Research on water rights trading based on dynamic differential game: a case study of the Yellow River basin

ABSTRACT

A two-layer game model optimizes water rights trading in the Yellow River Basin. Minimizing sewage parameters (h, I) boosts efficiency and equity. Price, driven by terminal value (k) and discount rate (r), peaks stability at a saddle point. Excessively long trading cycles cause price decay and imbalance.

Rapid industrialization and urbanization are sharply increasing water demand, so efficient management, equitable allocation, and sustainable use are imperative. Amid intensifying basin-scale supply–demand imbalances, water-rights trading is a key instrument for reallocation. Guided by game theory, we construct a two-tier dynamic differential-game model of water rights allocation and pricing, validate its robustness through dynamic simulation, and apply it empirically to the Yellow River Basin. Results show that: (1) Regional optimal allocation is governed by sewage discharge proportion and unit sewage output value proportion. When both shares approach their minima, basin-wide supply efficiency peaks, the regional Gini coefficient declines, and equity improves. (2) The equilibrium trading price is positively correlated with the water's terminal value and negatively correlated with the discount rate; their interaction yields an asymmetric response surface whose saddle point maximizes price stability. (3) Trading-cycle length is positively correlated with traded volume, yet excessively long cycles trigger price decay and spatial divergence: deficits accelerate in ecologically fragile areas while surplus regions enjoy rising rents, aggravating basin-wide imbalance. The findings provide dynamic decision support for basin water rights trading and promote balanced progress between ecological conservation and high-quality economic growth.