The evolution of cooperation in Prisoners’ Dilemma with an endogenous learning mutant

We consider a population initially consisting of cooperators and defectors, who are engaged in a Prisoners’ 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, these equilibria are globally stable. © 2000 Elsevier Science B.V. All rights reserved. JEL classification: D83; C73; C91