Hawk-Dove game

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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 \(r = 2 s / (s + i)\).