On agreements in a nonrenewable resource market: A cooperative differential game approach

We consider a nonrenewable resource duopoly with economic exhaustion. We characterize the set of Pareto efficient equilibria. We show that when firms are sufficiently patient, there exists no Pareto efficient agreement that yields short-run gains with respect to the noncooperative equilibrium. Given a pair of stocks, there exists a unique interior Pareto efficient agreement. We characterize the set of stocks where a Pareto efficient agreement results in larger discounted sum of profits for both players. We show that social welfare under the interior Pareto efficient agreement is smaller than under non-cooperation, despite the gains from a more cost effective extraction of the resources under an agreement. (C) 2018 Elsevier B.V. All rights reserved.