The hawk–dove game famously introduced strategic game theory thinking into biology and forms the basis of arguments for limited aggression in animal populations. However, aggressive ‘hawks’ and peaceful ‘doves’, with strategies inherited in a discrete manner, have never been documented in a real animal population. Thus, the applicability of game-theoretic arguments to real populations might be contested. Here, we show that the head-colour polymorphism of red and black Gouldian finches (Erythrura gouldiae) provides a real-life example. The aggressive red morph is behaviourally dominant and successfully invades black populations, but when red ‘hawks’ become too common, their fitness is severely compromised (via decreased parental ability). We also investigate the effects of real-life deviations, particularly sexual reproduction, from the simple original game, which assumed asexual reproduction. A protected polymorphism requires mate choice to be sufficiently assortative. Assortative mating is adaptive for individuals because of genetic incompatibilities affecting hybrid offspring fitness, but by allowing red ‘hawks’ to persist, it also leads to significantly reduced population sizes. Because reductions in male contributions to parental care are generally known to lead to lower population productivity in birds, we expect zero-sum competition to often have wide ranging population consequences.