If animals know their own fighting ability, the evolutionarily stable level of fighting is reduced

We consider a version of the Hawk-Dove game in which an animal knows its own fighting ability but not the ability of its opponent. For this game at evolutionary stability there is a critical level of ability such that animals with ability greater than the critical level play Hawk and animals with ability below the critical level play Dove. We define the level of fighting to be the probability of a Hawk-Hawk fight when two opponents meet. We show that even if an animal does not know the ability of its opponent, knowing its own ability results in a lower level of fighting at evolutionary stability than is found in the standard Hawk-Dove game in which there are no differences in ability or abilities are not known.