Emergence of cooperation in a coupled socio-ecological system through a direct or an indirect social control mechanism

The successful management of a common pool resource (CPR) by its social agents is key to its sustainability. In order to maintain the ecological resource of such a coupled socio-ecological system, cooperative effort from the whole society is required and this necessitates proper social control mechanism to regulate the social order. In this paper, we explore the effects of two social control mechanisms: ostracism and voluntary enforcement, on agents that actively exploit the CPR within societies of different social network structures (as encapsulated by its average network degree). By means of numerical simulations and analytical approximation, we made inference on the dynamical behavior of the system in terms of its phase diagram. The phase diagram is found to contain a plethora of phases and associated phase transitions as we enumerate them based on a social and an ecological parameter. At a large average network degree, the features of the phases are observed to be similar for the direct voluntary enforcement and indirect ostracism mechanisms. However, these features exhibit a unique difference at low average network degree, where we uncover a new phenomenon of non-equilibrium oscillatory phase attributed to the voluntary enforcement mechanism.