Editing Evolutionary game theory (section)

===Hawk dove===
[[File:HawkDove2.jpg|thumb|300px| Solution of the [[Chicken (game)|hawk dove]] game for V=2, C=10 and fitness starting base B=4. The fitness of a hawk for different population mixes is plotted as a black line, that of dove in red. An ESS (a stationary point) will exist when hawk and dove fitness are equal: Hawks are 20% of population and doves are 80% of the population.]]
{{main|Chicken (game)}}

The first game that [[Maynard Smith]] analysed is the classic ''[[Chicken (game)|hawk dove]]''{{efn|Maynard Smith chose the name "hawk dove" from descriptions of political views current during the [[Vietnam War]].}} game. It was conceived to analyse Lorenz and Tinbergen's problem, a contest over a shareable resource. The contestants can be either  a hawk or a dove. These are two subtypes or morphs of one species with different strategies. The hawk first displays aggression, then escalates into a fight until it either wins or is injured (loses). The dove first displays aggression, but if faced with major escalation runs for safety. If not faced with such escalation, the dove attempts to share the resource.<ref name=Price/>

{| class="wikitable" style="text-align:center"
|+style="white-space:nowrap"| Payoff matrix for hawk dove game
|-
|  || ''' 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:<ref name=Price/>

*If a hawk meets a dove, the hawk gets the full resource V 
*If a hawk meets a hawk, half the time they win, half the time they lose, so the average outcome is then V/2 minus C/2
*If a dove meets a hawk, the dove 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. That, in turn, is determined by the results of all of the previous contests. 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 [[evolutionarily stable strategy]] (ESS), a mix of the two strategies where the population of hawks is V/C. The population regresses 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 [[Ritualized aggression|ritual fighting]] behaviours in contests rather than outright battles. The result does not at all depend on "[[group selection|good of the species]]" behaviours as suggested by Lorenz, but solely on the implication of actions of so-called [[selfish genes]].<ref name=Price/>