Generalized Uncooperative Planar Game Theory Model for Water Distribution in Transboundary Rivers

摘要

Water distribution in transboundary rivers is a complex issue since it involves a number of environmental, socio-economic, technical, and national security factors. Based on the analysis of the characteristics of water distribution in transboundary rivers, this paper develops a generalized uncooperative planar game theory model to aid in analyzing transboundary river water distribution scenarios, in which the concept of diplomatic cost is proposed originally. The existence of a Nash equilibrium solution has been proved in terms of the model's Nikaido-Isoda function. Then, the optimal water quantity exploited from the transboundary river, and that obtained in other ways are solved with the first-order optimality conditions. A proper method for determining the ratio of exploited river water to the whole used water is proposed. Finally, a case study is used to analyze the influences of the Nash equilibrium solution's parameters on the solution itself.