Game Theory was fist applied to evolution by John Maynard-Smith and George Price in 1973. It differs from traditional game theory is that it focusses on dynamics of strategy change more than the properties of strategy equilibria, although equilibria still exist within EGT but are know as Evolutionary Stable Strategies as opposed to Nash Equilibria.
Imagine a situation in which 2 members of a species come into conflict over a resource. Within this conflict each animal has the optional to ‘fight’, ‘display’ or ‘run away’. There are 2 strategies within this species, either the Dove strategy or the Hawk strategy. In the Dave strategy, upon meeting someone also adopting the Dove strategy both “Doves” display and share the resource or upon meeting a “Hawk” the Dove runs away. Adopting the Hawk strategy entails always fighting. So upon meeting a Dove the Hawk will fight and the Dove will run away and the Hawk will take all of the resource, and upon meeting another Hawk, both will fight and one will win out. On average across many interactions with other Hawks, the payoff gained ends up being (v/2)-c where v=value of resource and c=cost.
|Dove||v/2, v/2||v, 0|
|Hawk||0, v||(v-c)/2, (v-c)/2|
The question to ask of this game is, given values v and c, which strategy will evolutionarily win out?