A tragedy of the commons case study: modeling the fishers king crab system in Southern Chile.

Illegal fishing in small-scale fisheries is a contentious issue and resists a straightforward interpretation. Particularly, there is little knowledge regarding cooperative interactions between legal and illegal fishers and the potential effects on fisheries arising from these interactions. Taking the Chilean king crab (; common name centolla) fishery as a case study, our goal is twofold: (i) to model the effect of illegal-legal fishers' interactions on the fishery and (ii) analyze how management and social behavior affect fishery's outcomes. We framed the analysis of this problem within game theory combined with network theory to represent the architecture of competitive interactions. The fishers' system was set to include registered (legal) fishers and unregistered (illegal) fishers. In the presence of unregistered fishers, legal fishers may decide to cooperate (ignoring the presence of illegal fishers) or defect, which involves becoming a "super fisher" and whitewashing the captures of illegal fishers for a gain. The utility of both players, standard fisher and super fisher depend on the strategy chosen by each of them, as well as on the presence of illegal fishers. The nodes of the network represent the legal fishers (both standard and super fishers) and the links between nodes indicate that these fishers compete for the resource, assumed to be finite and evenly distributed across space. The decision to change (or not) the adopted strategy is modeled considering that fishers are subjected to variable levels of temptation to whitewash the illegal capture and to social pressure to stop doing so. To represent the vital dynamics of the king crab, we propose a model that includes the Allee effect and a term accounting for the crab extraction. We found that the super fisher strategy leads to the decrease of the king crab population under a critical threshold as postulated in the tragedy of the commons hypothesis when there are: (i) high net extraction rates of the network composed of non-competing standard fishers, (ii) high values of the extent of the fishing season, and (iii) high density of illegal fishers. The results suggest that even in the presence of super fishers and illegal fishers, the choice of properly distributed fishing/closure cycles or setting an extraction limit per vessel can prevent the king crab population from falling below a critical threshold. This finding, although controversial, reflects the reality of this fishery that, for decades, has operated under a dynamic in which whitewashing and super fishers have become well established within the system.