  Monitoring with implicated punishment is common in human societies to avert
freeriding on common goods. But is it effective in promoting public
cooperation? We show that the introduction of monitoring and implicated
punishment is indeed effective, as it transforms the public goods game to a
coordination game, thus rendering cooperation viable in infinite and finite
well-mixed populations. We also show that the addition of within-group
enforcement further promotes the evolution of public cooperation. However,
although the group size in this context has nonlinear effects on collective
action, an intermediate group size is least conductive to cooperative
behaviour. This contradicts recent field observations, where an intermediate
group size was declared optimal with the conjecture that group-size effects and
within-group enforcement are responsible. Our theoretical research thus
clarifies key aspects of monitoring with implicated punishment in human
societies, and additionally, it reveals fundamental group-size effects that
facilitate prosocial collective action.
