Why doesn’t a species evolve into all-fighters? Hawks always fight (and sometimes get hurt); doves always share. All-dove invites a hawk to clean up; all-hawk means everyone bleeds. Evolution settles at a stable MIX where neither can do better by switching. Slide the cost of injury and watch the balance find itself.
Payoffs over a resource V, injury cost C: Hawk–Hawk (V−C)/2, Hawk–Dove V, Dove–Hawk 0, Dove–Dove V/2. When C>V the evolutionarily stable strategy is a MIXED population with hawk fraction p* = V/C — the point where a hawk and a dove earn the same, so neither type spreads. The instrument runs the replicator dynamics ṗ = p(w_H − w̄) live. A fail-loud self-check throws unless, for V=2 and C=4, the dynamics converge to p* = 0.5 = V/C from a low start — the balance emerging, not imposed.
A one-resource symmetric model — real contests add asymmetries (size, ownership → the Bourgeois strategy), repeated play, and kin. The ESS p*=V/C and the replicator convergence are exact (Maynard Smith & Price 1973).