Asymmetries in a Common Pool Natural Resource Oligopoly

We consider two groups of firms harvesting a common pool resource and selling their production on the same output market. They therefore compete on both the input and the output markets. Representative firms of these two groups (of potentially different sizes) differ from one another by their marginal costs. We then have a group of low marginal cost firms — referred to as “big ” firms — and a group high marginal cost firms — referred to as “small ” firms. We derive explicit Markov perfect equilibrium strategies and examine the effects of marginal cost differential and group size asymmetries on the outcomes of the game. The equilibrium strategies of the firms are characterized by three intervals of stocks over which they adopt different exploitation behavior. When the resource stock is less than a certain threshold, there is no exploitation at all. Above that threshold and below a second threshold, the firms exploit the resource at rates that are linear and increasing in the resource stock. From this second threshold on, the firms produce at the constant harvest rates they would adopt under a static Cournot game. We find that the presence of asymmetries induces discontinuities in the strategy of the big firms and consequently in the aggregate harvest rate. We also find that the small low cost firms begin exploiting the resource and revert to their static Cournot production at threshold resource stocks that are higher when they are in presence of big firms than when they are the only type in the industry. As for the big low cost firms, they begin exploiting the resource at a higher resource stock in the asymmetric case than in the symmetric case when their proportion in the industry is above some threshold, and at a lower resource stock when their share is below that threshold. They begin producing at their static Cournot harvest rate at a lower resource stock in the asymmetric setting than in the symmetric setting. We also find that the equilibrium outcomes admit one or three steady states depending on the range of the asymmetries. Moreover any of these steady states can be reached by varying the asymmetries.