Reclamation of a resource extraction site: A differential game approach

Abstract

We study an extraction site reclamation problem in a two-player differential game setting over a finite time horizon. Environmental regulation requires each firm to engage in reclamation efforts during the entire lifespan of the extraction site and to pay an abandonment reclamation fee at the end of its lease term for the unclaimed pollution caused by firms’ activities. Firms determine their reclamation efforts in order to minimize their reclamation cost. We analyze and compare individual firms’ choices and the pollution stock in the noncooperative and the cooperative cases by distinguishing between situations in which firms are homogeneous and heterogeneous. We study the case in which firms have different lease durations and different degrees of environmental liability. We show that the dynamics of the reclamation efforts may be substantially different under noncooperation and cooperation, and in both cases, it is mainly determined by how the rate of time preference and the growth rate of firms’ liabilities compare. Moreover, in all scenarios, the reclamation efforts generally rise with the degree of liability and fall with the lease duration, suggesting that in order to promote better environmental outcomes, the regulators should carefully determine the lease conditions by introducing intra-term reclamation fees along with stringent environmental accountability.