Hawk Dove
The most classic game (and Maynard Smith's starting point) is the Hawk Dove game. The game was conceived to analyse the animal contest problem highlighted by Lorenz and Tinbergen. It is a contest over a sharable resource, say some food. The contestants can be either Hawk or Dove… this is not two separate species of bird; it is ONE species with two different types of strategy in the same species (two different morphs). The term Hawk Dove was coined by Maynard Smith because he did his work during the Vietnam War when political views fell into one of these two camps. The strategy of the Hawk (a fighter strategy) is to first display aggression, then escalate into a fight till he either wins or else is injured. The strategy of the Dove (fight avoider) is to first display aggression but if when faced with major escalation by an opponent will run for safety. If not faced with this level of escalation the Dove will attempt to share the resource.
| meets Hawk | meets Dove | |
| if Hawk | V/2-C/2 | V |
| if Dove | 0 | V/2 |
Given that the resource is given the value V, the damage from losing a fight is given cost C:
- If a Hawk meets a Dove he gets the full resource V to himself
- If a Hawk meets a Hawk – half the time he wins, half the time he loses…so his average outcome is then V/2 minus C/2..
- If a Dove meets a Hawk he will back off and get nothing - 0
- If a Dove meets a Dove both share the resource and get V/2
The actual payoff however depends on the probability of meeting a Hawk or Dove, which in turn is a representation of the percentage of Hawks and Doves in the population when a particular contest takes place. But that population makeup in turn is determined by the results of all of the previous contests before the present contest- it is a continuous iterative process where the resultant population of the previous contest becomes the input population to the next contest. If the cost of losing C is greater than the value of winning V (the normal situation in the natural world) the mathematics ends in an ESS – an evolutionary stable strategy situation having a mix of the two strategies where the population of Hawks is V/C. The population will progress back to this equilibrium point if any new Hawks or Doves make a temporary perturbation in the population. The solution of the Hawk Dove Game explains why most animal contests involve only “ritual fighting behaviours” in contests rather than outright battles. The result does not at all depend on “good of the species” behaviours as suggested by Lorenz, but solely on the implication of actions of “selfish genes”.
Read more about this topic: Evolutionary Game Theory
Famous quotes containing the words hawk and/or dove:
“And Coleridge, too, has lately taken wing,
But like a hawk encumber’d with his hood,—
Explaining Metaphysics to the nation—
I wish he would explain his Explanation.”
—George Gordon Noel Byron (1788–1824)
“I long ago lost a hound, a bay horse, and a turtle-dove, and am still on their trail. Many are the travellers I have spoken concerning them, describing their tracks and what calls they answered to. I have met one or two who had heard the hound, and the tramp of the horse, and even seen the dove disappear behind a cloud, and they seemed as anxious to recover them as if they had lost them themselves.”
—Henry David Thoreau (1817–1862)