Given increasing environmental awareness and industrial upgrading demands, exploring technological innovation and water conservation strategies has become crucial for water-intensive industries’ sustainable development. This study examines the complex relationships between government intervention and strategic behaviors of upstream and downstream enterprises, emphasizing blockchain technology's role. Using a differential game approach, we analyze government intervention and enterprise operational strategies from a dynamic perspective, with Jiangsu J Paper Company as our case study. Results demonstrate that government intervention in water-intensive industries is both beneficial and necessary. Blockchain implementation has effectively encouraged greater government involvement and enhanced retailer marketing efforts. When manufacturers’ blockchain collaboration costs were minimal (below 0.01), significant improvements were observed: product technological sophistication increased by 28.57%, water conservation improved by 25.93%, government revenue rose by 28.22%, and manufacturer revenue grew by 35.46%. The study also determines optimal economic conditions for retailers’ successful blockchain implementation.These findings provide valuable guidance for policy formulation and strategic planning in water-intensive industries, contributing to their sustainable development through technological innovation and improved water management practices.

  • Novel tripartite differential game model for water-intensive industries.

  • Dynamic analysis of technological progress and water efficiency.

  • Multi-stakeholder optimization for government, enterprises, and retailers.

  • Blockchain integration scenarios in sustainable industrial practices.

  • Economic conditions favoring blockchain in water-intensive sectors.

Water resources are essential for maintaining ecosystem balance and ensuring sustainable development of human society (Agarwal et al. 2023). Water-intensive industries, including textile, paper, chemical, metallurgical, power generation, and food processing sectors, depend heavily on these resources. Consequently, water conservation strategies in these sectors are critical for resource preservation (Leng et al. 2024). As industrial upgrading progresses, enterprises face the concurrent challenges of transforming and upgrading their operations while also protecting water resources (Yuan et al. 2023). To address these challenges, companies must not only invest in technological innovation and industrial upgrades but also prioritize water-saving strategies to ensure sustainable resource utilization (Bashir et al. 2024; Shah et al. 2024). It is important to note that technological advancements can complement traditional water-saving initiatives by reducing manufacturing process water footprints. For example, in mining operations, dry or semi-dry processing technologies demonstrate significant water consumption reductions compared to conventional wet processing methods (Zhu et al. 2024). Similarly, in power generation and heavy industries, the implementation of air-cooling systems in lieu of water-cooling systems reduces thermal power plant water consumption (Yang et al. 2024). To achieve sustainable development, enterprises must consider these factors and strive to balance technological innovation with water conservation. Furthermore, government intervention in resource-intensive industries is essential for ensuring rational resource utilization and conservation (Wang et al. 2024). However, determining optimal intervention strategies to promote industrial development while protecting water resources remains a significant policy challenge.

Recent studies have highlighted the effectiveness of digital technologies, including blockchain, in documenting product water footprints and enhancing sustainable water conservation efforts (Ahmed & MacCarthy 2023). Currently, an increasing number of enterprises are implementing blockchain technology to facilitate sustainable industrial development (Dong et al. 2022; Kang et al. 2024). For instance, notable implementations include Ecolab's blockchain-based water management system, which enables real-time analytics and traceable water consumption records, and IBM's blockchain-enabled smart water management initiatives. The inherent characteristics of blockchain technology – distributed ledger architecture, consensus mechanisms, and cryptographic properties – provide novel approaches for enhancing transparency and efficiency in water resource management (Cao et al. 2024). Both theoretical and empirical studies have demonstrated that blockchain implementation significantly improves production process transparency, enhances consumer trust, reduces inter-organizational transaction costs, and eliminates requirements for third-party verification (Biswas et al. 2023; Xu et al. 2023). These advancements have attracted substantial attention from both academic researchers and industry practitioners.

Water conservation represents a multidimensional process that scholars have examined from diverse perspectives, including water resource assessment and analysis (Saravani et al. 2024), regulatory framework development and enhancement (Ouyang et al. 2024), and water-saving technology advancement and implementation (Far & Ashofteh 2024; Shah et al. 2024). Additionally, significant research attention has focused on environmental impacts of water resource utilization (Bagiouk et al. 2024), and strategies for water resource management and the optimal behaviors of different societal decision-makers (Cao et al. 2024; Leng et al. 2024). Enterprise technological innovation research has extensively examined innovation typologies and strategic frameworks (Saka-Helmhout et al. 2024), decision-making processes and models (Yuan & Li 2024), resource allocation and management (Song et al. 2021), and risk management (Eid et al. 2024). Furthermore, research on the application of blockchain technology to the traceability of industrial production and operational processes is increasingly emerging. Contemporary studies in this domain examine blockchain feasibility for product traceability (Ahmed & MacCarthy 2023), the critical role of blockchain in data security (Hui et al. 2024), implications of blockchain implementation for enterprise operations and development (Biswas et al. 2023), blockchain's role in operational efficiency enhancement and transaction cost reduction (Fang et al. 2024), and its capacity to improve information transparency and consumer trust (Ma & Hu 2022).

Several limitations exist in the current literature. First, while government guidance and regulation play a crucial role in enterprise operations and development (Leng & Qi 2024), there is insufficient quantitative analysis of government interventions in water-saving decision-making within high-water-consumption industries. Second, technological innovation and industrial upgrading influence manufacturing processes and product water footprints; however, existing research on enterprise water conservation strategies inadequately addresses the interrelationship between technological innovation and water conservation decisions, particularly regarding the impact of innovations on product-level water efficiency. Third, although blockchain technology demonstrates potential for reducing intermediate costs and enhancing consumer trust in water-intensive industries (Bhubalan et al. 2022), the mechanisms by which blockchain influences government intervention strategies and stakeholder decision-making remain inadequately understood. Moreover, the economic and operational conditions necessary for successful blockchain implementation have not been systematically identified.

To address the identified gaps and deficiencies, this study examines how technological innovation and water conservation strategies under government intervention can promote sustainable development in high-water-consumption industries, with particular focus on blockchain implementation. The key contributions of this study are as follows: (1) We develop a tripartite differential game model analyzing technological innovation and water conservation decision-making in high-water-consumption industries under government intervention, comparing scenarios with and without blockchain implementation. The model accounts for dynamic changes in technological advancement and water-saving efficiency of the product. This approach offers a novel perspective for dynamic optimization modeling, yielding innovative decision-making strategies for governments and enterprises in the high-water-consumption industry. (2) We conduct systematic analysis of the interactions between enterprise technological innovation and water conservation efforts under government intervention. This study derives optimal government intervention strategies and identifies best practices for manufacturers' technological innovation and water conservation initiatives, as well as retailers' promotional strategies. (3) We investigate the mechanisms through which blockchain technology promotes sustainable development in high-water-consumption industries, examining its transformative potential. The study identifies economic parameters conducive to successful blockchain implementation in these industries. This research provides both theoretical foundations and practical guidelines for sustainable development in high-water-consumption industries, demonstrating significant practical applicability and value.

The paper is structured as follows: Section 2 presents the research framework and fundamental assumptions. Section 3 develops the theoretical model and analytical framework. Section 4 describes the numerical simulation methodology and presents detailed analytical results. Section 5 discusses the theoretical and practical implications of the findings. Section 6 concludes with key insights and managerial implications.

Problem description

Consider a two-tier supply chain comprising manufacturers and retailers in a water-intensive industry. Manufacturers produce goods that are subsequently distributed through retailers. In the context of industrial upgrades and environmental protection initiatives, manufacturers are incentivized to pursue technological innovation and implement water conservation measures to enhance both product sophistication and water use efficiency. Simultaneously, government agencies establish reward and penalty mechanisms based on the technological advancement metrics and demonstrated water conservation outcome. Retailers strategically align their operations with manufacturers' innovation decisions through various promotional mechanisms aimed at stimulating consumer demand. At the sales level, market demand is significantly influenced by consumer preferences for water-efficient products and perceived transparency of water conservation performance.

In traditional supply chains lacking blockchain implementation, consumers face information asymmetry regarding product water-saving claims, while substantial intermediate transaction costs arise from inefficient data exchange between manufacturers and retailers. Additionally, government regulatory measures require the verification of relevant data, which incurs additional costs. The adoption of blockchain technology has fundamentally transformed operations in water-intensive industries. Through the establishment of a transparent traceability system, blockchain technology creates an immutable distributed ledger that documents comprehensive product lifecycle data from production through final sale. Consequently, consumers can confidently verify the water-saving attributes of products through blockchain-registered information. The technology allows manufacturers and retailers to minimize or eliminate third-party verification requirements and associated transaction costs through the utilization of cryptographically secured data. Furthermore, governments can access accurate product-process data, thereby reducing the costs associated with regulatory verification. Figure 1 delineates the structural framework of this study, while Figure 2 illustrates the game-theoretic relationships within the mode.
Figure 1

Schematic diagram of the research structure.

Figure 1

Schematic diagram of the research structure.

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Figure 2

Schematic diagram of the game relationship.

Figure 2

Schematic diagram of the game relationship.

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Basic assumptions

Drawing upon field investigations and empirical data from water-intensive industrial sectors, including steel, thermal power generation, petroleum refining, textiles, and papermaking, this study synthesizes the relevant policies and regulations implemented by the Chinese government. Based on prior research findings (Liu et al. 2020; Xu et al. 2023), theoretical models are constructed.

Manufacturers' technological innovation investments enhance the product's technological advancement. However, the technological contribution potential diminishes over time due to equipment degradation and technological obsolescence. Consequently, the product's technological advancement follows a dynamic trajectory. Building on existing literature on technological advancement degree (Song et al. 2021), the dynamic evolution of a product's technological advanced degree can be characterized by the following differential equation:
(1)
where is the technological advanced degree of the product, is the technological innovation effort level of the manufacturer, is the effectiveness coefficient of technological innovation investment, and is the natural decay rate of technological advanced degree.
Technological advancements have demonstrably reduced the water footprint in manufacturing processes (Yang et al. 2024; Zhu et al. 2024). Additionally, corporate water-saving initiatives enhance the water efficiency of the products. However, equipment degradation and other temporal factors can diminish these water conservation benefits over time. Consequently, the dynamic evolution of product water-saving efficiency can be characterized by the following differential equation (Liu et al. 2020):
(2)
where is the water conservation degree of the product, is the manufacturer's water conservation effort level, is the effectiveness coefficient of product water-saving investment, is the influence coefficient of product technological advance on product water conservation degree, and is the natural decay rate of product water-saving degree.
Consumers demonstrate a preference for environmentally sustainable and water-saving products (Wang et al. 2021), where enhanced water conservation capabilities correlate with increased market demand. Retailers' advertising efforts also positively influence demand. However, the absence of reliable water footprint traceability throughout the product lifecycle generates consumer skepticism regarding claimed water conservation benefits (Leng et al. 2024). Considering these factors, the market demand for a product can be expressed as:
(3)
where represents the market demand, denotes the initial value of the market demand, signifies the degree of consumers' distrust in the authenticity of the product's water-saving degree, and represent the degree of water saving of the product and the impact of retailers' publicity efforts on the market demand, respectively, is the level of retailers' publicity efforts. In addition, for each unit of product sold, the marginal revenue that manufacturers and retailers can obtain is and . In addition, due to the lack of reliable data support and trust mechanisms between manufacturers and retailers, the cooperation between them needs to involve intermediate transaction costs such as product quality verification, and the unit transaction cost for manufacturers and retailers is and , respectively.
The government intervention costs, manufacturer's technological innovation and water-saving costs, and retailer's promotional costs are assumed to follow quadratic convex functions in relation to their respective effort levels. This formulation implies that marginal costs increase with effort levels, consistent with established literature (Liu et al. 2020; Fang et al. 2024). Consequently, the expenditure for each decision maker's actions can be described as follows:
(4)
where , , and are the cost coefficients corresponding to government intervention behavior, manufacturers' technological innovation and water-saving behavior, and retailers' publicity behavior respectively. The government verification cost factor describes the additional costs of government intervention due to the lack of reliable data in high-water-consumption industries. is the level of government intervention effort.
The decentralized, immutable, and transparent nature of blockchain allows decision-makers to track information pertaining to product origin, manufacturing processes, and distribution of all relevant information. This functionality enhances product information credibility and transparency while mitigating consumer skepticism regarding water conservation claims (). Furthermore, it reduces additional verification costs for manufacturers and retailers ( and ) by providing detailed data records that are accepted by both upstream and downstream stakeholders in the supply chain. Additionally, secure and reliable data records lower the cost of information verification during government interventions . Consequently, the market demand following the blockchain technology implementation reflects these advantages:
(5)

Retailers, as consumer-facing entities, demonstrate an increased propensity to adopt blockchain technology. In practice, platforms, such as Tmall and JD.com, have developed their proprietary blockchain-based product traceability systems. However, the implementation of these blockchain services necessitates recurring operational costs, denoted as , which must be considered in the retailers' cost structure.

The State Council of China implemented the ‘Action Plan for Promoting Large-Scale Equipment Renewal and Replacing Old Consumer Goods with New Ones,’ which emphasizes subsidization of manufacturing equipment acquisition and renovation while mandating the elimination of obsolete production capacity. Within the framework of national initiatives for industrial structure optimization, outdated capacity elimination, and growth driver transformation, empirical studies on governmental reward-penalty mechanisms (Wang et al. 2021; Kang et al. 2024) indicate that the government imposes penalties on enterprises failing to meet technological standards while providing subsidies to those achieving advanced technological benchmarks. Analogously, monetary penalties are levied on enterprises whose products fail to meet water conservation standards, while targeted subsidies are allocated to those achieving compliance. The influence of government intervention is as follows:
(6)
where and represent the impact of government intervention on manufacturers' earnings relative to technological progress and water conservation, respectively. and are the given product technology advanced level and product water-saving level, respectively. The model also assumes that the government assigns importance to the technological advancement and water-saving degree of the product. The government, manufacturers, and retailers are conceptualized as rational decision-makers who independently maximize their respective profits over an infinite time horizon under complete information conditions, sharing a common discount rate .

No blockchain scenario (model ON)

The interaction among government, manufacturers, and retailers is formulated as a three-stage Stackelberg differential game. In this sequential framework, the government initially establishes intervention levels targeting manufacturers. Subsequently, the manufacturer determines the investment in technological innovation and water conservation. Finally, the retailer selects the optimal publicity strategy. In this baseline model, blockchain technology is not implemented, consumer skepticism regarding product water efficiency persists, manufacturers and retailers incur cooperative transaction costs, and governmental bodies face elevated verification costs associated with regulatory intervention. Within this tripartite game framework, the decision objectives for government, manufacturers, and retailers are formulated as follows:
(7)
(8)
(9)
(10)

The Nash equilibrium for feedback strategy is derived through the Hamilton–Jacobi–Bellman (HJB) equation. The proof procedure is described in the Supplementary material. Proposition 1 characterizes the optimal equilibrium strategy and benefits of the government, manufacturers, and retailers, as well as the optimal trajectory of the product's advanced technological level and product water-saving level in the absence of blockchain implementation.

Proposition 1. In the ON model, in which blockchain technology is not implemented.
  • (1) The optimal equilibrium strategies for governments, manufacturers, and retailers are obtained as follows:
  • (2) The optimal trajectories of product technological advancement and water conservation levels are
where
  • (3) The trajectories of the benefits to governments, manufacturers, and retailers are as follows:
where

Blockchain scenario (model BC)

Blockchain implementation effectively mitigates consumer skepticism regarding product water conservation metrics, reduces manufacturer-retailer transaction costs, and minimizes governmental verification costs associated with regulatory oversight. However, retailers must bear the costs associated with implementing blockchain. The government, manufacturers, and retailers must thoroughly evaluate these factors when making decisions, which are modeled as a three-stage Stackelberg differential game. In this system, the objective functions for the respective stakeholders are formulated as follows:
(11)
(12)
(13)
(14)

For this tripartite differential game control system, the Nash equilibrium feedback strategy is derived using the HJB equation. The solution employs backward induction methodology within the Stackelberg game framework. As the solution procedure parallels that of the previous section, it is omitted to avoid redundancy. Proposition 2 presents the equilibrium results derived from the solution analysis.

Proposition 2. In the mode BC, where blockchain is implemented.
  • (1) The optimal equilibrium strategies for government, manufacturers, and retailers are as follows:
  • (2) The optimal trajectories of the technically advanced and water-saving levels of the product are
where
  • (3) The trajectories of the benefits to governments, manufacturers, and retailers are as follows:
where

Result analysis

Corollary 1. Regardless of whether blockchain is implemented or not, the government should adopt intervention strategies in high-water-consumption industries ( and ).

Corollary 1 establishes the fundamental requirement for governmental oversight in promoting technological innovation and water conservation within high-water-consumption industries. Such interventions would not only incentivize manufacturers to pursue technological advancements and industrial upgrades, thereby enhancing the technical content of their products and sustaining competitive advantages, but would also encourage the adoption of water-saving technologies. This, in turn, would improve the efficiency of water resource utilization and contribute to environmental sustainability.

Corollary 2. The comparative analysis of optimal decisions pre- and post-blockchain implementation yields: (1) Optimal government intervention intensity: ; (2) The manufacturer's optimal technical innovation level: when , , otherwise ; (3) The manufacturer's optimal water-saving level: when , , otherwise ; (4) The optimal promotion strategy of retailers: .

Corollary 2 demonstrates blockchain technology's significant impact on stakeholder behavior in water-intensive industries under government intervention. Blockchain's transparency and immutability provide retailers with verified information platforms, enhancing product visibility and market competitiveness through readily verifiable authenticity and compliance metrics. This is because consumers and regulators can readily verify the authenticity and compliance of products, thereby boosting market competitiveness. Additionally, the adoption of blockchain technology has motivated governments to increase subsidies to companies, as it allows for more precise monitoring of subsidy usage, ensuring alignment with sustainable development goals, such as water conservation and technological innovation. Moreover, the impact of blockchain on manufacturers' behavior is influenced by both its benefits and the associated collaboration costs. When manufacturers encounter lower costs in blockchain collaboration, they mitigate the information asymmetry and transaction expenses. This facilitates access to accurate data on market demand, technological trends, and policy directions, thereby improving manufacturers' efficiency in obtaining information and incentivizing investments in technological innovation and water conservation. However, high implementation costs may constrain innovation and conservation initiatives through reduced information-seeking and investment incentives.

Corollary 3. (1) A comparison of the advanced level of product technology before and after the implementation of blockchain is as follows: when , is valid; otherwise . (2) The results of the comparison of product water-saving level before and after the implementation of blockchain are as follows: when , inequality is established; otherwise .

Corollary 3 establishes that blockchain implementation's efficacy in enhancing product technological advancement and water conservation is contingent upon specific operational parameters. Notably, when manufacturers in China encounter low cooperation costs associated with blockchain adoption, the technology demonstrates significant positive effects on both product technological sophistication and water conservation efficiency. Blockchain technology enables manufacturers to track and manage resource usage more effectively and optimize production processes, thereby fostering technological innovation and water conservation. Conversely, high implementation costs may diminish blockchain's beneficial effects, potentially creating economic constraints that impede investments in technological advancement and water conservation measures. Thus, blockchain's effectiveness as a catalyst for technological progress and water efficiency optimization is predicated upon favorable cost-benefit conditions within the operational environment.

Corollary 4. If is satisfied, the inequality is true; otherwise, .

Corollary 4 establishes the economic feasibility threshold for blockchain adoption by retailers. Specifically, it identifies the threshold level at which blockchain implementation becomes economically viable. Retailers are incentivized to adopt blockchain only if the cyclical costs associated with its implementation fall below this threshold. Conversely, if these costs exceed the threshold, the adoption of blockchain may become suboptimal, potentially exacerbating the financial pressure on retailers.

To enhance the clarity and rigor of theoretical findings, this section supplements the previously derived equilibrium results by conducting numerical experiments. These simulations examine the sensitivity of equilibrium strategies to key parameter variations, providing actionable insights for managerial decision-making. The paper industry was selected as a representative case of high-water-consumption industries. Furthermore, detailed data analysis and a summary of trends across other water-intensive sectors, such as textiles, food processing, chemicals, metallurgy, mining, and pharmaceuticals, were conducted. The findings reveal that the technological innovation and water-saving strategies observed in these industries align with those identified in the study industry. This alignment further validates the generalizability and rigor of the numerical analysis presented in this study.

Jiangsu J Paper Co., Ltd, a leading paper manufacturer, specializes in the production of double-sided, single-sided, and matte-coated paper products, with an annual production capacity exceeding 2 million metric tons. In recent years, companies have made significant investments in technological innovation, enhancing the technical content and added value of their products through the research and development of advanced technologies. Regarding water conservation, the J Paper has improved water use efficiency by implementing recycled water reuse, optimizing water consumption through precise management and monitoring, and providing water-saving education and training for its employees. Additionally, the company primarily distributes its paper products through major e-commerce platforms, including Taobao and JD.com.

A quantitative analysis was conducted utilizing multi-source data from Company J, evaluating the economic efficiency and technical performance of their water treatment facility's water conservation retrofit project. The analysis incorporated comprehensive financial documentation, operational performance indicators, and facility-specific water consumption metrics from their water treatment operations. This analysis was supported by one-on-one structured interviews with 42 key practitioners, including eight plant managers, 15 technical engineers, seven environmental compliance officers, and 12 operational staff. The technical transformation data included real-time monitoring records from IoT sensors, maintenance logs, and operational performance indicators, all verified through blockchain technology implementation (accuracy rate >98.5%). Primary data were analyzed using regression analysis to identify key influential factors and their corresponding correlation coefficients. The correlation coefficients were calculated with a confidence interval of 95%. The variance inflation factor test was conducted to check for multicollinearity, with all values falling below the threshold of 5.0, confirming the independence of our variables. To ensure parameter validity and comparability, dimensionless processing techniques were applied following established methodologies (Liu et al. 2011; Leng & Qi 2024). The baseline parameters are as follows: , , , , , , , , , , , , , , , , , , , , , , , . Note that the above notations represent relative changes or impacts rather than absolute values. In addition, to isolate the effect of blockchain implementation on earnings, the baseline parameter also assumes .

The data presented in Figure 3 illustrate that, as time (t) approaches infinity, the technological advancement and water-saving efficiency of products produced by high-water-consumption industries evolve dynamically, ultimately converging to steady-state values. The costs associated with blockchain collaboration for manufacturers remain relatively low( and ). In the steady state, as depicted in Figure 3(a), blockchain implementation increased the technological sophistication of products by more than 28.57%. Similarly, Figure 3(b) indicates a corresponding 25.93% improvement in water efficiency. Moreover, Figure 3(a) indicates a monotonic increase in the product's technological advancement, while Figure 3(b) reveals a non-monotonic change in water-saving efficiency, initially decreasing and then increasing over time. Notably, at t = 3 in Figure 3(b), the water-saving efficiency reaches a minimum point (20.09 in ON mode and 22.07 in BC mode).

The benefits of the government, manufacturers, and retailers, as shown in Figure 4, follow a similar dynamic pattern to the previous state variables, exhibiting initial fluctuations before converging to a specific steady-state value. This dynamic convergence process indicates that, in the early stages of policy intervention and market competition, the benefits of the supply chain participants experience fluctuations. However, as time progresses, the system will eventually reach an equilibrium state. This suggests that decision-makers should recognize that short-term profit fluctuations are an inevitable stage of the system's self-adjustment process. Consequently, excessive intervention or frequent strategy adjustments in response to initial fluctuations should be avoided, and the focus should be on achieving long-term steady-state objectives.
Figure 3

Time-series trajectories of state variables. (a) Advanced technology level. (b) Water-saving level.

Figure 3

Time-series trajectories of state variables. (a) Advanced technology level. (b) Water-saving level.

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Figure 4

Time-series trajectories of benefits. (a) Government. (b) Manufacturer. (c) Retailer.

Figure 4

Time-series trajectories of benefits. (a) Government. (b) Manufacturer. (c) Retailer.

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This study presents sensitivity analyses under steady-state conditions to examine parametric effects. Figures 5 and 6 explore the effect of the discount rate, which reflects the patience of decision-makers, on the product's technological advancement, water-saving efficiency, and the income of each decision maker. The results demonstrate that as the discount rate increases from 0 to 1, the technological advancement, water-saving efficiency, and income of each decision maker all decline, albeit with varying elasticities. Specifically, when the discount rate increases from 0 to 0.2, the retailer's revenue decreases by 24.17% in BC mode and 33.42% in ON mode, respectively. In contrast, an increase in the discount rate from 0.8 to 1 results in more substantial declines of 91.6% (BC mode) and 88.64% (ON mode) in retailer revenue. This result indicates that the sensitivity of each equilibrium outcome diminishes as the discount rate increases across its value range.
Figure 5

Analysis of the impact of discount rate on state variables. (a) Advanced technology level. (b) Water-saving level.

Figure 5

Analysis of the impact of discount rate on state variables. (a) Advanced technology level. (b) Water-saving level.

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Figure 6

Analysis of the impact of discount rate on benefits. (a) Government. (b) Manufacturer. (c) Retailer.

Figure 6

Analysis of the impact of discount rate on benefits. (a) Government. (b) Manufacturer. (c) Retailer.

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Figures 7 and 8 examine the effects of the government's verification cost coefficient and the degree of consumer distrust on technological advancement, water-saving levels, and the income of decision-makers across different scenarios. In the model without blockchain implementation, increases in the government's verification cost factor and consumer distrust negatively impact the product's technological advancement, water-saving levels, and benefits to various decision-makers. Specifically, within the analyzed parameter space, the level of technological advancement varies between 20.3 and 43.4, while the water-saving levels range from 15.4 to 32.8, indicating that the water-saving degree is particularly sensitive to the combined effects of these parameters. Furthermore, the variation in government revenue ranges from 41.5 to 99.6, manufacturers' revenue from 237.8 to 443.61, and retailers' revenue from 216.2 to 287.6. Among these, manufacturers' revenue exhibits the highest sensitivity to the coupling effects of the parameters. Notably, in the blockchain-implemented model (BC), the avoidance of government verification costs and elimination of consumer distrust result in equilibrium outcomes that are independent of these parameter changes.
Figure 7

Analysis of the influence of parameters and on state variables. (a) Advanced technology level. (b) Water-saving level.

Figure 7

Analysis of the influence of parameters and on state variables. (a) Advanced technology level. (b) Water-saving level.

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Figure 8

Analysis of the influence of parameters and on benefits. (a) Government. (b) Manufacturer. (c) Retailer.

Figure 8

Analysis of the influence of parameters and on benefits. (a) Government. (b) Manufacturer. (c) Retailer.

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Figures 9 and 10 illustrate the effects of the technological innovation effectiveness coefficient and the water-saving effectiveness coefficient on technological advancement, product water efficiency, and decision-makers' income. The data clearly show that increases in these coefficients positively influence both the technological advancement and water-saving capabilities of the products, as well as profits for governments and retailers. When blockchain technology is implemented, equilibrium outcomes exhibit enhanced sensitivity to effectiveness coefficient variations. However, the relationship between these coefficients and manufacturer revenue follows a more complex pattern. Notably, when , manufacturers' income reaches its lowest point (ranging from 210.2 to 220.5 in ON mode and from 228.3 to 238.8 in BC mode). To maintain stable cooperation, it is crucial to avoid such a scenario.
Figure 9

Analysis of the influence of parameters q and on state variables. (a) Advanced technology level. (b) Water-saving level.

Figure 9

Analysis of the influence of parameters q and on state variables. (a) Advanced technology level. (b) Water-saving level.

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Figure 10

Analysis of the influence of parameters q and on benefits. (a) Government. (b) Manufacturer. (c) Retailer.

Figure 10

Analysis of the influence of parameters q and on benefits. (a) Government. (b) Manufacturer. (c) Retailer.

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The next step is to analyze the relationship between the threshold and parameters influencing the retailer's decision to implement blockchain technology, as discussed in Corollary 4. According to Figure 11(a), the minimum threshold value in the sample range is 2.92, which occurs when both the government verification cost coefficient and degree of consumer distrust are zero. As these factors increase, the threshold for retailers to implement blockchain technology also increases. When both the government verification cost coefficient and the level of consumer distrust reached 1, the threshold increased to 70.66. Figure 11(b) indicates that when both the technological innovation efficiency coefficient and the water-saving efficiency coefficient are at their lowest, the threshold for retailers to adopt blockchain technology is also at its lowest at 2.14. Increases in these coefficients contribute to increasing the threshold. When both the technological innovation and water-saving efficiency coefficients reach their maximum values, the threshold for blockchain implementation increases to 28.84. Furthermore, Figure 11 indicates positive correlations between the blockchain adoption threshold and both the discount rate and initial market demand.
Figure 11

Impact of different parameters on blockchain cost implementation thresholds. (a) and . (b) and q. (c) and r.

Figure 11

Impact of different parameters on blockchain cost implementation thresholds. (a) and . (b) and q. (c) and r.

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Implications of government intervention strategies

Government intervention plays a critical role in high-water-consumption industries through targeted policy mechanisms. Such interventions facilitate technological innovation, enhance water conservation efficiency, and optimize resource allocation. By implementing regulatory frameworks and incentive structures for technological advancement and water-saving investments, governments can promote sustainable industrial development while improving resource utilization efficiency. These findings corroborate previous research on the effectiveness of government intervention mechanisms (Kang et al. 2024).

Coordinated development of technological innovation and water saving

While extensive literature has also been conducted (Song et al. 2021; Li et al. 2022) to examine firms' innovation decision-making, limited research has investigated the role of technological innovation in contributing to water-saving effects. This study focuses on high-water-consumption industries and investigates how companies can develop effective operational strategies for both technological innovation and water conservation. The results demonstrate that concurrent advancement in technological innovation and water conservation measures is essential in water-intensive manufacturing sectors. Manufacturers must pursue technological competitiveness while prioritizing water resource efficiency, enabling simultaneous economic and environmental optimization.

Positive implications of blockchain implementation

The implementation of blockchain technology in water-intensive industries represents a paradigm shift in operational practice. This study departs from previous discussions of the conditions for blockchain adoption (Leng et al. 2024). The findings suggest that, when retailers adopt blockchain, it can substantially benefit other stakeholders within the industry, demonstrating considerable altruistic effects. However, the decision of retailers to implement blockchain technology involves a careful trade-off between costs and benefits. Therefore, a comprehensive evaluation is essential when considering the integration of blockchain into high-water-consumption industries. This evaluation should combine market demand, water conservation efficiency, and technological innovation effectiveness to determine the optimal timing and economic feasibility of blockchain implementation.

Applicability of the model

This study presents a multidimensional analytical framework for enterprise operational decision-making under various government interventions, including tax incentives, subsidies, and emission standards. The framework provides decision support tools applicable to resource-intensive sectors, encompassing carbon-intensive industries, land resource management, energy production, and analogous policy-constrained environments. By examining cases from high-water-consumption industries, this study yields generalizable and applicable principles and strategies, such as resource optimization, cost-benefit analysis, and risk management. These insights can be utilized by other industries with resource constraints or adjusting to government policy changes to develop more scientific and sustainable operational plans.

This research, based on differential game theory, examines sustainable development strategies in high-water-consumption industries under government intervention, specifically investigating the impact of blockchain implementation and conditions conducive to its adoption. The analysis yields three principal findings: (1) Blockchain implementation demonstrates a positive effect by facilitating increased government intervention and incentivizing retailers to enhance promotional activities. Retailers' adoption of blockchain technology results in higher revenues for both the government and manufacturers, exhibiting significant altruistic effects. (2) Blockchain implementation facilitates technological advancement and improves water conservation measures in product development, highlighting its potential role in promoting sustainable development within water-intensive industries. (3) The study demonstrates the efficacy and necessity of government intervention strategies while identifying optimal economic parameters for successful blockchain implementation by retailers.

This research provides a comprehensive analysis of operational dynamics in high-water-consumption industries under government intervention. However, the study is constrained by its model assumptions. In practice, these industries encompass multiple stakeholders, including upstream and downstream enterprises and consumers, interconnected through complex networks and exhibiting heterogeneous strategic behaviors. These complexities merit further investigation. While this study primarily employs game-theoretical analysis, emerging technologies such as big data analytics and machine learning present novel approaches for management decision-making in water-intensive industries. Future research could leverage these technologies to extract insights from large-scale datasets, forecast industry trends, optimize resource allocation, and facilitate evidence-based management decisions.

We would like to express our sincere gratitude to Mr Wang Peng and Mr Cao Zeng for their invaluable suggestions. We also extend our appreciation to the anonymous reviewers and members of the editorial team for their constructive feedback.

All authors contributed to the conception and design of the study. J.L. assumed primary responsibility for writing, constructing models, and performing calculations for the document. D. H. checked and clarified the accuracy of the proposed results. Additionally, all authors provided feedback on earlier versions of the manuscript. All the authors have thoroughly reviewed and approved the final manuscript.

This study was supported by the Qihang Project of Zhejiang University (No. 202016).

We certify that the submission is an original work and is not published in any other publications.

All authors gave explicit consent to participate in this work.

All authors gave explicit consent to publish this manuscript.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.

Agarwal
S.
,
Araral
E.
,
Fan
M.
,
Qin
Y.
&
Zheng
H.
(
2023
)
The effects of policy announcement, prices and subsidies on water consumption
,
Nature Water
,
1
(
2
),
176
186
.
https://doi.org/10.1038/s44221-023-00028-1
.
Ahmed
W. A. H.
&
MacCarthy
B. L.
(
2023
)
Blockchain-enabled supply chain traceability – How wide? How deep?
,
International Journal of Production Economics
,
263
,
108963
.
https://doi.org/10.1016/j.ijpe.2023.108963
.
Bagiouk
S.
,
Sotiriadis
D.
&
Katsifarakis
K. L.
(
2024
)
Combining pocket parks with ecological rainwater management techniques in high-density urban environments
,
Environmental Processes
,
11
(
1
),
7
.
https://doi.org/10.1007/s40710-024-00690-x
.
Bashir
M. A.
,
Qing
L.
,
Raza Syed
Q.
,
Barwińska-Małajowicz
A.
&
Hashmi
S. M.
(
2024
)
Resources policy from extraction to innovation: the interplay of minerals, geothermal energy, technological advancements, and ecological footprint in high-ecological footprint economies
,
Resources Policy
,
95
,
105182
.
https://doi.org/10.1016/j.resourpol.2024.105182
.
Bhubalan
K.
,
Tamothran
A. M.
,
Kee
S. H.
,
Foong
S. Y.
,
Lam
S. S.
,
Ganeson
K.
,
Vigneswari
S.
,
Amirul
A.-A.
&
Ramakrishna
S.
(
2022
)
Leveraging blockchain concepts as watermarkers of plastics for sustainable waste management in progressing circular economy
,
Environmental Research
,
213
,
113631
.
https://doi.org/10.1016/j.envres.2022.113631
.
Biswas
D.
,
Jalali
H.
,
Ansaripoor
A. H.
&
De Giovanni
P.
(
2023
)
Traceability vs. sustainability in supply chains: the implications of blockchain
,
European Journal of Operational Research
,
305
(
1
),
128
147
.
https://doi.org/10.1016/j.ejor.2022.05.034
.
Cao
Y.
,
Li
H.
&
Su
L.
(
2024
)
Blockchain-driven incentive mechanism for agricultural water-saving: a tripartite game model
,
Journal of Cleaner Production
,
434
,
140197
.
https://doi.org/10.1016/j.jclepro.2023.140197
.
Dong
L.
,
Jiang
P.
&
Xu
F.
(
2022
)
Impact of traceability technology adoption in food supply chain networks
,
Management Science
,
69
(
3
),
1518
1535
.
10.1287/mnsc.2022.4440
.
Eid, M. H., Eissa, M., Mohamed, E. A., Ramadan, H. S., Tamás, M., Kovács, A. & Szűcs, P. (2024) New approach into human health risk assessment associated with heavy metals in surface water and groundwater using Monte Carlo Method, Scientific Reports, 14 (1), 1008. https://doi.org/10.1038/s41598-023-50000-y.
Fang
C.
,
Chi
M.
,
Fan
S.
&
Choi
T.-M.
(
2024
)
Who should invest in blockchain technology under different pricing models in supply chains?
,
European Journal of Operational Research
,
319 (3), 777–792. https://doi.org/10.1016/j.ejor.2024.07.006
.
Far
S. M.
&
Ashofteh
P.-S.
(
2024
)
Optimization operation of water resources using game theory and marine predator algorithm
,
Water Resources Management
,
38
(
2
),
665
699
.
https://doi.org/10.1007/s11269-023-03692-w
.
Hui
L.
,
Xie
H.
&
Chen
X.
(
2024
)
Digital technology, the industrial internet, and cost stickiness
,
China Journal of Accounting Research
,
17
(
1
),
100339
.
https://doi.org/10.1016/j.cjar.2023.100339
.
Kang
Y.
,
Dong
P.
,
Ju
Y.
&
Zhang
T.
(
2024
)
Differential game theoretic analysis of the blockchain technology investment and carbon reduction strategy in digital supply chain with government intervention
,
Computers & Industrial Engineering
,
189
,
109953
.
https://doi.org/10.1016/j.cie.2024.109953
.
Leng
J.
,
Qi
X.
&
Hao
D.
(
2024
)
Optimizing water conservation strategies and blockchain integration in high-Water consumption industries across diverse power structures: a differential game approach
,
Water Resources Management.
, 38, 6079–6101.
https://doi.org/10.1007/s11269-024-03945-2
.
Li
R.
,
Rao
J.
&
Wan
L.
(
2022
)
The digital economy, enterprise digital transformation, and enterprise innovation
,
Managerial and Decision Economics
,
43
(
7
),
2875
2886
.
https://doi.org/10.1002/mde.3569
.
Liu
D.
,
Kumar
S.
&
Mookerjee
V. S.
(
2011
)
Advertising strategies in electronic retailing: a differential games approach
,
Information Systems Research
,
23
(
3–2
),
903
917
.
https://doi.org/10.1287/isre.1110.0377
.
Liu
D.
,
Kumar
S.
&
Mookerjee
V. S.
(
2020
)
Flexible and committed advertising contracts in electronic retailing
,
Information Systems Research
,
31
(
2
),
323
339
.
https://doi.org/10.1287/isre.2019.0886
.
Ma
D.
&
Hu
J.
(
2022
)
The optimal combination between blockchain and sales format in an internet platform-based closed-loop supply chain
,
International Journal of Production Economics
,
254
,
108633
.
https://doi.org/10.1016/j.ijpe.2022.108633
.
Ouyang
R.
,
Mu
E.
,
Yu
Y.
,
Chen
Y.
,
Hu
J.
,
Tong
H.
&
Cheng
Z.
(
2024
)
Assessing the effectiveness and function of the water resources tax policy pilot in China
.
Environment, Development and Sustainability
,
26
(
1
),
2637
2653
.
https://doi.org/10.1007/s10668-022-02667-y
.
Saka-Helmhout
A.
,
Álamos-Concha
P.
,
López
M. M.
,
Hagan
J.
,
Murray
G.
,
Edwards
T.
,
Kern
P.
,
Martin
I.
&
Zhang
L. E.
(
2024
)
Stakeholder engagement strategies for impactful corporate social innovation initiatives by multinational enterprises
,
Journal of International Management
,
30
(
4
),
101159
.
https://doi.org/10.1016/j.intman.2024.101159
.
Saravani
M. J.
,
Saadatpour
M.
&
Shahvaran
A. R.
(
2024
)
A web GIS based integrated water resources assessment tool for Javeh Reservoir
,
Expert Systems with Applications
,
252
,
124198
.
https://doi.org/10.1016/j.eswa.2024.124198
.
Shah
W. U. H.
,
Hao
G.
,
Yasmeen
R.
,
Yan
H.
&
Qi
Y.
(
2024
)
Impact of agricultural technological innovation on total-factor agricultural water usage efficiency: evidence from 31 Chinese provinces
,
Agricultural Water Management
,
299
,
108905
.
https://doi.org/10.1016/j.agwat.2024.108905
.
Song
J.
,
Chutani
A.
,
Dolgui
A.
&
Liang
L.
(
2021
)
Dynamic innovation and pricing decisions in a supply-chain
,
Omega
,
103
,
102423
.
https://doi.org/10.1016/j.omega.2021.102423
.
Wang
Y.
,
Xu
X.
&
Zhu
Q.
(
2021
)
Carbon emission reduction decisions of supply chain members under cap-and-trade regulations: a differential game analysis
,
Computers & Industrial Engineering
,
162
,
107711
.
https://doi.org/10.1016/j.cie.2021.107711
.
Wang
S.
,
Liu
C.
&
Zhou
Z.
(
2024
)
Government-enterprise green collaborative governance and urban carbon emission reduction: empirical evidence from green PPP programs
,
Environmental Research
,
257
,
119335
.
https://doi.org/10.1016/j.envres.2024.119335
.
Xu
X.
,
Yan
L.
,
Choi
T.-M.
&
Cheng
T. C. E.
(
2023
)
When is It wise to use blockchain for platform operations with remanufacturing?
,
European Journal of Operational Research
,
309
(
3
),
1073
1090
.
https://doi.org/10.1016/j.ejor.2023.01.063
.
Yang
Y.
,
Wu
Z.
,
Wang
B.
,
Yao
J.
,
Yang
F.
,
Zhang
Z.
&
Ren
J.
(
2024
)
Efficient water recovery and power generation system based on air-cooled fuel cell with semi-closed cathode circulation mode
,
Applied Energy
,
364
,
123125
.
https://doi.org/10.1016/j.apenergy.2024.123125
.
Yuan
N.
&
Li
M.
(
2024
)
Research on collaborative innovation behavior of enterprise innovation ecosystem under evolutionary game
,
Technological Forecasting and Social Change
,
206
,
123508
.
https://doi.org/10.1016/j.techfore.2024.123508
.
Yuan
K.
,
Cui
J.
,
Zhang
H.
&
Gao
X.
(
2023
)
Do cleaner production standards upgrade the global value chain position of manufacturing enterprises? Empirical evidence from China
.
Energy Economics
,
128
,
107185
.
https://doi.org/10.1016/j.eneco.2023.107185
.
Zhu
R.
,
Zhang
Z. J.
&
Lin
B.
(
2024
)
Impact of technological innovation on China's mining industry: perspectives of energy and environmental performance
,
Environmental Impact Assessment Review
,
108
,
107586
.
https://doi.org/10.1016/j.eiar.2024.107586
.
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