Optimizing water rights allocation for the Hebei section of China’s South-to-North Water Diversion Middle Route Project using asymmetric game theory

Sharing a Lifeline of Water

In northern China, millions of people and a fast-growing economy depend on water that simply is not there. To keep taps flowing and farms and factories running, China built a giant canal system that diverts water from the wetter south to the drier north. This study asks a deceptively simple question with high stakes: when there is not enough water to satisfy everyone, how should that lifeline be fairly and efficiently shared among cities in Hebei Province along the South-to-North Water Diversion Middle Route?

Why the Old Plan No Longer Fits

The current rules for dividing diverted water in Hebei were set back in 2008. Since then, the region has changed dramatically. New national plans, rapid urbanization, and the rise of Xiong’an New Area as a flagship development zone have reshaped where people live and where industry grows. Yet the official water rights—essentially each city’s guaranteed share of diverted water—have not kept pace. Some cities, such as Xiong’an New Area and Xinji, already use more water than their official share, while others cannot fully use the water they are allotted and send the excess back to rivers and lakes. This mismatch wastes scarce resources and leaves fast-growing areas undersupplied.

Turning Water Allocation into a Negotiation

Most past efforts to divide water in big transfer projects treat cities like pieces in a mathematical puzzle. A central planner runs an optimization model and announces a solution that looks ideal on paper. In reality, local governments have their own interests and bargaining power, and they can resist plans that feel unfair. To reflect this, the authors frame water allocation as a negotiation among cities rather than a one-way decision. They first build an indicator system that scores each city on three aspects: how much water it needs (for homes, factories, farms, ecosystems, and past use of diverted water), how well endowed it is with its own local water, and how efficiently it uses water. Combined weights, based on both expert judgment and data, keep this evaluation from being biased toward one viewpoint.

Giving Cities a Voice and Setting a Floor

In the first stage, each city effectively “argues” for its ideal share of diverted water. The model allows cities to emphasize the criteria that favor them, within limits that prevent gaming the system. This produces a proposed claim from each city, and together these claims exceed the total water available. The second stage introduces a bargaining framework borrowed from game theory. Here, each city is assigned a negotiation weight that blends fairness (its share of total demand) and efficiency (how much economic value it creates per unit of water). At the same time, the researchers define a breakdown point for each city: the minimum volume needed to cover basic household and industrial needs, derived from official water-use standards and recent efficiency levels. Any final allocation must respect these minimums, so no city falls below a reasonable survival threshold.

Finding a Compromise That Cities Can Live With

Using these ingredients, the authors apply an asymmetric bargaining model that rewards cities with greater demand and stronger water-use benefits, yet still anchors them to their basic needs. The result is an optimized 2030 allocation for Hebei’s share of the Middle Route: a total of 4.207 billion cubic meters is initially requested, but within the fixed national quota of 3.04 billion cubic meters, the model reshapes how much each city actually receives. Water rights for Xiong’an New Area increase sharply, by about 600 percent, and Langfang also receives a large boost, reflecting their strategic roles in national development plans. Several traditional industrial and agricultural cities, including Shijiazhuang and Hengshui, see their shares reduced, nudging them toward tighter water-saving measures, greater use of recycled water, and adjustments in industrial structure. A measure of inequality in allocation relative to demand, the Gini coefficient, falls from 0.17 to 0.04, indicating a much closer match between water supply and real needs.

What This Means for People and Policy

For a layperson, the key takeaway is that this study offers a way to split limited water that is both more realistic and more acceptable than purely top-down formulas. By treating cities as negotiating partners with different needs and strengths, and by guaranteeing basic domestic and industrial use, the method delivers a sharing plan that better supports emerging growth zones like Xiong’an New Area while still protecting other cities from serious shortages. The approach can be adapted to other large canal and river-transfer projects around the world, helping decision-makers move from rigid, outdated rules toward flexible, negotiated arrangements that balance fairness, economic benefit, and the everyday water security of millions of people.

Citation: Zhang, S., Guo, D., Wang, T. et al. Optimizing water rights allocation for the Hebei section of China’s South-to-North Water Diversion Middle Route Project using asymmetric game theory. Sci Rep 16, 13940 (2026). https://doi.org/10.1038/s41598-026-44363-1

Keywords: water allocation, inter-basin transfer, game theory, Hebei Province, South-to-North Water Diversion