Leader- Follower and Nash Bargaining Game Theory Models for Optimum Waste Load Allocation, Gheshlagh River as Case Study

Waste load allocation (WLA) is one of the most important elements when evaluating in water quality management problems. Due to multiple and sometimes conflict objectives in WLA problems, a set of Pareto optimal solutions is derived with evolutionary algorithms in which one of these Pareto fronts could be influenced by conflicts. In this research study, simulation-optimization approach was applied by QUAL2Kw simulation model and particle swarm optimization (PSO) as optimization algorithm to assign cBOD point source pollutions for specific location along Gheshlagh River. To reduce the conflicts between beneficiaries for the optimum operation of water resources in river, the level leader-follower and the Nash bargaining game theory models were applied. The results showed that the construction, maintenance and operation costs of the treatment plants for leader-follower and Nash bargaining game theories were about 192 and 293 billion Rial, respectively. The penalties for violating the environmental regulations set by the Iranian environmental protection agency (EPA) for the above theory models were found to be about 32 and 3.9 billion Rial, respectively. Furthermore, the estimated penalty tariff for each overdischarge of allowed cBOD under Stackelberg and Nash bargaining game theories were about 10.8 and 3 Rial, per environmental violation, respectively. The estimated penalty tariff in Stackelberg game is extremely close to current Iran’s EPA penalty tariff.