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Tragedy of Open Ecosystem
Luc Doyen  1@  
1 : CNRS  (GREThA)
Centre National de la Recherche Scientifique - CNRS, Université de Bordeaux

This paper examines the role played by cooperation for the sustainable harvesting of an ecosystem. To achieve this, a bio-economic model based on a multi-species dynamics with inter-specific 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 analytically how harvesting pressure is larger in the non-cooperative case for every species. Then it is investigated to what extent gains from cooperation can also be derived for the state of the ecosystem. It turns out that cooperation clearly promotes the conservation of every species when the number of agents is high. When the number of agents remains limited, results are more complicated, especially if a species-by-species viewpoint is adopted. However, we identify two metrics involving the state of every species and accounting for their ecological interactions which exhibit gains from cooperation at the ecosystem scale in the general case. Numerical examples illustrate the mathematical findings.


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