Estimation of Initial Stock in Pollution Control Problem

Abstract

A two-player differential game of pollution control with uncertain initial disturbance stock is considered. In pace with contemporary policy in the resource extraction industry, we initiate our research based on a resource extraction differential model with a rehabilitation process in which the firms are required to compensate the local to rehabilitate the polluted and dilapidated areas. Given the reality that the initial pollution stock plays a critical role in the production, and we cannot rigorously determine its actual value, a simulation of the estimation of the initial stock is alternatively investigated through the Pontryagin maximum principle (PMP). The later analytical results by normalized value of information (NVI) indicate the precious influence brought to the final payoff under various estimations of the initial stock both in the cooperative and non-cooperative cases. With such guidance, the player is capable of making a much more judicious decision when it comes to the determination of the initial stock. Furthermore, a numerical example is additionally presented for better comprehension.