  The evolution and maintenance of cooperation fascinated researchers for
several decades. Recently, theoretical models and experimental evidence show
that costly punishment may facilitate cooperation in human societies, but may
not be used by winners. The puzzle how the costly punishment behaviour evolves
can be solved under voluntary participation. Could the punishers emerge if
participation is compulsory? Is the punishment inevitably a selfish behaviour
or an altruistic behaviour? The motivations behind punishment are still an
enigma. Based on public goods interactions, we present a model in which just a
certain portion of the public good is divided equally among all members. The
other portion is distributed to contributors when paying a second cost.
Contributors who are willing to pay a second cost can be costly (and then
altruistic) punishers, but they can also flourish or dominate the population,
in this case we may call them "advantageous punishers". We argue that most of
successful cooperators and punishers in nature are advantageous punishers, and
costly punishment mostly happens in humans. This indicates a universal
surviving rule: contributing more and gaining more. Our models show
theoretically that the original motivation behind punishment is to retrieve
deserved payoff from their own contributions, a selfish incentive.
