Author(s): Ruidong An
Linked Author(s): Ruidong An
Keywords: Water pollution; Synergetic control; Cooperative game; Dynamic equilibrium; Kernel
Abstract: A 1-D mathematical model of synergetic water pollution control in rivers with single pollutant was established. It was based on the classical cooperative game model. The essential concept of synergetic control is that the total discharged load and concentration of every individual pollutant source were restricted according to the impartial principle and the pollution level in the river should be controlled not to violate the criterion designated by the government. The total load allocation, the systematic planning and the laws and regulations were all taken into consideration. Based on the important static power index, or Shapley value, and the Core of the imputation sets of n-person cooperative game, the dynamic equilibrium solution, Kernel, of n-person cooperative game was introduced. The Kernel was such imputation set K, for every imputation in K, when the concentration contribution of every two distinct pollution sources were evaluated under this imputation, the available load assigned to them should be even. It assures that any pollution source can not find a reason to bargain over the price with other pollution sources.