A Double-Layer Dynamic Differential Game Model for the Optimal Trading Quantity of Water and Price Setting in Water Rights Transactions

The increase in water demand due to industrial development and agricultural expansion and the need for ecosystem improvement call for the efficient, equitable and sustainable management of water resources. This is particularly essential in basins where water management authorities are the distributor of the initial water allocation and where incentives are lacking for improving water use efficiency. The purpose of this paper is to present an administrative and market-based game model for solving the problem of water rights transactions in a basin. To accomplish this, a double-layer dynamic differential game model is developed based on the water reallocation in the basin. In this model, the water management authorities of the basin and surrounding regions seek to maximize their own comprehensive value of the water resource/target revenue function. To obtain the optimal trading quantity of water in each region and the bargain price, the Hamiltonian and Lagrangian are introduced. A case study is presented in the Yellow River basin to demonstrate the applicability and efficiency of this method. The proposed dynamic differential game and pricing game show good performance for determining the optimal trading quantity of water in each region and the bargain price with optimal results of yen 204.3384 billion per half year and yen 409.4115 billion per year, outperforming other methodologies.