of meeting a dove + payoff in the chance of meeting a hawk Taking the payoff matrix results and plugging them into the above equation: Similarly for a dove: so.... Equating the two fitnesses, hawk and dove ... and solving for p so for this "static point" where the population percent is an ESS solves to be ESS(percent Hawk)=V/C Similarly, using inequalities, it can be shown that an additional hawk or dove mutant entering this ESS state eventually results in less fitness for their kind – both a true Nash and an ESS equilibrium. This example shows that when the risks of contest injury or death (the cost C) is significantly greater than the potential reward (the benefit value V), the stable population will be mixed between aggressors and doves, and the proportion of doves will exceed that of the aggressors. This explains behaviours observed in nature. Unstable games, cyclic patterns Rock paper scissors Rock paper scissors incorporated into an evolutionary game has been used for modelling natural processes in the study of ecology. Using experimental economics methods, scientists have used RPS games to test human social evolutionary dynamical behaviours in laboratories. The social cyclic behaviours, predicted by evolutionary game theory, have been observed in various laboratory experiments. Side-blotched lizard plays the RPS, and other cyclical games The first example of RPS in nature was seen in the behaviours and throat colours of a small lizard of western North America. The side-blotched lizard (Uta stansburiana) is polymorphic with three throat-colour morphs that each pursue a different mating strategy: The orange throat is very aggressive and operates over a large territory – attempting to mate with numerous females The unaggressive yellow throat mimics the markings and behavior of female lizards, and "sneakily" slips into the orange throat's territory to mate with the females there (thereby taking over the population) The blue throat mates with, and carefully guards, one female – making it impossible for the sneakers to succeed and therefore overtakes their place in a population However the blue throats cannot overcome the more aggressive orange throats. Later work showed that the blue males are altruistic to other blue males, with three key traits: they signal with blue color, they recognize and settle next to other (unrelated) blue males, and they will even defend their partner against orange, to the death. This is the hallmark of another game of cooperation that