  The observed cooperation on the level of genes, cells, tissues, and
individuals has been the object of intense study by evolutionary biologists,
mainly because cooperation often flourishes in biological systems in apparent
contradiction to the selfish goal of survival inherent in Darwinian evolution.
In order to resolve this paradox, evolutionary game theory has focused on the
Prisoner's Dilemma (PD), which incorporates the essence of this conflict. Here,
we encode strategies for the iterated Prisoner's Dilemma (IPD) in terms of
conditional probabilities that represent the response of decision pathways
given previous plays. We find that if these stochastic strategies are encoded
as genes that undergo Darwinian evolution, the environmental conditions that
the strategies are adapting to determine the fixed point of the evolutionary
trajectory, which could be either cooperation or defection. A transition
between cooperative and defective attractors occurs as a function of different
parameters such a mutation rate, replacement rate, and memory, all of which
affect a player's ability to predict an opponent's behavior.
