Monday, May 25, 2015

evolutionary game theory


wikipedia |  Evolutionary game theory (EGT) is the application of game theory to evolving populations of lifeforms in biology. EGT is useful in this context by defining a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. EGT originated in 1973 with John Maynard Smith and George R. Price's formalisation of the way in which such contests can be analysed as "strategies" and the mathematical criteria that can be used to predict the resulting prevalence of such competing strategies.[1]

Evolutionary game theory differs from classical game theory by focusing more on the dynamics of strategy change as influenced not solely by the quality of the various competing strategies, but by the effect of the frequency with which those various competing strategies are found in the population.[2]

Evolutionary game theory has proven itself to be invaluable in helping to explain many complex and challenging aspects of biology. It has been particularly helpful in establishing the basis of altruistic behaviours within the context of Darwinian process. Despite its origin and original purpose, evolutionary game theory has become of increasing interest to economists, sociologists, anthropologists, and philosophers.

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 non-shareable resource. The contestants can be either a Hawk or a Dove. These are not two separate species of bird; they are two subtypes of one species with two different types of strategy (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 until he either wins or is injured. The strategy of the Dove (fight avoider) is to first display aggression but if faced with major escalation by an opponent to run for safety. If not faced with this level of escalation the Dove will attempt to share the resource.

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:
  • 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 evolutionarily 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”.