  Economic studies have shown that there are two types of regulation schemes
which can be considered as a vital part of today's global economy:
self-regulation enforced by self-regulation organizations to govern industry
practices, and government regulation which is considered as another scheme to
sustain corporate adherence. An outstanding problem of particular interest is
to understand quantitatively the role of these regulation schemes in
evolutionary dynamics. Typically, punishment usually occurs for enforcement of
regulations. Taking into account both types of punishments to curve the
regulations, we develop a game model where six evolutionary situations with
corresponding combinations of strategies are considered. Furthermore, a
semi-analytical method is developed to allow us to give an accurate estimations
of the boundaries between the phases of full defection and nondefection. We
find that, associated with the evolutionary dynamics, for infinite well-mixed
population, the mix of both punishments performs better than one punishment
alone in promoting public cooperation, but for networked population the
cooperator-driven punishment turns out to be a better choice. We also uncover
monotonous facilitating effects of synergy effect, punishment fine and feedback
sensitivity on the public cooperation for infinite well-mixed population.
Conversely, for networked population an optimal intermediate range of feedback
sensitivity is needed to best promote punishers' populations. Overall,
networked structure is overall more favorable for punishers and further for
public cooperation, because of both network reciprocity and mutualism between
punishers and cooperators who do not punish defectors.
