# Hawk-Dove game

In behavioral ecology the Snowdrift game is bettern known as the Hawk-Dove game which models intraspecific competition. When competing for resources or mates hawks escalate conflicts while doves are conciliatory. If two doves meet they share the resource s and both get $$R = s / 2$$ but when facing a hawk the dove takes flight ($$S = 0$$) and the hawks gets the entire resource $$T = s$$. However, if two hawks meet they escalate the conflict until one is injured at a cost $$i$$ ($$i > s$$). Escalation thus yields on average $$P = (s - i) / 2$$. Consequently it pays to escalate when facing a dove but the dove is better off when facing a hawk. It is important to note that hawk and dove may refers to behavioral patterns of a single individual which are adopted with a certain probability. Thus the Hawk-Dove game can be viewed as a mixed strategy game. Such Hawk-Dove interactions are equivalent to the Snowdrift game with $$b = (s + i) / 2$$ and $$c = s$$.
Since the Hawk-Dove game is equivalent to the Snowdrift game the payoffs can be rescaled in an analogous way which again results in $$R = 1$$,$$P = 0$$, $$T = 1 + r$$ and $$S = 1 - r$$ with $$r = 2 s / (s + i)$$.