Oligopoly equilibria in nonrenewable resource markets

Most Nash-Cournot oligopoly models of nonrenewable resources apply open-loop equilibrium concepts and are based on physical resource depletion. This paper studies feedback equilibria and economic depletion. Assuming affine-quadratic functional forms, the existence, uniqueness, and explicit solutions for the equilibria are derived for duopoly and n-player oligopoly with multiple resource stocks. For the cases of nonquadratic criteria, we develop a numeric solution scheme for the Nash feedback equilibrium. This scheme is an application of a discrete time, discrete state controlled Markov chain approximation method originally developed for solving deterministic and stochastic dynamic optimization problems. In our Nash-Cournot equilibrium, the degree of concentration in supply declines over time whereas the previous models with physical depletion and open-loop equilibrium concepts predict that a Nash-Cournot resource market will develop in the direction of monopoly supply. (C) 2001 Elsevier Science B.V. All rights reserved.