We consider a population initially consisting of cooperators and defectors, who are engaged in a Prisoner's Dilemma. A knowledgeable mutant is introduced who memorizes other players by experience. We derive a formal model which allows us to describe the growth of the mutant's knowledge of defectors in a precise way. When meeting known defectors, the mutant is assumed to avoid exploitation by refusing interaction. Otherwise the mutant chooses the cooperative action. According to replicator dynamics there exists a fully mixed equilibrium, a two-type equilibrium with sophisticated cooperators and defectors and the defectors-only corner solution. Depending on the parameters, the equilibria are globally stable.
Vogt, Carsten (2000), The evolution of cooperation in Prisoners Dilemma with an endogeneous learning mutant, Journal of Economic Behavior and Organization Vol. 42, 347-73.