Competition and cooperation in natural resources exploitation: An evolutionary game approach

We propose a dynamic model to describe the commercial exploitation, by a populationof strategically interacting agents, of a common property renewable resource. The population ofplayers is assumed to be divided into two groups: cooperators, that decide their harvesting policyby maximizing the overall profit of their group, and defectors, that just maximize their own profit.An evolutionary mechanism, based on the replicator dynamics, is introduced to describe the timechanges in the proportions of defectors and cooperators within the population. This leads us to thequalitative study of a two dimensional nonlinear dynamical system that describes the time evolutionof the resource stock and the population share between cooperators and defectors. The long runevolution of this dynamical system is analyzed by analytical and numerical methods, and the role ofsome economic and ecologic parameters is investigated.