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 [math]\displaystyle{ R = s / 2 }[/math] but when facing a hawk the dove takes flight ([math]\displaystyle{ S = 0 }[/math]) and the hawks gets the entire resource [math]\displaystyle{ T = s }[/math]. However, if two hawks meet they escalate the conflict until one is injured at a cost [math]\displaystyle{ i }[/math] ([math]\displaystyle{ i \gt s }[/math]). Escalation thus yields on average [math]\displaystyle{ P = (s - i) / 2 }[/math]. 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 [math]\displaystyle{ b = (s + i) / 2 }[/math] and [math]\displaystyle{ c = s }[/math].

Since the Hawk-Dove game is equivalent to the Snowdrift game the payoffs can be rescaled in an analogous way which again results in [math]\displaystyle{ R = 1 }[/math],[math]\displaystyle{ P = 0 }[/math], [math]\displaystyle{ T = 1 + r }[/math] and [math]\displaystyle{ S = 1 - r }[/math] with [math]\displaystyle{ r = 2 s / (s + i) }[/math].