The tragedy of ecosystems in open-access

This paper investigates the role played by cooperation for the sustainable harvesting of an ecosystem. To achieve this, a bio-economic model based on a multi-species Gompertz dynamics with interspecific relationships and multi-agent catches is considered. A comparison between the non cooperative and cooperative optimal strategies is carried out. Revisiting the tragedy of open-access and over exploitation issues, it is first proved how harvesting pressure is larger in the non cooperative case for every species. Then it is examined to what extent gains of cooperation can also be derived for the state of the ecosystem. It turns out that cooperation clearly promotes the biodiversity when the number of agents is high. By contrast, when the number of agents remains limited, results are more ambiguous especially if a species by species viewpoint is adopted. However, an indicator is proposed at the ecosystem scale to highlight the gain of cooperation in the general case. Numerical examples illustrate the analytical findings.