A game theoretic approach for trading discharge permits in rivers

In this paper, a new Cooperative Trading Discharge Permit (CTDP) methodology is designed for estimating equitable and efficient treatment cost allocation among dischargers in a river system considering their conflicting interests. The methodology consists of two main steps: (1) initial treatment cost allocation and (2) equitable treatment cost reallocation. In the first step, a Pareto front among objectives is developed using a powerful and recently developed multi-objective genetic algorithm known as Nondominated Sorting Genetic Algorithm-II (NSGA-II). The objectives of the optimization model are considered to be the average treatment level of dischargers and a fuzzy risk of violating the water quality standards. The fuzzy risk is evaluated using the Monte Carlo analysis. The best non-dominated solution on the Pareto front, which provides the initial cost allocation to dischargers, is selected using the Young Bargaining Theory (YBT). In the second step, some cooperative game theoretic approaches are utilized to investigate how the maximum saving cost of participating dischargers in a coalition can be fairly allocated to them. The final treatment cost allocation provides the optimal trading discharge permit policies. The practical utility of the proposed methodology for river water quality management is illustrated through a realistic case study of the Zarjub river in the northern part of Iran.