  In this paper, we study how the pro-social impact due to the vigilance by
other individuals is conditioned by both environmental and evolutionary
effects. To this aim, we consider a known model where agents play a Prisoner's
Dilemma Game (PDG) among themselves and the pay-off matrix of an individual
changes according to the number of neighbors that are "vigilant", i.e., how
many neighbors watch out for her behavior. In particular, the temptation to
defect decreases linearly with the number of vigilant neighbors. This model
proved to support cooperation in specific conditions, and here we check its
robustness with different topologies, microscopical update rules and initial
conditions. By means of many numerical simulations and few theoretical
considerations, we find in which situations the vigilance by the others is more
effective in favoring cooperative behaviors and when its influence is weaker.
