Oligopoly equilibria in nonrenewable resource markets

Abstract

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.