  Inspired by the fact that people have diverse propensities to punish
wrongdoers, we study a spatial public goods game with defectors and different
types of punishing cooperators. During the game, cooperators punish defectors
with class-specific probabilities and subsequently share the associated costs
of sanctioning. We show that in the presence of different punishing cooperators
the highest level of public cooperation is always attainable through a
selection mechanism. Interestingly, the selection not necessarily favors the
evolution of punishers who would be able to prevail on their own against the
defectors, nor does it always hinder the evolution of punishers who would be
unable to prevail on their own. Instead, the evolutionary success of punishing
strategies depends sensitively on their invasion velocities, which in turn
reveals fascinating examples of both competition and cooperation among them.
Furthermore, we show that under favorable conditions, when punishment is not
strictly necessary for the maintenance of public cooperation, the less
aggressive, mild form of sanctioning is the sole victor of selection process.
Our work reveals that natural strategy selection can not only promote, but
sometimes also hinder competition among prosocial strategies.
