Evolutionary Dynamics in Heterogenous Oligopolies for the Exploitation of Renewable Natural Resources

In this paper we provide an overview of some dynamic oligopoly models proposed in the literature to describe the exploitation of a common pool renewable natural resource (e.g. the fisheries) when agents can switch between different harvesting strategies. We suggest a switching mechanism which is an alternative version of the discrete-time replicator dynamics based on expected profits and myopic imitation of the better performing behaviors, often denoted as exponential replicator. We finally provide a general framework for modeling situations where authorities allow for different alternative strategies to exploit a natural resource and agents can choose among such possibilities by updating their decisions at discrete times on the basis of profitability considerations.