Reclamation of a Resource Extraction Site Model with Random Components

Abstract

We compute the cooperative and the Nash equilibrium solutions for the discounted optimal control problem in a two-player differential game of reclamation of a resource extraction site, where each firm’s planning horizon presents the period that extraction of the resources from their site is economically viable. Hence, the planning horizon is defined by a random duration determined on the infinite time horizon. The comparison of the cooperative and Nash solutions and also the comparative statics are provided numerically. We also define the concept of “normalized value of cooperation” and explain how this concept could help us to better characterize the losses the players will face if they continue to refrain from cooperation.