In this paper we analyse a differential game comparing free trade vs autarky, with \(n=2\) heterogeneous players exploiting a common pool renewable natural resource. Players care not only about their direct performance but also about their relative achievement with comparison to other players. We introduce this "keeping up with the Joneses" or "status concern" concept as in Benchekroun and Long (2016). We first study the behaviour of each agent when they play under autarky, and we later compare it to the scenario where they can trade the resource in a common integrated market à la Benchekroun et al. (2020). Both previously mentioned papers study the symmetric case while we introduce heterogeneities between agents. Moreover, we introduce a component capturing what we call the "environmental awareness" where players also care directly about the amount of resource left. Introducing asymmetries allows us to obtain a new steady state under autarky which we call Natural Resource Poverty Trap. Furthermore, we also observe in a region how the efficient agent benefits the most, even at the expense of the inefficient player who can be worse off. An interesting novel point is the appearance of new segments in the total extraction, fragmenting this strategy into \(2n+1\) sections. We find a part in the region where the resource is relatively scarce where total welfare under free trade is greater than the total welfare under autarky in contrast to the findings of the previous researchers. In addition, our results show that when there is abundant resource, the result obtained in Benchekroun et al. (2020) holds for the efficient player while it is the opposite for the inefficient agent.

(with Jesús Marín-Solano and Jorge Navas).