Developing environmental penalty functions for river water quality management: application of evolutionary game theory

In this paper, a new evolutionary game theoretic methodology is proposed to determine penalty functions that an environmental protection agency should impose on dischargers to achieve water quality standards at monitoring points along the river when the monitoring points are limited. In the proposed methodology, the concept of evolutionary stable strategy in asymmetric matrix games is utilized to model the interactions among dischargers more realistically. A heuristic optimization–simulation model is developed for calculating the evolutionary stable treatment strategies of dischargers considering the mass transport equations, main characteristics of river flow and pollution loads. The proposed methodology is applied to the Zarjub River in the northern part of Iran to illustrate its practical utility. The results show that the proposed approach can determine penalty functions which guarantee that the water quality standards are met. The results of the suggested model are compared with those of a traditional optimization waste load allocation model. The comparisons show that the evolutionary game theory-based model provides stable wastewater treatment strategies which would not be violated by dischargers in practice.