Game Theory-Based Water-Carbon-Economic Synergistic Optimization Evaluation of Gray-Green Infrastructure

WANG Lei, REN Yu, XIAO Hui-zhi, TIAN Qing-hua, XIA Chen-lang, WU Yu-meng, HU Ming-xuan, CAO Yi-ning

Journal of Changjiang River Scientific Research Institute ›› 2026, Vol. 43 ›› Issue (3) : 98-109.

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Journal of Changjiang River Scientific Research Institute ›› 2026, Vol. 43 ›› Issue (3) : 98-109. DOI: 10.11988/ckyyb.20250222
Soil and Water Conservation and Ecological Restoration

Game Theory-Based Water-Carbon-Economic Synergistic Optimization Evaluation of Gray-Green Infrastructure

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Abstract

[Objective] To address the lack of carbon footprint accounting and insufficient multi-objective synergy in evaluating existing gray-green infrastructure in Sponge Cities, this study proposes a game theory-based method for life-cycle synergistic optimization evaluation of water-carbon-economic performance. [Methods] By analyzing the synergistic relationships among water environment improvement, carbon emission reduction, and economic cost over the life cycle of gray-green infrastructure, a three-dimensional (3D) indicator system—“water environment-carbon reduction-economic cost”—was developed. This system integrated key indicators such as runoff reduction rate, pollutant removal rate, life-cycle carbon emissions, and economic cost. The entropy weighting method and the analytic hierarchy process (AHP) were integrated with a game theory model to optimize indicator weights based on multi-source weighting and multi-criteria decision-making theory. The Nash equilibrium was applied to balance conflicting objectives, and the TOPSIS method was employed for the comprehensive evaluation of multiple schemes. [Results] The main campus of Hebei University of Water Resources and Electric Engineering was selected as a case study, with seven gray-green infrastructure combination schemes designed. The results indicated that Scheme 5 (a combination of storage tank, sunken green space, and rain barrel) achieved effective runoff reduction, pollutant removal rates above 48%, low economic cost, and a significant carbon sink effect, demonstrating the best overall performance. The subsequent ranking of schemes was: Scheme 3, Scheme 7, Scheme 6, Scheme 1, Scheme 4, and Scheme 2. Sensitivity analysis confirmed that Scheme 5 exhibited good stability. [Conclusion] Case study indicates that, in the game theory-based comprehensive weighting model, the carbon emission indicator carries the highest weight. This highlights the critical importance of advancing low-carbon development goals within the current decision-making framework. Concurrently, the study reveals a significant divergence in the weighting of the life-cycle cost indicator between subjective and objective weighting methods. This reflects inherent differences arising from distinct evaluation perspectives—namely, expert judgment versus quantitative data. Notably, the advantage of the game theory model lies in its ability to integrate and balance the contributions of these two methods through an equilibrium optimization mechanism, thereby effectively mitigating potential systemic biases inherent in single weighting methods. Importantly, water environment indicators, such as runoff reduction rate and pollutant removal rate, play an essential “bottom-line” role within the entire evaluation system. In pursuing low-carbon goals, these critical water environment performance indicators cannot be compromised, and the core requirements for water environment management must be strictly maintained. This research addresses the limitations of traditional methods that overemphasize technology at the expense of synergy, providing methodological support for transforming and upgrading Sponge Cities from “engineering compliance” to achieving “synergistic benefits in water-carbon-economic performance”. It provides both theoretical foundations and practical pathways for promoting low-carbon development of Sponge Cities and facilitating their synergy with the “dual carbon” goals (carbon peaking and carbon neutrality).

Key words

carbon emissions / entropy weight method / analytic hierarchy process / game theory / TOPSIS evaluation / gray-green infrastructure

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WANG Lei , REN Yu , XIAO Hui-zhi , et al . Game Theory-Based Water-Carbon-Economic Synergistic Optimization Evaluation of Gray-Green Infrastructure[J]. Journal of Changjiang River Scientific Research Institute. 2026, 43(3): 98-109 https://doi.org/10.11988/ckyyb.20250222

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