Selection of Imitation Strategies in Populations When to Learn or When to Replicate?

A question in the modeling of populations of imitators is if simple imitation or imitation based on learning rules can improve the fitness of the individuals. In this investigation this problem is analyzed for two kinds of imitators involved in a cooperative dilemma: One kind of imitators has a replicator heuristics, i.e. individuals which decide its new action based on actions of their neighbors, whereas a second type has a learning heuristics, i.e. individuals which use a learning rule (for short learner) in order to determine their new action. The probability that a population of learners penetrates in a population of replicators depends on a training error parameter assigned to the replicators. I show that this penetration is similar to a site percolation process which is robust to changes in the individual learning rule.