  Here we study the effects of adopting different strategies against different
opponent instead of adopting the same strategy against all of them in the
prisoner dilemma structured in well-mixed populations. We consider an
evolutionary process in which strategies that provide reproductive success are
imitated and players replace one of their worst interactions by the new one. We
set individuals in a well-mixed population so that network reciprocity effect
is excluded and we analyze both synchronous and asynchronous updates. As a
consequence of the replacement rule, we show that mutual cooperation is never
destroyed and the initial fraction of mutual cooperation is a lower bound for
the level of cooperation. We show by simulation and mean-field analysis that
for synchronous update cooperation dominates while for asynchronous update only
cooperations associated to the initial mutual cooperations are maintained. As a
side effect of the replacement rule, an "implicit punishment" mechanism comes
up in a way that exploitations are always neutralized providing evolutionary
stability for cooperation.
