assessment of a superior opponent appears only in the informal “Real Animals” section, as argument (NOTE-404, C6).
- Ownership or division. There is no owner–intruder asymmetry, and the war of attrition is about who takes the whole prize.
- That the strategy space was searched. Five strategies were chosen by hand, and only means of the simulated contests are reported.
Connections
- Hamilton’s Part II (LIT-506, THEORY-655) explains restraint between relatives by relatedness. This explains it between non-relatives by retaliation.
- Axelrod & Hamilton (LIT-498, THEORY-672) take the ESS concept from here. Their TIT FOR TAT is neutrally stable in the same way Retaliator is.
- Morality-as-cooperation (LIT-503) and NOTE-034 credit this paper with “hawk–dove contests”. NOTE-404 corrects that: it grounds restraint backed by retaliation, and only informally the retreat from a superior and the honest signal.