This paper analyzes the extent to which two factors—social networks and the severity of the scarcity of a common property resource—affect norm-complying behavior that favors cooperation. It assumes that those who comply with the social norm exercise social pressure on defectors. We develop an analytical framework that allows us to determine the minimum (maximum) share of norm-complying agents at which social networks start (stop) having an influence on cooperation. Knowing these shares allows policymakers to identify the conditions under which legal and/or informal enforcement policies for cooperation are effective and how different types of social networks affect the design of these policies. We find that stable steady states exist in which compliers and defectors coexist (partial cooperation), but the stability of such states requires that the costs of coordination among compliers to exercise social pressure are high. Full cooperation is another possible steady state but is unlikely to prevail if the agents do not perceive the scarcity of the common property resource as severe. A numerical study, empirically calibrated for an aquifer in Spain, shows that subsidizing the compliers' costs of exerting social pressure may impede the attainment of a steady state based on partial cooperation. Although social networks can promote cooperation, their influence is limited. The minimum share of compliers for attaining cooperation can be reduced by informal enforcement policies by not more than 26%. We show that combinations of different types of informal enforcement policies should be applied cautiously because they may cancel each other out.