  Although empirical and theoretical studies affirm that punishment can elevate
collaborative efforts, its emergence and stability remain elusive. By
peer-punishment the sanctioning is something an individual elects to do
depending on the strategies in its neighborhood. The consequences of
unsustainable efforts are therefore local. By pool-punishment, on the other
hand, where resources for sanctioning are committed in advance and at large,
the notion of sustainability has greater significance. In a population with
free-riders, punishers must be strong in numbers to keep the "punishment pool"
from emptying. Failure to do so renders the concept of institutionalized
sanctioning futile. We show that pool-punishment in structured populations is
sustainable, but only if second-order free-riders are sanctioned as well, and
to a such degree that they cannot prevail. A discontinuous phase transition
leads to an outbreak of sustainability when punishers subvert second-order
free-riders in the competition against defectors.
