A hybrid game theory and mathematical programming model for solving trans-boundary water conflicts

Abstract In this research, a hybrid game theory and mathematical programming model (HGT-MPM) is proposed for solving trans-boundary water conflicts in Guanting reservoir basin (GRB) between two cities (i.e., Zhangjiakou and Beijing) in north China. A water allocation model, which considers both water quality and quantity, is developed for optimizing water use and pollutant discharge in the two cities, maximizing the net aggregate benefits from these activities and reducing the costs for water supply and pollution removal. The initial rights of water use and pollutant discharge are allocated to the cities of Beijing and Zhangjiakou, as two players based on the incorporation of a negotiation method for ill-defined water rights within the watershed. At this stage, equal treatment of every player’s benefit claim can be addressed. The strategy spaces of the two players are delineated through solving the proposed HGT-MPM with mutual benefit claim constraints. The Rubinstein bargaining solution method is employed to identify the equilibrium of bargaining. To achieve maximal benefits for the two players, starting from allocating the results of the second step, the concepts of Core and Nash solutions of cooperative games are used to generate stable basin-wide cooperative solutions. Both players find it beneficial to cooperate with side payment from the downstream to upstream. At this stage, the principle of maximum economic benefits is mainly considered. The results indicate that unclear initial water rights and pollutant discharge rights can be fairly defined through bilateral negotiations between upstream and downstream. Without side payment, the initial water rights and pollutant discharge allocation will be the final outcome, which is suboptimal, although it is better than the status quo in term of both total and individual benefits. Full cooperation with side payment leads to the greatest total net benefits and the greatest benefits to each individual city. The results not only provide a basis to allocate trans-jurisdictional water rights and pollutant discharge rights in an equal and efficient way but also provide certain inspirations for management policy improvement, such as establishing a water right trading system.

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