Two animals want one resource. Fight like a hawk, or back off like a dove?
Two animals meet over a resource worth a fixed payoff. A 'hawk' strategy always escalates to a fight, risking serious injury; a 'dove' strategy always backs off without a fight, settling for nothing if the other animal fights. If a population could be made entirely of hawks, or entirely of doves, would either state be stable against an invader?
Reveal the answer
Neither pure strategy is stable. An all-dove population can always be invaded by a single hawk, who wins every contest without a fight. But an all-hawk population does worse than a mixed one, since every contest risks costly injury, so doves can creep back in. The stable outcome is a mixed population, or mixed individual strategy, in a specific ratio set by the relative value of winning versus the cost of injury, a result from the 1973 model that founded evolutionary game theory.
— John Maynard Smith, George R. Price, The Logic of Animal Conflict — Nature, 1973