Oligopolies in pollution permit markets: A dynamic game approach

We reconsider the pollution permit concept in a setting extended to include dynamics, spatially diversified firms, and an oligopoly in product markets. The firms can manage their pollution emissions or stocks by (1) buying pollution permits and emitting pollution, (2) shipping pollutants to other nodes and paying such shipping costs, or (3) paying environmental costs to mitigate or recycle pollution. Firms manage these controls strategically to maximize net profits while facing non-cooperative rivals. Within this setting, we show that the non-cooperative competition among firms may be represented as a differential variational inequality (DVI) framework. Furthermore, we propose decision rules on permit purchase, establish necessary conditions, and prove the existence of solution in the formalism of the DVI. We also show that the DVI can be equivalently converted to a nonlinear complementarity problem (NCP), and show this problem, despite high dimensions, is efficiently solvable using off-the-shelf software (GAMS with the PATH solver). We illustrate this method's feasibility with a computationally intensive numerical example.