We consider a population initially consisting of cooperators and defectors,
who are engaged in a Prisoners' Dilemma. A knowledgeable mutant is introdu
ced who memorizes other players by experience. We derive a formal model whi
ch 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 av
oid exploitation by refusing interaction. Otherwise the mutant chooses the
cooperative action. According to replicator dynamics there exists a fully m
ixed equilibrium, a two-type equilibrium with sophisticated cooperators and
defectors and the defectors-only corner solution. Depending on the paramet
ers, these equilibria are globally stable. (C) 2000 Elsevier Science B.V. A
ll rights reserved. JEL classification: D83; C73; C91.