On the convergence to the Cournot equilibrium in a productive asset oligopoly

We derive a feedback equilibrium of a dynamic Cournot game where production requires exploitation of a renewable asset. As in the classical Cournot model, quantity-setting firms compete in the same market for a given homogeneous good. We show that, when the asset stock grows sufficiently fast, the unique globally asymptotically stable steady state of the dynamic Cournot game corresponds to the static Cournot solution. Initial differences between firms' production rates due to asymmetric allocations of asset stocks tend to disappear over time. When instead the asset stock grows slowly, the system does not converge to any stationary point. We also show that, within the class of linear feedback equilibrium strategies, besides the couple of strategies that stabilizes the states for every possible initial conditions, there exists another couple which is more efficient, in that it leads to higher stationary equilibrium profits for both firms, closer to the collusive outcome. Finally, we show that, as the discount rate approaches zero, there exist multiple linear feedback equilibrium strategies that induce a price trajectory that converges asymptotically to a price which is above the static Cournot equilibrium price.