Research on Green Supply Chain Financing Problems Empowered by Federated Learning and Blockchain

Abstract

Amid the global transition toward carbon neutrality, digital technologies such as blockchain and federated learning offer a viable pathway to alleviating green financing constraints for small- and medium-sized enterprises (SMEs) and advancing supply chain decarbonization. Against this backdrop, this paper proposes a digital intelligence-driven financing model for green supply chains. A dynamic game model is developed to capture strategic interactions between financial institutions and SMEs in financing mode selection and credit decisions, with an evolutionary game-theoretic approach within a two-layered complex network subsequently employed to examine how key factors shape evolutionary outcomes. The results reveal that the federated learning and blockchain-enabled green supply chain financing model reshapes traditional services via digital credit construction, markedly improving lending willingness, lowering default probabilities, and deterring greenwashing. Additionally, technology usage costs, federated training incentives, and data breach risks are identified as critical determinants of bilateral financing mode choices.

1. Introduction

Against the backdrop of global climate action and the continued push for sustainable development, the low-carbon transformation of supply chains has become an inevitable trend. For many large lead firms, emissions from their own operations account for only a small proportion of total emissions. By contrast, upstream and downstream emissions across the value chain (i.e., Scope 3 emissions) account for an average of 75% of the total [1]. To achieve their emissions reduction targets, these focal firms must promote coordinated abatement efforts among small- and medium-sized enterprises (SMEs) within their supply chains. However, green transformation typically requires substantial capital investment, while most SMEs lack sufficient internal financing. Furthermore, they often face significant credit rationing when seeking external green finance due to limited collateral, low financial transparency, and incomplete environmental information. As a result, financing costs remain persistently high, creating a significant bottleneck for SMEs’ green transformation.

Green supply chain finance (GSCF) provides an effective way to broaden SMEs’ access to green financing. By combining green supply chain management, supply chain finance, and green finance, this model enables financial institutions to incorporate environmental performance criteria into conventional supply chain financing arrangements. In doing so, it facilitates targeted credit support for SMEs that meet green certification standards. A notable example is the Sustainable Supply Chain Finance Program launched by Walmart and HSBC, under which suppliers with a qualifying CDP Climate Change Report score are eligible for preferential lending rates [2].

Although existing green supply chain financing models have alleviated SMEs’ green financing constraints to some extent, there still exist considerable practical challenges. First, data silos and information asymmetry are particularly pronounced. Data fragmentation across supply chain segments, compounded by SMEs’ poor information disclosure and weak data infrastructure, constrains the efficiency of green credit assessment and financing decisions. Second, risk assessment and supervision mechanisms remain underdeveloped. Traditional risk control models struggle to effectively identify risks specific to green projects, and lax monitoring of fund usage can readily give rise to greenwashing, thereby undermining the sustainable development of green finance. Third, the coverage of green financial services continues to be narrow. The existing centralized financing system hinges heavily on focal firms’ credit endorsement, with financing services largely confined to their direct counterparties. Consequently, the green financing needs of numerous SMEs in the long-tail markets at the upstream and downstream ends of the supply chain are largely unmet.

The rapid advancement of digital intelligence technologies, notably blockchain and federated learning, has not only reshaped traditional financial service models but also serves as a critical enabler for alleviating SMEs’ financing constraints. Blockchain is a distributed digital ledger featuring decentralization, immutability, transparency, and anonymity. In green supply chain financing, it can ensure the authenticity and transparency of transaction information, thus lowering financial institutions’ risk management costs. However, blockchain alone can only ensure that on-chain information is tamper-resistant. Owing to privacy concerns, participants may be reluctant to share data, making it difficult to fully unlock the value of information. To address this limitation, Google developed federated learning, a distributed machine learning approach that enables “data availability without visibility; algorithmic mobility without data movement.” Specifically, participating entities can achieve training outcomes comparable to direct data fusion by exchanging only encrypted model parameters for aggregation and optimization, without exposing their raw data. Federated learning has thus been recognized as a pivotal solution for enabling privacy-preserving data integration [3].

In summary, blockchain ensures data authenticity and immutability, while federated learning enables effective data utilization under privacy-preserving conditions. These two technologies are mutually reinforcing and collectively propel green finance toward greater efficiency, transparency, and security. This study examines green supply chain financing driven by the integration of federated learning and blockchain, seeking to answer the following research questions: (1) Can the introduction of blockchain and federated learning effectively alleviate green financing constraints for SMEs, enhance financial institutions’ lending willingness, and reduce SMEs’ default rates? (2) Can the green financing model empowered by blockchain and federated learning effectively curb greenwashing risks? What role does government regulation play in this process? (3) If this model demonstrates advantages over traditional financing approaches in green financing contexts, what are the underlying mechanisms driving such improvements? (4) What are the key barriers and enablers influencing the adoption of this model among various stakeholders?

The marginal contributions of this study are threefold. First, it proposes a blockchain-federated learning integrated green financing model, broadening the technological governance perspective on green supply chain financing. Second, by combining sequential game analysis with dual-layer complex network evolutionary game simulation, it reveals both the mechanisms of individual strategic interactions and the evolutionary dynamics of collective behavior in green financing contexts. Third, it quantifies the effects of technological costs, training incentives, and data leakage risks on stakeholder decisions, providing implications for policy formulation.

The remainder of this paper is organized as follows. Section 2 reviews the relevant literature. Section 3 presents the implementation process of the green supply chain financing model integrating federated learning and blockchain. Section 4 develops a sequential game model and derives the equilibrium via backward induction. Section 5 introduces a dual-layer complex network evolutionary game model. Section 6 validates the theoretical results through numerical simulations. Section 7 offers extended discussion of the key findings. Section 8 concludes the paper and discusses managerial implications.

2. Literature Review

2.1. Application of Blockchain and Federated Learning in Green Finance

Blockchain presents a viable approach to addressing centralized governance risks and data trust issues within the financial sector. Its application is associated with improved transactional transparency, reduced intermediation, and lower costs [4]. In recent years, as the global sustainable development agenda has gained momentum, the application of blockchain in green finance has attracted growing scholarly interest. Extant research generally suggests that blockchain serves as a significant driver for advancing green finance. Qin et al. employed the TVP-SV-VAR model to investigate the dynamic relationships among China’s blockchain market, green finance, and the carbon neutrality process. The results indicate that a long-term positive mutual influence exists between the blockchain market and green finance [5]. Jiang et al.’s analysis based on the Dynamic Stochastic General Equilibrium (DSGE) model demonstrates that blockchain-based green finance platforms can significantly expand the scale of green credit, reduce financing costs for green enterprises, and decrease pollution emissions [6].

While scholars have widely examined blockchain-driven supply chain financing models [7,8,9], research on the application of blockchain in green financing remains relatively limited. Wang et al. focused on green manufacturers’ capital constraints and green information misreporting, constructing a blockchain-enabled green supply chain financing model. Comparing the equilibrium solutions before and after blockchain adoption, they found that blockchain enhances banks’ green credit identification efficiency, strengthens consumers’ green sensitivity, and reduces optimal carbon emissions [10]. Zhang and Kou comparatively analyzed six green supply chain financing models with and without blockchain, finding that blockchain’s promotional effects on product greenness and sales volume are constrained by adoption costs. The ‘blockchain + bank financing’ strategy constitutes the manufacturer’s optimal choice only when both blockchain costs and financing rates fall below certain thresholds [11].

Blockchain applications in green finance have attracted considerable scholarly attention. By comparison, research on federated learning in this domain remains relatively limited. Unlike blockchain, the core value of federated learning lies in its ability to enable cross-institutional collaborative modeling while preserving user privacy. This feature gives it significant potential in finance, particularly in areas such as credit evaluation, risk control, and fraud detection [12]. Wang et al. proposed the Federated Knowledge Transfer (FedKT) method, which integrates horizontal federated learning with knowledge transfer techniques such as model fine-tuning and knowledge distillation, enabling privacy-preserving collaborative modeling across multiple credit data sources while significantly mitigating the adverse impact of class imbalance on credit scoring model performance [13]. Researchers at WeBank adopted vertical federated learning for SME-lending scenarios, enabling invoice data holders and banks to jointly build a risk-control model without exposing raw data. Experimental results demonstrated that the federated model substantially outperformed the isolated model trained by the bank solely using its proprietary data [14]. Existing studies on federated learning have mainly concentrated on its technical foundations, whereas research from an economic perspective has largely revolved around incentive mechanism design [15]. Few studies have explored how federated learning can empower green finance and generate economic benefits.

2.2. Greenwashing in Green Finance

In the development of green finance, greenwashing has emerged as a critical challenge that cannot be ignored. The term “greenwashing” was coined by environmentalist Jay Westerveld in 1986 to criticize hotels that encouraged guests to reuse towels under the guise of water conservation, a practice that cloaks self-serving business interests in the language of environmental stewardship. According to Delmas and Burbano, greenwashing refers to the deliberate exaggeration by firms of either their environmental practices or the environmental benefits of their products and services, with the goal of misleading consumers [16]. Terra Choice, an environmental marketing organization in the United States, systematically identified common corporate practices of environmental misrepresentation and summarized seven typical forms, including hidden trade-offs, no proof, and vagueness [17]. Greenwashing initially emerged in the market for goods and services, but following the signing of the Paris Agreement in 2016, it has increasingly extended to areas of information disclosure, such as ESG reporting.

Greenwashing behaviors severely constrain the healthy and orderly development of the green economy. By making false or exaggerated environmental claims, greenwashing companies disrupt market information symmetry. This not only drives up investors’ screening costs and risks but also diverts capital away from genuinely low-carbon projects, ultimately impeding tangible progress in climate action. Digital technologies have emerged as promising solutions for governing greenwashing, among which the application potential of blockchain has been validated by multiple studies. Arne Nygaard and Ragnhild Silkoset used questionnaire survey data to develop and validate a structural equation model. Their findings show that, compared with traditional green certification systems, the transparent, traceable, and tamper-resistant information enabled by blockchain technology can more effectively help consumers guard against greenwashing risks and enhance their trust in green products [18]. Grounded in stakeholder theory and institutional theory, Li et al. constructed a tripartite evolutionary game model incorporating enterprises, financial institutions, and the government. By comparing stable strategies before and after blockchain adoption, they found that the reputation mechanism enabled by the consortium blockchain architecture incentivizes firms to actively pursue green innovation even under low-intensity government regulation [19]. Xu and Tian developed an evolutionary game model of bank–enterprise green credit with blockchain support. They found that corporate greenwashing can expose banks to excessive losses or high regulatory costs. Compared with traditional fines, smart contract-based automatic penalty enforcement, combined with the reputational risk from blockchain-disclosed data, is more effective in curbing corporate misconduct [20].

Current research on greenwashing modeling and analysis remains limited. First, prior studies often reduce greenwashing to a binary choice—either “truly green” or “greenwashing.” This overlooks its complexity and prevalence, failing to capture how greenwashing varies in severity and concealment, from mild misinformation to outright false advertising. Second, existing work has paid insufficient attention to greenwashing by financial institutions in green finance. For instance, they may extend loans to non-green projects to exploit preferential policies, causing resource misallocation and eroding market trust.

2.3. Application of Complex Network Evolutionary Game in Green Finance

Evolutionary game theory serves as an important analytical tool for examining green financing strategies. However, existing studies predominantly adopt the replicator dynamics framework, with models that implicitly assume an infinitely large, well-mixed population. This means that the number of players approaches infinity and any two players can interact randomly. In practice, the groups involved in green financing often exhibit structured characteristics, where actors are not randomly mixed but are embedded in complex networks of cooperation and competition. Therefore, more in-depth research on green financing requires the use of complex network evolutionary game methods that can capture the structural properties of these networks.

Complex network evolutionary game theory represents an interdisciplinary field at the intersection of complex network theory and evolutionary game theory, dedicated to examining the evolutionary dynamics of strategy interactions constrained by specific network topologies. It moves beyond the idealized assumption of a “well-mixed” population in traditional evolutionary games and situates players in more realistic social networks marked by heterogeneous connections. As such, it has become an important analytical tool for investigating decision-making interactions and behavioral diffusion among agents. For example, Yang et al. developed an evolutionary game model of green investment between suppliers and manufacturers on scale-free networks, quantitatively revealing the bidirectional effects of blockchain technology in enhancing supply chain greenness and increasing corporate profits [21]. Pan et al. built an evolutionary game model of CCUS technology diffusion among coal-to-hydrogen enterprises on small-world networks, examining how carbon trading mechanisms, technology investment costs, hydrogen prices, and policy subsidies affect firms’ technology adoption [22]. Similarly, Fan et al. employed this approach to explore how government policies drive the diffusion of green innovation among peer enterprises [23]. Although many scholars have recognized the applicability of complex network game models and applied them to the analysis of evolutionary paths and strategy diffusion, few studies to date have extended such models to the exploration of green financing strategies. Furthermore, certain studies employing single-layer complex network evolutionary game models have failed to effectively distinguish game relationships from network neighbor relationships [24].

3. Green Supply Chain Financing Model Driven by Federated Learning and Blockchain

To examine how federated learning and blockchain technologies help address the constraints of traditional green financing, this section first constructs an analytical framework drawing on information asymmetry theory, reputation theory, and data asset pricing theory, and then describes the implementation process of green supply chain financing supported by these two technologies.

3.1. Theoretical Foundation

3.1.1. Asymmetric Information Theory

The theory of asymmetric information [25,26] posits that in credit markets, borrowing firms typically possess more private information regarding their own operating conditions and project quality than financial institutions. This informational advantage tends to induce adverse selection and moral hazard. In the context of green financing, key information such as the scale of corporate environmental investment and carbon emission reduction performance is inherently opaque and dynamic, making it difficult for financial institutions to effectively distinguish genuine green projects from others through traditional credit assessment methods alone. Consequently, this leads to distorted credit rationing: on the one hand, high-quality green projects may be adversely driven out of the market due to their inability to credibly signal environmental benefits; on the other hand, high-pollution enterprises may exploit greenwashing strategies to obtain financing. This informational dilemma significantly elevates the ex-ante screening and ex-post monitoring costs for financial institutions, thereby undermining the resource allocation efficiency of green credit markets.

Federated learning and blockchain offer technological pathways to alleviate the informational constraints. Federated learning enables the integration of multi-source data from enterprises, financial institutions, and other relevant stakeholders without exposing raw data directly, enhancing the precision of identifying corporate creditworthiness, green performance, and default risk through collaborative model training. Blockchain, leveraging its traceability and immutability characteristics, strengthens the authenticity and verifiability of critical information. The organic integration of these two technologies can substantially ameliorate the information asymmetry inherent in conventional credit models and provide a more reliable data foundation for credit decision-making.

3.1.2. Reputation Theory

Reputation theory emphasizes that in repeated transactions or long-term cooperative relationships, an agent’s current behavior influences its future trading opportunities and payoff levels through the accumulation of reputation. Consequently, the reputation mechanism can serve as an important informal institutional arrangement to constrain opportunistic behavior [27]. Under the traditional green credit model, corporate default or greenwashing is narrowly identified and slowly disseminated, and penalties often rely on external government regulation. As a result, the reputational cost of dishonest behavior is insufficient to form a sustained and effective compliance constraint.

In this context, consortium blockchain provides a technological solution to this challenge. As a blockchain deployment model positioned between public and private blockchains, the consortium blockchain is jointly maintained by multiple pre-authorized nodes, with its permissions and consensus mechanisms negotiated among consortium members. This architecture combines the trust advantages of decentralization with controllable governance efficiency. In the green credit domain, key information such as corporate financing applications, project execution, compliance performance, and default records can be stored and verified in a distributed manner through the consortium blockchain, enabling cross-institutional sharing among authorized members [28]. Once a firm defaults or is found to engage in greenwashing, it faces the loss of future financing opportunities and cooperative qualifications within the consortium blockchain ecosystem, leading to a substantial increase in the reputational cost of such misconduct.

3.1.3. Data Asset Pricing Theory

As a byproduct of economic activities, data is not merely a static record of information, but a critical asset capable of enhancing prediction accuracy, mitigating uncertainty, and continuously generating economic value. Veldkamp notes that data is essentially “digitized information used for prediction,” and its core value lies in resolving risks and reducing the uncertainty faced by individuals and firms in their decision-making processes through improved prediction. If confined to the traditional cost–benefit analysis framework, the true value of data assets would be significantly underestimated [29].

In the context of green supply chain financing, federated learning enables the full realization of data asset value through cross-party collaborative modeling while preserving data privacy. Upstream and downstream enterprises in green supply chains possess dispersed yet complementary data resources, including transaction fulfillment, order flows, warehousing and logistics, and energy consumption. Under the traditional model, these data are difficult to share fully due to privacy and security concerns and ambiguous property rights boundaries. Federated learning transforms the data accumulated from corporate production operations and supply chain collaboration into digitized credit assets that can be utilized for credit assessment. Unlike the traditional model, which relies on collateral to cover default risk, the financing model driven by federated learning achieves ex-ante resolution of risk through data assets, thereby reducing dependence on the ex-post disposal of physical assets.

3.2. Implementation Process of Green Supply Chain Financing Driven by Federated Learning and Blockchain

Building upon the theoretical analysis, this section designs a consortium blockchain platform that integrates the technical advantages of blockchain and federated learning. The specific implementation process comprises the following four stages, as shown in Figure 1:

(1)

Ecosystem Collaboration and Alliance Initiation. First, the government, financial institutions, and enterprises serve as founding members to jointly establish a consortium blockchain governance committee, whose primary responsibilities include formulating alliance charters, data governance rules, and usage protocols to clarify the rights and obligations of all parties. Second, the governance committee establishes green credit admission standards and scoring systems, which serve as the basis for encoding smart credit contracts. On this foundation, a federated learning training incentive mechanism is designed to quantify and reward each party’s specific contributions. Finally, technical service providers develop a federated learning global model (which can predict a firm’s indicator scores within the green credit scoring system based on its relevant data) and, together with the governance committee, deploy the consortium blockchain platform. Financial institutions and enterprises can connect through the platform. Financial institutions joining the consortium blockchain formulate preset rules based on firm scores and their own risk control strategies within the platform’s unified framework and admission standards, designing personalized smart credit contracts to automatically complete loan approval and disbursement. After evaluating the platform’s credit and incentive policies, enterprises can access the consortium blockchain through agreement signing, becoming data nodes on the platform. Upon completion of federated learning training, the system will automatically distribute rewards to enterprises based on their data contribution values.

(2)

Data Collection and Federated Model Training. After the establishment of the consortium blockchain platform, the system will periodically coordinate internal members for federated learning training. The iterative process proceeds as follows. First, the central server uniformly distributes the initial global model to all enterprises within the consortium. Second, each participant trains the global model locally using its own proprietary data (including energy and emission data from IoT sensors, production and transportation data from smart devices, and business data from enterprise ERP systems) and subsequently uploads the encrypted parameter updates to the central server. Meanwhile, smart contracts automatically calculate each participant’s contribution based on a predefined incentive mechanism and distribute corresponding rewards to their blockchain addresses. Concurrently, the central server employs federated aggregation algorithms to update and synthesize the submitted parameters, generating an enhanced version of the global model. Finally, the server redistributes the updated model to all participants, and this training–aggregation cycle repeats iteratively until the model achieves the preset performance benchmarks. Upon convergence, the trained model can be licensed to financial institutions for a fee, enabling its application in subsequent financing scenarios.

(3)

Green Approval and Intelligent Credit. First, member enterprises within the consortium blockchain that have financing needs submit relevant data to initiate loan applications. Second, after the connected financial institutions complete preliminary reviews, they invoke the trained federated learning model on the platform, which outputs indicator scores based on the enterprise-submitted data. Subsequently, the scoring results are fed into the smart contracts pre-deployed by financial institutions, and the system automatically renders approval decisions according to the predefined credit rules, completing disbursement for approved financing projects. Key information throughout the entire loan process is recorded on the blockchain in real time, forming immutable and permanent evidence.

(4)

Online Supervision and Intelligent Audit. Regulatory authorities access the consortium blockchain platform and rely on it to build a regulatory dashboard, with its data sourced from blockchain records, enabling online and real-time monitoring of fund flows and implementation status of green credit businesses. In parallel, authorized audit institutions can directly retrieve relevant data through the platform to efficiently conduct audit work, ensuring from the source the credibility of audit results.

4. Model Construction and Game Equilibrium Analysis

4.1. Problem Description and Basic Assumptions

To demonstrate the advantages of the federated learning and blockchain-driven green supply chain financing model, this paper examines a green project financing scenario through a dynamic game model. The participating entities are financial institutions and enterprises, and their interactive decisions can be structured as a dynamic game. At the initial stage, the enterprise first chooses a loan mode: (1) Traditional mode. The enterprise applies for loans offline with financial institutions. (2) Blockchain and Federated Learning mode (BF mode). The enterprise joins the consortium blockchain and contributes to regular federated learning training, and submits online loan applications when financing needs arise.

If the enterprise chooses the traditional mode, the financial institution can respond in two ways: (1) Traditional mode. The financial institution completes credit investigation and loan approval offline following its conventional workflows. (2) BF mode. The financial institution uses the federated aggregation model to assist decision-making, while contract signing, loan disbursement, and other steps still follow traditional methods. If the enterprise chooses the BF mode, the counterparty financial institution has to be a consortium-blockchain member and also adopt the BF mode, and all business processes follow the steps described in Section 3. After the loan mode is determined, the financial institution decides whether to grant the loan. If the loan is approved, the enterprise invests the funds in the project and decides whether to repay when the loan matures. The game decision process diagram is illustrated in Figure 2.

Assumption 1.

Let $m_1$ and $m_2$ denote the return rates of green and traditional project investments, respectively. Due to the longer cycles and higher risks inherent in green projects, the return rate satisfies $m_1 <{ m}_2$ [19].

Assumption 2.

Compared with the traditional mode, the BF mode leverages the traceability, immutability, and authorized data sharing of the consortium chain to expand the dissemination of default and greenwashing behaviors, thereby strengthening reputational sanctions against relevant entities. On the other hand, it enhances the synergistic benefits of cooperation between financial institutions and enterprises. Specifically, under the traditional mode, the cooperative benefits for financial institutions and enterprises are denoted as $Y_f$ and $Y_e$, respectively; the enterprise’s reputation loss from default is $B$; and the reputation losses caused by greenwashing to the enterprise itself and to the lending institution are $N_e$ and $N_f$, respectively. Under the BF mode, the corresponding parameters become $Y_{f1}$, $Y_{e1}$, $B_1$, $N_{e1}$, and $N_{f1}$, satisfying: $Y_{f1} >{ Y}_f,{ Y}_{e1} >{ Y}_e,{ B}_1 > B, N_{e1} >{ N}_e,{ N}_{f1} >{ N}_f$.

Assumption 3.

Under the traditional mode, the probability that regulators detect the enterprise’s greenwashing behavior is $q_1$; under the BF mode, this probability is $q_2$. Through the data-sharing mechanism of blockchain and the collaborative training mechanism of federated learning, the BF mode improves the regulators’ detection probability of greenwashing, satisfying $q_2 >{ q}_1$. Correspondingly, the concealment cost increases from $H_e$ under the traditional mode to $H_{e1}$ under the BF mode, satisfying $H_{e1} >{ H}_e$.

Assumption 4.

Under the BF mode, the enterprise’s operational and production data, after computation by the federated learning global model, generate a green credit score $S_c$($S_c > 0$), which is recorded and certified by the consortium chain. The financial institution uses $S_c$ as an important basis for credit decision-making, and the enterprise thereby obtains digital credit enhancement beyond physical collateral. If the enterprise repays the loan, the score remains valid and can be used for future financing. If the enterprise defaults under the BF mode, the original credit score has failed to support its repayment ability, so $S_c$ becomes invalid and loses its predictive value for subsequent financing.

Assumption 5.

When a financial institution chooses the BF mode, it obtains information gain $W_f = {\mu }_f{I}_t$, where $I_t$ is the total information obtained by the financial institution, and ${\mu }_f$ is the information gain coefficient. The cost of using the BF mode is $T_f ={ E}_f$, including model invocation fees, blockchain operation and maintenance costs, etc. The net benefit of the financial institution’s BF participation is denoted as $W_f - T_f$. When an enterprise chooses the BF mode, it obtains digital credit $S_c$ and federated learning training rewards ${\rho }_e(I_e+O_e)$, where $I_e$ is the information contributed by the enterprise, $O_e$ is the computing and storage resources consumed in participating in federated training, and ${\rho }_e$ is the reward allocation coefficient. The total benefit for the enterprise is: $W_e = S_c + {\rho }_e(I_e +{ O}_e)$. The total cost is $T_e ={ E}_e +{ \xi }_e{O}_e +{ \epsilon }_e{I}_e$, including usage cost $E_e$, computing and storage resource cost ${\xi }_e{O}_e$, and data leakage risk cost ${\epsilon }_e{I}_e$, where ${\xi }_e$ and ${\epsilon }_e$ are the corresponding cost coefficients. The enterprise’s net benefit of BF participation is denoted as $W_e - T_e$ [30].

For ease of model construction, the relevant parameters are summarized in

Table 1. Parameter settings and meanings.

Parameter	Meaning	Parameter	Meaning
$R$	Enterprise loan amount	$r$	Green credit loan interest rate
$\gamma$	Government regulatory inspection rate	$p$	Corporate greenwashing probability
$S_m$	Collateral disposal value upon default	$C_e$	Enterprises’ financing cost under traditional mode
$q_1$	Regulatory detection probability of greenwashing under traditional mode	$q_2$	Regulatory detection probability of greenwashing under BF mode
$C_{f1},C_{f2}$	Credit investigation and lending costs for financial institutions under traditional mode	$Y_f,Y_{f1}$	Financial institutions’ cooperative benefits under traditional and BF modes
$Y_e,Y_{e1}$	Enterprises’ cooperative benefits under traditional and BF modes	$B,B_1$	Enterprises’ reputational losses from default under traditional and BF modes
$N_e,N_{e1}$	Enterprises’ reputational losses from greenwashing under traditional and BF modes	$D_f,D_e$	Government penalties on financial institutions and enterprises for detected greenwashing
$H_e,H_{e1}$	Enterprises’ concealment costs for greenwashing under traditional and BF modes	$N_f,N_{f1}$	Reputational losses inflicted on financial institutions by enterprise greenwashing under traditional and BF modes

.

4.2. Model Construction

Based on the above problem description and related assumptions, the game between the financial institution and the enterprise yields nine strategy combinations, as shown in Figure 2. Let E represent the enterprise’s payoff, and F represent the financial institution’s payoff. The derivation of the payoffs for both parties under different strategy combinations is as follows:

Case 1: Both the financial institution and the enterprise adopt the traditional mode, with the loan approved and the enterprise repaying as agreed, abbreviated as AC. In this case, the enterprise uses the loan funds for project investment, with the total revenue being $[1 + p{m}_2+(1 - p\left)m_1\right]R$, and the cooperation benefit from contract compliance being $Y_e$. The enterprise’s costs include the loan principal and interest $\left(1 + r\right)R$, and it must pay the greenwashing concealment cost $p{H}_e$ and financing cost $C_e$. If the government conducts a spot check and discovers the enterprise’s greenwashing behavior, the enterprise must pay a fine $D_e$ and suffer reputation loss $N_e$, with the total cost denoted as $\gamma p{q}_1(D_e+N_e)$. On the financial institution side, it receives loan interest income $\mathit{rR}$, gains cooperation benefits $Y_f$, and at the same time needs to pay credit investigation $C_{f1}$ and lending costs $C_{f2}$; if the government spot check finds that the financial institution has granted a loan to an enterprise engaged in greenwashing, the financial institution suffers a loss $\gamma p{q}_1(D_f+N_f)$. By organizing the above, the payoffs for the enterprise and the financial institution, $E_{\mathit{AC}}^1$ and $F_{\mathit{AC}}^1$, are:

$$E_{\mathit{AC}}^1=[p{m}_2+(1-p)m_1-r]R+Y_e-[\gamma p{q}_1(D_e+N_e) + p{H}_e+C_e]$$

(1)

$$F_{\mathit{AC}}^1=\mathit{rR}+Y_f-\left[\gamma p{q}_1\right(D_f+N_f) + C_{f1}+C_{f2}]$$

(2)

Case 2: Both the financial institution and the enterprise adopt the traditional mode, with the loan approved and the enterprise defaulting, abbreviated as AD. In this case, the enterprise’s project revenue is $[1 + p{m}_2+(1-p\left)m_1\right]R$. Although defaulting relieves the enterprise from the obligation to repay the principal and interest, it must bear default penalties ${ S}_m$ and suffer reputation loss $B$. The greenwashing concealment cost $p{H}_e$ and financing cost $C_e$ remain unchanged, and the loss from being caught greenwashing is still $\gamma p{q}_1(D_e+N_e).$ The lending financial institution loses the principal and interest amounting to $(1 + r)R$, pays credit investigation and lending costs $C_{f1}$ and $C_{f2}$, and obtains default penalty ${ S}_m$ from disposing of the enterprise’s collateral. In accordance with the relevant policy guidance of Guangdong Province, which establishes a sound risk compensation mechanism for green projects whereby financial institutions engaged in green credit and other financing businesses are provided with risk compensation based on their loss amount, when the financial institution grants a loan and the enterprise defaults, if the government discovers that the enterprise engages in greenwashing, it will no longer penalize the financial institution. Based on the above, the payoffs for the enterprise and the financial institution, $E_{\mathit{AD}}^1$ and $F_{\mathit{AD}}^1$, are:

$$E_{\mathit{AD}}^1=[1 + p{m}_2+(1-p\left)m_1\right]R - [\gamma p{q}_1(D_e+N_e) + p{H}_e+S_m+C_e+B]$$

(3)

$$F_{\mathit{AD}}^1=S_m-\left[\right(1 + r)R+C_{f1}+C_{f2}]$$

(4)

Case 3: Both the financial institution and the enterprise adopt the traditional mode, with the loan rejected, abbreviated as NN. In this case, the enterprise incurs greenwashing concealment and financing costs $p{H}_e$ and $C_e$, while the financial institution incurs credit investigation costs $C_{f1}$. The payoffs for the enterprise and the financial institution, $E_{\mathit{NN}}^1$ and $F_{\mathit{NN}}^1$, are:

$$E_{\mathit{NN}}^1 = -p{H}_{e }- C_e$$

(5)

$$F_{\mathit{NN}}^1= -C_{f1}$$

(6)

Case 4: The enterprise adopts the traditional mode and the financial institution adopts the BF mode, with the loan approved and the enterprise repaying as agreed. In this case, the enterprise does not join the consortium blockchain, so its overall revenues and costs are essentially the same as in Case 1, except that its greenwashing concealment cost increases to $p{H}_{e1}$, because the financial institution has joined the consortium blockchain and can effectively identify green projects. For the financial institution, joining the consortium blockchain allows it to use the federated aggregation model for credit assessment, without incurring traditional credit investigation costs. Meanwhile, it still incurs lending costs but earns participation benefits from the BF mode. The resulting payoffs for the enterprise and the financial institution, $E_{\mathit{AC}}^2$ and $F_{\mathit{AC}}^2$, are:

$$E_{\mathit{AC}}^2=[p{m}_2+(1-p)m_1-r]R+Y_e-[\gamma p{q}_1(D_e+N_e) + p{H}_{e1}+C_e]$$

(7)

$$F_{\mathit{AC}}^2=\mathit{rR}+Y_f-\left[\gamma p{q}_1\right(D_f+N_f) + C_{f2}] + W_f-T_f$$

(8)

Case 5: The enterprise adopts the traditional mode and the financial institution adopts the BF mode, with the loan approved and the enterprise defaulting. The payoffs can be analyzed with reference to Case 2 and Case 4. The resulting payoffs for the enterprise and the financial institution, $E_{\mathit{AD}}^2$ and $F_{\mathit{AD}}^2$, are:

$$E_{\mathit{AD}}^2=[1+p{m}_2+(1-p)m_1]R-[\gamma p{q}_1(D_e+N_e)+p{H}_{e1}+S_m+C_e+B]$$

(9)

$$F_{\mathit{AD}}^2=S_m-\left[\right(1+r)R+C_{f2}]+W_f-T_f$$

(10)

Case 6: The enterprise adopts the traditional mode and the financial institution adopts the BF mode, with the loan rejected. The payoffs can be analyzed with reference to Case 3 and Case 4. The resulting payoffs for the enterprise and the financial institution, $E_{\mathit{NN}}^2$ and $F_{\mathit{NN}}^2$, are:

$$E_{\mathit{NN}}^2= -p{H}_{e1}-C_e$$

(11)

$$F_{\mathit{NN}}^2=W_f-T_f$$

(12)

Case 7: Both the enterprise and the financial institution adopt the BF mode, with the loan approved and the enterprise repaying as agreed. In this case, the enterprise’s project investment revenue $[1+p{m}_2+(1-p\left)m_1\right]R$ remains unchanged. Nevertheless, both the enterprise and the financial institution join the consortium blockchain; their transaction information is recorded on the chain in real time. Correspondingly, the enterprise’s cooperative benefits increase to $Y_{e1}$, greenwashing concealment costs rise to $p{H}_{e1}$, and reputational loss from greenwashing increases to $N_{e1}$. In addition, the government connects to the consortium blockchain for real-time monitoring. The supervision and inspection ratio approaches $\gamma \to 1$, and the probability of detecting greenwashing increases from $q_1$ to $q_2$. Consequently, the total loss borne by the enterprise from greenwashing is $p{q}_2(D_e+N_{e1})$. Furthermore, the enterprise does not need to pay financing costs and receives BF-mode participation benefits $W_e-T_e$. The financial institution earns loan interest income $\mathit{rR}$, cooperative benefits $Y_{f1}$, and BF-mode participation benefits $W_f-T_f$, without incurring credit investigation or lending costs. However, when regulatory inspection identifies greenwashing by its cooperating enterprise, the financial institution incurs a loss of $p{q}_2(D_f+N_{f1})$. The resulting payoffs for the enterprise and the financial institution, $E_{\mathit{AC}}^3$ and $F_{\mathit{AC}}^3$, are:

$$E_{\mathit{AC}}^3=[p{m}_2+(1-p)m_1-r]R+Y_{e1}-\left[p{q}_2\right(D_e+N_{e1})+p{H}_{e1}]+W_e-T_e$$

(13)

$$F_{\mathit{AC}}^3=\mathit{rR}+Y_{f1}-p{q}_2(D_f+N_{f1})+W_f-T_f$$

(14)

Case 8: Both the enterprise and the financial institution adopt the BF mode, with the loan approved and the enterprise defaulting. The payoffs can be analyzed with reference to Case 2 and Case 7. Unlike the traditional mode, under the BF mode, once the enterprise defaults, in addition to bearing default penalties $S_m$, it also loses its digital credit $S_c$. The resulting payoffs for the enterprise and the financial institution, $E_{\mathit{AD}}^3$ and $F_{\mathit{AD}}^3$, are:

$$E_{\mathit{AD}}^3=[1+p{m}_2+(1-p\left)m_1\right]R-\left[p{q}_2\right(D_e+N_{e1})+p{H}_{e1}+S_m+S_c+B_1]+W_e-T_e$$

(15)

$$F_{\mathit{AD}}^3=S_m-(1+r)R+W_f-T_f$$

(16)

Case 9: Both the enterprise and the financial institution adopt the BF mode, with the loan rejected. Similar to Case 3, except that both parties obtain BF mode participation benefits and incur no credit investigation or financing costs. The resulting payoffs for the enterprise and the financial institution, $E_{\mathit{NN}}^3$ and $F_{\mathit{NN}}^3$, are:

$$E_{\mathit{NN}}^3=-p{H}_{e1}+W_e-T_e$$

(17)

$$F_{\mathit{NN}}^3=W_f-T_f$$

(18)

4.3. Game Equilibrium Analysis

In summary, the green supply chain financing decision can be characterized as a finite-stage complete-information dynamic game, as shown in Figure 3. The backward induction method is employed to solve for the subgame perfect Nash equilibria, starting with the credit decision stage and then moving backward to the mode selection stage.

4.3.1. Subgame Perfect Nash Equilibrium Analysis of the Credit Decision Stage

The credit decision stage comprises three subgames, as shown in Figure 4. Following the backward induction method, we first analyze the enterprise’s performance under the condition that the financial institution approves the loan, then derive the financial institution’s optimal lending decision. Taking Subgame I as an example, after the financial institution grants the loan, the enterprise compares the payoff from performance, $E_{\mathit{AC}}^1$, with the payoff from default, $E_{\mathit{AD}}^1$. The enterprise’s optimal strategy is to perform if and only if $E_{\mathit{AC}}^1>E_{\mathit{AD}}^1$. Rearranging the inequality yields the necessary and sufficient condition for the enterprise to perform:

$$B+S_m+Y_e>(1+r)R$$

(19)

If Equation (19) holds, the enterprise chooses to perform. On this basis, the financial institution compares its payoff from lending under enterprise performance, $F_{\mathit{AC}}^1$, with that from rejection, $F_{\mathit{NN}}^1$. The financial institution’s optimal strategy is to lend only if $F_{\mathit{AC}}^1>F_{\mathit{NN}}^1$. Rearranging this inequality yields the financial institution’s lending condition under enterprise performance:

$$\mathit{rR}+Y_f>\gamma p{q}_1(D_f+N_f)+C_{f2}$$

(20)

If Equation (19) fails, i.e., $B+S_m+Y_e<(1+r)R$, the enterprise’s optimal strategy after the financial institution grants the loan is to default. In this case, the financial institution compares its payoff from lending under enterprise default, $F_{\mathit{AD}}^1$, with that from rejection, $F_{\mathit{NN}}^1$. The condition for the financial institution to choose lending is $F_{\mathit{AD}}^1>F_{\mathit{NN}}^1$, which can be further rearranged as:

$$S_m>(1+r)R+C_{f2}$$

(21)

Since both $B$ and $Y_e$ are positive, the failure of Equation (19) implies $S_m<(1+r)R$, which contradicts Equation (21). Therefore, the equilibrium of grant with enterprise default does not exist in Subgame I. In summary, the subgame perfect Nash equilibrium of Subgame I can be concluded as follows: if Equations (19) and (20) hold simultaneously, the equilibrium is (Grant, Perform); otherwise, the equilibrium is (Reject, —). The analysis for Subgame II and Subgame III is similar, and the equilibrium results and parameter constraints for the credit decision stage are summarized in

Table 2. Subgame perfect equilibrium and parametric conditions in credit decision stage.

Subgame	Equilibrium Outcome	Parameter Constraints
I: TM + TM	(Grant, Perform)	$B+S_m+Y_e>(1+r)R$, and $\mathit{rR}+Y_f>\gamma p{q}_1(D_f+N_f)+C_{f2}$
	(Reject, —)	The above conditions are not met
II: TM + BF	(Grant, Perform)	$B+S_m+Y_e>(1+r)R$, and $\mathit{rR}+Y_f>\gamma p{q}_1(D_f+N_f)+C_{f2}$
	(Reject, —)	The above conditions are not met.
III: BF + BF	(Grant, Perform)	$B_1+S_m+S_c+Y_{e1}>(1+r)R$, and $\mathit{rR}+Y_{f1}>p{q}_2(D_f+N_{f1})$
	(Reject, —)	The above conditions are not met.

.

Proposition 1.

The BF model strengthens enterprise performance incentives through reputational constraints and digital credit enhancement.

Proof of Proposition 1.

From Assumptions 2 and 4, $B_1>B$, $Y_{e1}>Y_e$, and $S_c>0$. Therefore, $B_1+S_m+S_c+Y_{e1}>B+S_m+Y_e$. Combined with the enterprise performance threshold conditions in Table 2, the enterprise’s performance incentive in Subgame III is significantly stronger than in Subgames I and II. □

Proposition 1 characterizes the intrinsic mechanism by which the BF mode mitigates enterprise default risk. In the traditional mode, the condition for enterprise performance is $B+S_m+Y_e>(1+r)R$, where $B$ is the reputational loss from default, $S_m$ represents the asset loss from collateral disposal, and $Y_e$ is the cooperative benefits from performance. In the traditional mode, information is fragmented and opaque, which hinders the effective transmission of enterprise conduct. The reputational loss from default $B$ and the cooperative benefits from performance $Y_e$ are both relatively limited. The enterprise’s performance decision primarily depends on the comparison between collateral value $S_m$ and debt repayment $(1+r)R$. For enterprises with insufficient collateral assets, the inequality $B+S_m+Y_e<(1+r)R$ holds, making default the optimal strategy.

Distinct from the traditional mode, the BF mode relies on the consortium blockchain for trusted information storage and leverages federated learning to extract digital credit value, thereby reshaping the enterprise’s payoff structure. On the one hand, once both financial institutions and enterprises access the consortium blockchain, the entire transaction process becomes traceable, and relevant information can be shared and circulated with member authorization. Consequently, the enterprise’s cooperative benefits from performance $Y_{e1}$ and reputational loss from default $B_1$ are significantly quantified (enterprise performance is more easily translated into continuous cooperation opportunities or financing convenience, while default may lead to exclusion from the consortium chain, hindering future cooperation with other chain members or financing through the chain). Their impact far exceeds the corresponding values in the traditional mode ($Y_e$ and $B$). This explicit reputation mechanism constitutes a powerful external constraint. On the other hand, the application of federated learning breaks down information silos, enhances the financial institution’s ability to acquire and verify information, promotes the release of supply chain data value, and strengthens the enterprise’s credit capital accumulation ($S_c>0$). In summary, within a quantified reputational mechanism and a symmetric, traceable information environment, performance emerges as the enterprise’s optimal strategy.

Proposition 2.

Compared to the traditional mode, financial institutions are more sensitive to corporate greenwashing risk under the BF mode.

Proof of Proposition 2.

From Equations (1) and (13), the partial derivatives of $F_{\mathit{AC}}^1$ and $F_{\mathit{AC}}^3$ (the lending payoffs under the traditional and BF modes, respectively) with respect to the enterprise’s greenwashing probability $p$ are:

$${\displaystyle \frac{\partial F_{\mathit{AC}}^1}{\partial p}}=-\gamma q_1(D_f+N_f)$$

(22)

$${\displaystyle \frac{\partial F_{\mathit{AC}}^3}{\partial p}}=-q_2(D_f+N_{f1})$$

(23)

From Assumption 2, $q_2>q_1$, $N_{f1}>N_f$, and $0<\gamma \le 1$. Comparing Equations (22) and (23) yields:

$$\left|{\displaystyle \frac{\partial F_{\mathit{AC}}^3}{\partial p}}\right|>\left|{\displaystyle \frac{\partial F_{\mathit{AC}}^1}{\partial p}}\right|$$

(24)

Equation (24) indicates that the magnitude of the decrease in the financial institution’s lending payoff as the corporate greenwashing probability rises is greater under the BF mode than under the traditional mode. □

Proposition 2 reveals the difference in financial institutions’ sensitivity to corporate greenwashing risk between the two financing modes. Under the traditional mode, constrained by limited regulatory resources and immature greenwashing-detection technologies, both the regulatory authority’s inspection ratio $\gamma$ and its capacity to detect greenwashing behavior $q_1$ are relatively low. Coupled with limited reputational losses $N_f$, the financial institution’s lending payoff exhibits relatively low sensitivity to variations in the greenwashing probability. Under such circumstances, financial institutions lack economic incentives to proactively screen greenwashing-prone enterprises. Instead, pressured by green-credit-related performance appraisals, they may be motivated to grant loans to enterprises with severe greenwashing. Under the BF mode, the consortium blockchain ensures data transparency and authorized sharing, expanding reputational losses to $N_{f1}$, while federated learning improves identification accuracy through collaborative modeling, raising the detection probability to $q_2$. The marginal sensitivity of the financial institution’s lending payoff to the greenwashing probability increases substantially. If a financial institution grants loans to enterprises with a high greenwashing probability, its expected payoff declines sharply, rendering proactive loan rejection its dominant strategy. This proposition characterizes, from a marginal perspective, the superiority of the BF mode over the traditional mode in curbing greenwashing.

Proposition 3.

Unilateral adoption of the BF mode by financial institutions does not alter the credit decision equilibrium.

Proof of Proposition 3.

Through backward induction, it is found that the equilibrium outcomes and parameter conditions for Subgame I and Subgame II are completely identical. □

Financial institutions adopting the BF mode can help reduce credit investigation costs and improve approval efficiency. However, unilateral digitalization by financial institutions is insufficient to eliminate information asymmetry. Since enterprises are not part of the on-chain verifiable information system, their true green attributes and operational status lack effective data support. The reputational constraint mechanism of the consortium blockchain and the digital credit enhancement effect of federated learning cannot take effect. Consequently, Subgame II does not yield a fundamental equilibrium improvement compared to Subgame I. This proposition indicates that the governance effect of the BF mode exhibits synergistic characteristics. Only when both financial institutions and enterprises jointly adopt it can the technology truly play its empowering role.

4.3.2. Subgame Perfect Nash Equilibrium Analysis of the Mode Selection Stage

In the mode selection stage, based on the equilibrium results of the credit decision stage, both the financial institution and the enterprise compare their final payoffs under the traditional mode and the BF mode, and choose the optimal financing mode accordingly. According to Table 1, each subgame in the credit decision stage has two possible equilibrium outcomes, and the equilibrium outcomes and their parameter conditions for Subgame I and Subgame II are identical. Therefore, the mode selection stage can be summarized into four subgames, whose specific types and meanings are shown in Figure 5.

The backward induction method is also employed here. First, we analyze the financial institution’s optimal response after the enterprise selects a financing mode. Then derive the enterprise’s mode selection strategy. The equilibrium outcomes and parameter constraints are shown in

Table 3. Subgame perfect equilibrium and parametric conditions in mode selection stage.

Subgame	Equilibrium Outcome	Mode Selection Stage Parameter Constraints
IV: Insufficient collateral, low greenwashing	(BF, BF, Grant, Perform)	$W_f-T_f>-C_{f1}$, and $[p{m}_2+(1-p)m_1-r]R+Y_{e1}-p{q}_2(D_e+N_{e1})+W_e-T_e>-C_e$
	(TM, BF, Reject, —)	$W_f-T_f>-C_{f1}$, and $[p{m}_2+(1-p)m_1-r]R+Y_{e1}-p{q}_2(D_e+N_{e1})+W_e-T_e<-C_e$
	(TM, TM, Reject, —)	$W_f-T_f<-C_{f1}$, and $[p{m}_2+(1-p)m_1-r]R+Y_{e1}-p\left[q_2\right(D_e+N_{e1})+(H_{e1}-H_e\left)\right]+W_e-T_e<-C_e$
V: Sufficient collateral, high greenwashing, high regulation	(BF, BF, Reject, —) (TM, BF, Reject, —)	$W_f-T_f>-C_{f1}$, and $W_e-T_e>-C_e$ $W_f-T_f>-C_{f1}$, and $W_e-T_e<-C_e$
	(TM, TM, Reject, —)	$W_f-T_f<-C_{f1}$, and $-p{H}_{e1}+W_e-T_e<-p{H}_e-C_e$
VI: Sufficient collateral, high greenwashing, low regulation	(BF, BF, Reject, —)	$W_f-T_f>-C_{f1}$, and $[p{m}_2+(1-p)m_1-r]R+Y_e-[\gamma p{q}_1(D_e+N_e)+C_e]<W_e-T_e$
	(TM, BF, Grant, Perform)	$W_f-T_f>-C_{f1}$, and $[p{m}_2+(1-p)m_1-r]R+Y_e-\left[\gamma p{q}_1\right(D_e+N_e)+C_e]>W_e-T_e$
	(TM, TM, Grant, Perform)	$W_f-T_f<-C_{f1}$, and $[p{m}_2+(1-p)m_1-r]R+Y_e-p\left[\gamma q_1\right(D_e+N_e)+(H_e-H_{e1}\left)\right]-C_e>W_e-T_e$
VII: Sufficient collateral, low greenwashing	(BF, BF, Grant, Perform) (TM, BF, Grant, Perform)	$W_f-T_f>-C_{f1}$, and $\left(Y_{e1}-Y_e\right)+W_e-T_e>p\left[q_2\left(D_e+N_{e1}\right)-\gamma q_1\left(D_e+N_e\right)\right]-C_e$ $W_f-T_f>-C_{f1}$, and $(Y_{e1}-Y_e)+W_e-T_e<p\left[q_2\right(D_e+N_{e1})-\gamma q_1(D_e+N_e)]-C_e$
	(TM, TM, Grant, Perform)	$W_f-T_f<-C_{f1}$, and $(Y_{e1}-Y_e)+W_e-T_e<p\left[q_2\right(D_e+N_{e1})-\gamma q_1(D_e+N_e)+(H_{e1}-H_e)]-C_e$

.

Proposition 4.

The net participation benefit of the BF mode is a key factor influencing mode selection. Specifically:

(1) 

The basic condition for a financial institution to adopt the BF mode is that its net participation benefit exceeds the credit investigation cost under the traditional mode:

$$W_f-T_f>-C_{f1}$$

(25)

(2) 

The basic condition for an enterprise to adopt the BF mode is:

$$W_e-T_e>-C_e+{\delta }_k,\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}(k=\mathit{IV},V,\mathit{VI},\mathit{VII})\hspace{0.33em}$$

(26)

Here, $W_e-T_e$ is the enterprise’s net participation benefit from the BF mode, $C_e$ is the enterprise’s financing cost under the traditional mode, and ${\delta }_k$ takes different values across the four subgame scenarios:

$${\delta }_k=\{\begin{array}{cc}p{q}_2(D_e+N_{e1})-[p{m}_2+(1-p)m_1-r]R-Y_{e1}& k=\mathit{IV}\\ 0& k=V\\ [p{m}_2+(1-p)m_1-r]R+Y_e-\gamma p{q}_1(D_e+N_e)& k=\mathit{VI}\\ p\left[q_2\right(D_e+N_{e1})-\gamma q_1(D_e+N_e\left)\right]-(Y_{e1}-Y_e)& k=\mathit{VII}\end{array}$$

(27)

Proof of Proposition 4.

The equilibrium outcomes and parameter constraints for the mode selection decision stage are obtained via backward induction and summarized in Table 3. Across all four subgames, the condition for the financial institution to choose the BF mode is uniformly $W_f-T_f>-C_{f1}$. Similarly, after rearrangement, the condition for the enterprise to choose the BF mode is $W_e-T_e>-C_e+{\delta }_k$. □

Proposition 4 indicates that financial institutions and enterprises have different decision mechanisms for adopting the BF mode. As the capital supplier, the financial institution’s adoption decision depends on whether its net participation benefit from the BF mode (the difference between information gain and participation cost) exceeds the credit investigation cost under the traditional mode. The adoption threshold for financial institutions is constant across all subgames ($-C_{f1}$), unaffected by factors like cooperative payoff, regulatory intensity, or corporate greenwashing probability. That is, a financial institution’s decision to adopt the BF mode depends solely on whether the BF mode offers cost improvements over traditional credit investigation methods. In contrast, the enterprise’s decision logic is far more complex. It depends not only on whether the net participation benefit can cover the financing cost under the traditional mode, but also on multiple factors, including project gains, regulatory intensity, cooperative benefits, greenwashing penalties, and greenwashing probability.

In Subgames V and VII, the equilibrium outcomes in the credit decision stage are identical between the traditional and BF modes. However, in Subgames IV and VI, if both the financial institution and the enterprise adopt the BF mode, it can promote lending and performance in scenarios with insufficient collateral and low greenwashing probability; whereas in scenarios with sufficient collateral and high greenwashing probability, even under weak regulation, the financial institution will still choose to reject the loan. The following two corollaries present the factors affecting the BF-mode adoption threshold in Subgames IV and VI.

Corollary 1.

In scenarios with insufficient collateral and low greenwashing probability, the higher the cooperative payoff of the BF mode, the lower the adoption threshold for the BF mode.

Proof of Corollary 1.

From the expression for ${\delta }_{\mathit{IV}}$ in Proposition 4, ${\displaystyle \frac{\partial {\delta }_{\mathit{IV}}}{\partial Y_{e1}}}=-1<0$. □

Corollary 2.

In scenarios with sufficient collateral, high greenwashing probability, and weak regulation, a lower traditional mode cooperative payoff and a stronger greenwashing detection capability both reduce the BF mode adoption threshold, facilitating the enterprise’s switch from the traditional mode to the BF mode. The impact of the greenwashing probability on the adoption threshold is conditional. When $(m_2-m_1)R>\gamma q_1(D_e+N_e)$, the excess project payoff from greenwashing dominates, and an increase in the greenwashing probability raises the BF mode adoption threshold (inhibiting the enterprise’s switch to BF). When $(m_2-m_1)R<\gamma q_1(D_e+N_e)$, the deterrent effect of penalties dominates, and an increase in the greenwashing probability lowers the BF mode adoption threshold (promoting the enterprise’s switch to BF).

Proof of Corollary 2.

${\displaystyle \frac{\partial {\delta }_{\mathit{VI}}}{\partial Y_e}}>0,{\displaystyle \frac{\partial {\delta }_{\mathit{VI}}}{\partial q_1}}<0$, and the derivative with respect to p is given by:

$${\displaystyle \frac{\partial {\delta }_{\mathit{VI}}}{\partial p}}=\underset{\begin{array}{c}Marginal project payoff \\ increment from greenwashing\end{array}}{\underbrace{(m_2-m_1)R}}-\underset{\begin{array}{c}Marginal penalty increment\\ from greenwashin\end{array}}{\underbrace{\gamma q_1(D_e+N_e)}}$$

(28)

When $(m_2-m_1)R>\gamma q_1(D_e+N_e)$, ${\displaystyle \frac{\partial {\delta }_{\mathit{VI}}}{\partial p}}>0$; otherwise, ${\displaystyle \frac{\partial {\delta }_{\mathit{VI}}}{\partial p}}<0$. □

5. Diffusion and Evolution Rules of Strategic Behavior in Green Supply Chain Financing

The previous section, based on a finite-stage complete information dynamic game, characterized the optimal decision-making process of a single financial institution and a single enterprise under a given information structure. It derived the subgame perfect Nash equilibria under different parameter scenarios using backward induction. However, green supply chain financing is not an isolated single-instance game between a financial institution and an enterprise. Instead, it is embedded in a complex network where multiple financial institutions and enterprises interact and interconnect. An individual’s strategy choice is driven not only by its own payoff but also by the payoffs of neighboring agents and group interactions. Therefore, relying solely on the static equilibrium analysis in Section 4 is insufficient to reveal the diffusion path of the BF mode at the group level and its long-term stability. On this basis, this paper further introduces a two-layer complex network evolutionary game framework. While retaining the payoff settings from Section 4, it examines the dynamic evolutionary process of financial institution and enterprise strategies within group interactions, aiming to verify and expand upon the previous theoretical analysis conclusions.

The two-layer network model for green supply chain financing based on complex network theory is depicted in Figure 6. The upper and lower network layers consist of financial institutions and enterprises, respectively. Edges between nodes within the same layer represent imitative learning and interaction relationships among financial institutions (or among enterprises). Edges between nodes across the two layers represent the credit game relationships between financial institutions and enterprises. Referring to previous studies, the topological structures of both the financial institution network and the enterprise network are set as scale-free networks, implying the existence of a few hub nodes with high connectivity, such as dominant financial institutions or core enterprises in the supply chain.

During the evolution process, although agents cannot predict other players’ strategies in the next round, they can infer from the previous round’s outcomes and determine their own next-round strategies under the principle of payoff maximization. The specific evolution rules are as follows. First, each node sequentially interacts with all its neighboring nodes in the other layer and accumulates payoffs. Second, it observes neighbors within its own layer that adopt different strategies and computes the average payoff for each strategy. Meanwhile, assuming the strategies of inter-layer neighbors remain fixed from the previous round, the node selects the neighbor strategy with the highest average payoff for imitative learning, and applies this strategy to the previous round’s interactions to obtain a virtual payoff. Finally, by comparing the payoffs from the two rounds, each node’s strategy update probability follows the Fermi rule [31]:

$$P_{S_i\to S_j}={\displaystyle \frac{1}{1+\mathit{exp}\left[\right(U_i-U_j)/k]}}$$

(29)

Here, $S_i$ and $S_j$ denote the strategy actually adopted by the node in the previous round and the strategy to be updated in the next round, respectively. $U_i$ and $U_j$ are the actual payoff from the previous round and the virtual payoff from the second game, respectively. The parameter $k$ is the irrationality intensity parameter, reflecting the degree of irrational behavior of each node due to environmental noise. $k\to \infty$ implies completely random strategy updates, while $k\to 0$ implies completely rational updates, meaning if the actual payoff is less than the virtual payoff $(U_i<U_j)$, the agent will imitate the neighbor’s strategy with probability 1. During the evolution process on the two-layer network, after nodes update their strategies with probability $P_{S_i\to S_j}$, the inter-layer edges also need to be updated simultaneously (reconnecting with nodes in the other layer with a certain probability). Based on the preferential attachment characteristic of connections between nodes in scale-free networks (nodes with stronger resource endowments are more likely to establish cooperative relationships with other nodes), the probability ${\omega }_{\mathit{ij}}$ that node $i$ rewires to node $j$ is defined as follows [32]:

$${\omega }_{\mathit{ij}}={\displaystyle \frac{D_j^{\eta }}{\sum _{i\in G}{D}_i^{\eta }}},j\in G$$

(30)

$D_i$ and $D_j$ represent the current degrees of node $i$ and node $j$, respectively, $G$ is the set of all nodes in the network, and $\eta$ is the preference tendency coefficient. A larger $\eta$ gives more weight to node degree in the reconnection probability, leading to a stronger preferential attachment effect in the network.

6. Numerical Simulation and Analysis

6.1. Numerical Simulation Procedure

Based on the two-layer complex network game model and evolutionary strategy update rules described above, the simulation algorithm is designed as follows:

Step 1: Initialize the two-layer complex network. Randomly assign strategies to all nodes in the upper and lower layers, and set initial values for the simulation iteration count and all relevant parameters.

Step 2: Each node plays games with all its inter-layer neighbors and calculates both the accumulated payoff and the virtual payoff.

Step 3: Each node updates its strategy according to the Fermi rule presented in the preceding section, using Equation (29).

Step 4: Based on the preferential attachment mechanism characteristic of scale-free networks, perform edge breaking and rewiring according to Equation (30).

Step 5: Iterate Steps 2–4 until the preset maximum number of iterations is reached.

6.2. Numerical Simulation Analysis

Blockchain and related digital technologies have gained significant traction in China’s green supply chain finance sector. A notable example is Hubei Yihua Chemical Industry Co., Ltd., which collaborated with the Hubei Branch of China Construction Bank to implement blockchain-enabled intelligent management across its entire supply chain. Building upon the preceding theoretical analysis, this section presents numerical simulations implemented in Python 3.9, with parameters set based on the real-world case of Hubei Yihua and the established literature.

The simulation parameters are specified as follows. The complex network is constructed with 200 financial institution nodes and 200 enterprise nodes. The evolution period is set to $T=200$, and the total loan amount $R$ is normalized to 100. In the traditional mode, financial institutions bear a credit investigation cost of $C_{f1}=5$ and a lending operation cost of $C_{f2}=5$, while enterprises incur a financing cost of $C_e=3$. The benchmark interest rate for green credit is set at $r=1.5\%$, and the government inspection rate is $\gamma =0.2$. The return rates for green investment projects and traditional high-pollution projects are $m_1=6\%$ and $m_2=15\%$. Additionally, the strategic preference coefficient is $\eta =0.5$ [32], and the irrationality intensity parameter is $k=0.5$ [31]. For the BF mode, this paper assumes that the cooperative benefits of both financial institutions and enterprises, as well as the concealment cost of corporate greenwashing behavior, are doubled relative to the traditional mode. Meanwhile, all reputation losses (including the reputation losses incurred by financial institutions and enterprises due to greenwashing, and the reputation losses suffered by enterprises from loan defaults) are scaled up by a factor of 10 [19]. The remaining baseline parameter configurations are presented in

Table 4. Initial parameter setting.

Parameter	Value	Parameter	Value	Parameter	Value
$p$	0.1	$N_f$	5	$E_f$	10
$q_1$	0.6	$N_{f1}$	50	$E_e$	5
$q_2$	0.9	$N_e$	10	$I_t$	1000
$Y_f$	5	$N_{e1}$	100	$I_e$	20
$Y_{f1}$	10	$H_e$	5	$O_e$	10
$Y_e$	5	$H_{e1}$	10	${\mu }_f$	0.015
$Y_{e1}$	10	$S_c$	10	${\rho }_e$	0.3
$D_f$	20	$B$	10	${\xi }_e$	0.1
$D_e$	50	$B_1$	100	${\epsilon }_e$	0.1

.

6.2.1. Impacts of Parameters $S_c$, $\gamma$ and $p$ on System Evolution Equilibrium

According to the theoretical derivation results in Section 4, the collateral disposal value $S_c$, government supervision inspection rate $\gamma$, and corporate greenwashing probability $p$ constitute three core factors affecting the evolutionary game equilibrium. This section employs simulation experiments to examine the effects of the three aforementioned factors on the strategic evolution of financial institutions and enterprises.

(1)

Insufficient Collateral: Financing Dilemma of Traditional Mode vs. Digital Credit Enhancement of BF Mode

To compare the differences in credit supply between the traditional mode and BF mode under the scenario of insufficient corporate collateral and low greenwashing probability, the parameters are set as $S_m=50$ and $p=0$.

As illustrated in Figure 7a, the trajectory of the lending ratio under the traditional mode can be decomposed into three phases. During the initial phase (approximately rounds 0–30), tentative lending prevails, with the proportion of financial institutions choosing to lend fluctuating around 0.5. This pattern indicates that, when information is limited, financial institutions do not immediately resort to credit rejection. Instead, some institutions earn normal returns from compliant enterprises in the early market, which enables lending strategies to persist in the short term. The second phase (approximately rounds 30–90) is marked by a stepwise contraction of the lending ratio. As default events accumulate, the expected returns from lending diminish, and credit rejection becomes an increasingly dominant strategy. The third phase (after round 90) is characterized by comprehensive credit rejection. Following multiple rounds of strategy adjustment, financial institutions ultimately converge toward full credit rejection, and the lending ratio falls to zero. Figure 7b further reveals that, under the traditional mode, the proportion of compliant enterprises does not decline to zero correspondingly but instead persists at approximately 0.5. This persistence suggests that the green credit market still contains high-quality enterprises with both the capacity and willingness to fulfill their obligations. Nevertheless, the failure of reputation mechanisms, coupled with information asymmetry, exacerbates adverse selection within the credit market, hindering financial institutions from effectively identifying high-quality borrowers. As a result, even for enterprises with genuine investments in green projects and a willingness to meet repayment obligations, financial institutions tend to adopt the conservative strategy of blanket credit rejection.

This phenomenon reflects structural constraints within the traditional green credit model. First, SMEs typically lack sufficient tangible assets to serve as effective collateral. Second, information asymmetry pervades the market, reflected in limited green operational data, hard-to-quantify environmental benefits, and the absence of effective credit guarantees and enhancement instruments. Third, reputation mechanisms have limited efficacy in curbing opportunistic behavior, resulting in persistently high default risks. Under these conditions, credit rejection becomes the rational strategy for financial institutions.

The BF mode restructures traditional credit assessment and risk management paradigms in green supply chain financing, thereby offering a resolution to the financing constraints. As shown by the BF curves in Figure 7a,b, when the probability of greenwashing is low, both the lending ratio of financial institutions and the compliance ratio of enterprises rise rapidly during the initial rounds of the game (approximately the first ten rounds), converging toward unity and subsequently remaining at this elevated level. The formation of this steady-state equilibrium is attributable to the technology governance mechanism of the BF mode. Federated learning enables the integration of multi-dimensional supply chain data through parameter encryption and collaborative training, without disclosing the original enterprise data, thereby enabling the construction of precise digital credit profiles. Blockchain provides a trust foundation that is traceable and tamper-proof, thereby substantially increasing the reputational cost of default. The integration of federated learning and blockchain achieves the dual objectives of data value release and privacy protection, while effectively curbing corporate incentives for fraud. Under this mechanism, financial institutions are able to more accurately discern the true operating conditions of enterprises, which in turn reduces lending risk and strengthens the willingness to extend credit. As the cost of default is high for enterprises, compliance emerges as their dominant strategy. Therefore, when enterprises lack sufficient collateral and the probability of greenwashing is low, the BF mode can effectively facilitate a stable equilibrium in which financial institutions lend and enterprises comply.

Figure 8 further validates the effects of the reputation constraint mechanism and digital credit enhancement on the evolutionary equilibrium of the BF mode. As shown in the figure, as enterprise cooperation benefits increase, default reputational losses rise, and the digital credit level improves, the equilibrium strategies of financial institutions and enterprises under the BF mode shift from (credit rejection, default) to (lending, compliance). This indicates that the BF mode can enhance enterprise compliance incentives, strengthen the willingness of financial institutions to lend, and facilitate cooperation through reputation constraints and digital credit enhancement. Nevertheless, the influence of these parameters is not linear but exhibits a pronounced threshold effect. At low parameter levels, the system converges to a non-cooperative equilibrium of (credit rejection, default). Once enterprise cooperation benefits, default reputational losses, and the digital credit level exceed their respective critical values, enterprise strategies rapidly shift from default to compliance, financial institutions subsequently switch to lending, and both the lending ratio and the compliance rate jump rapidly within a narrow interval near the critical value, converging toward a fully cooperative equilibrium. The underlying mechanism is as follows. Higher enterprise cooperation benefits strengthen the long-term incentives for compliance, increased default reputational losses raise the implicit costs of default, and an improved digital credit level reduces the information screening costs and risk expectations of financial institutions. When any of the above parameters improves sufficiently to make the expected net benefit of cooperation exceed that of non-cooperation, the system transitions to a cooperative state characterized by high lending and high compliance. It should be noted that, within the parameter range of this model, the cooperation benefits of financial institutions do not exert a significant influence on the lending ratio or the compliance rate. A possible explanation is as follows. Under weak compliance incentives on the enterprise side and severe information asymmetry, financial institutions may find that despite high prospective cooperation benefits, an enterprise default would wipe out these gains and leave them with uncovered losses. This, in turn, suppresses their lending willingness. Therefore, the enhancement of benefits on the financial institution side is not the primary variable driving system evolution; rather, improvements in enterprise compliance incentives and the credit environment constitute the key factors.

Building upon the baseline simulation results, the BF mode effectively facilitates expanded credit supply by financial institutions and promotes enterprise compliance when parameters satisfy the critical threshold under conditions of insufficient collateral and a low degree of greenwashing. However, participants in reality exhibit heterogeneity in risk appetite, digitalization level, and strategic objectives, and their strategy adjustment behavior is not homogeneous. To capture heterogeneity in behavioral decision-making, this study introduces agent heterogeneity within the Fermi strategy updating framework. Participants are classified into three stylized types, namely aggressive, neutral, and conservative, each endowed with a distinct irrationality intensity parameter $k$. The aggressive type is characterized by an irrationality parameter approaching zero $\left(k_{\mathit{agg}}=0.01\right)$, which approximates full rationality and corresponds to agents with strong digital capabilities and high willingness to transform. The neutral type retains the baseline parameter ($k_{\mathit{neu}}=0.5)$, reflecting the behavioral characteristics of the majority of market participants. The conservative type exhibits a higher irrationality parameter ${(k}_{\mathit{con}}=1)$ and stronger decision inertia, such that strategy switching remains sluggish even when payoff advantages are evident.

Figure 9a reports the evolutionary trajectories of BF mode adoption rates across the three types of agents. The adoption rate among aggressive agents rises rapidly in the early stages of the simulation, exceeding 80 percent within the first three rounds before reaching saturation. The adoption rate among neutral agents exhibits a steady growth pattern, approaching a similarly high level after approximately five rounds. Conservative agents display a pronounced lag, with cumulative adoption below 50 percent during the first three rounds, followed by a gradual increase that approaches the group average only after round ten. The divergence of the three curves along the temporal dimension reflects differences in adoption speed across heterogeneous agents. Figure 9b presents the distribution of adoption time for the three agent types using box plots. The median adoption time for aggressive agents occurs in the first round, indicating that adoption behavior is highly concentrated in the early phase of the simulation. The median for neutral agents falls around the second round, with a relatively concentrated distribution. The median for conservative agents approaches the third round; the upper whisker extends to the ninth round, and the interquartile range is wider with more outliers, suggesting that this group not only delays adoption overall but also exhibits more significant inter-agent variation and higher internal dispersion. It should be noted that heterogeneity primarily affects the convergence speed and evolutionary path of BF mode adoption without altering the steady-state outcome of the system. Provided that the critical parameter conditions are satisfied, the system ultimately converges to a dominant equilibrium in which all agents adopt the BF mode.

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Sufficient Collateral: Greenwashing Predicament of Traditional mode vs. Restraint Effect of BF mode

Figure 10 depicts the impact of varying parameter combinations ($\gamma$ and $p$) on the evolutionary game equilibrium under the traditional mode with sufficient collateral. The three-dimensional surface delineates three distinct regimes. In the blue regime, where corporate greenwashing is relatively low, the system stabilizes at an equilibrium where (lending, compliance) dominates. In the green regime, where there is a high level of greenwashing and stringent regulatory enforcement, financial institutions converge on credit rejection as their stable strategy. Notably, in the orange regime, a high level of greenwashing combined with weak regulatory enforcement still leads to (lending, compliance) as the stable equilibrium. This indicates that under lax external oversight, financial institutions have incentives to lend to high-greenwashing enterprises, creating moral hazard through lender-enterprise collusion that sustains greenwashing activities. These results suggest that while the traditional mode can sustain credit transactions under certain conditions, it falls short of effectively curbing greenwashing. Addressing this inherent dilemma within the traditional framework requires strong external regulatory intervention.

The comparative analysis in Figure 11 shows that the BF mode enhances financial institutions’ sensitivity to corporate greenwashing risks, thereby reducing the credit accessibility of greenwashing enterprises. Under the traditional mode, if government supervision intensity remains low ($\gamma =0.2$), financial institutions will ultimately choose to lend regardless of the variations in greenwashing probability. By contrast, financial institutions’ lending decisions under the BF mode are highly correlated with corporate greenwashing probability and present strong risk sensitivity. Once the greenwashing probability exceeds the threshold of 0.2, financial institutions’ loan approval ratio plummets to zero.

This unique advantage of the BF mode derives from four core technical and institutional mechanisms: (1) Establishment of standardized green digital archives. Core project data including environmental impact assessment reports, real-time energy consumption and carbon emission indicators are verified and permanently recorded on the distributed ledger of the consortium blockchain, generating traceable, tamper-resistant and publicly verifiable green digital archives. (2) Collaborative construction of risk control models. Consortium blockchain participants are not required to share raw data but can collaboratively train high-performance greenwashing risk identification models solely through encrypted parameter exchange. (3) Reinforced reputation punishment mechanism. Any single greenwashing record of enterprises will be permanently stored on the consortium blockchain and form an irreversible digital credit stain for life. The transparent reputation penalty system greatly increases the concealment cost of greenwashing and fundamentally weakens enterprises’ fraud motivation. Meanwhile, it makes financial institutions bear joint reputation risks, forcing them to strengthen the auditing of corporate environmental information. (4) Real-time penetrating digital supervision. Authorized government regulators can access the full on-chain data of the consortium blockchain platform, transforming the original offline periodic reporting and manual sampling supervision into real-time, full-coverage and penetrating online supervision. Regulators can accurately capture abnormal environmental data and potential illegal acts based on continuous enterprise environmental data streams, greatly lifting supervision efficiency and regulatory deterrence.

6.2.2. Core Influencing Parameters of BF Mode Adoption

The experimental analysis in the previous section demonstrates that the BF mode can facilitate credit cooperation between financial institutions and enterprises while curbing corporate greenwashing. Based on the derivation from dynamic game theory, the net benefit of both parties from participating in the BF mode serves as the core determinant of the mode’s adoption rate. Among the components of the net benefit expression, system usage cost, reward allocation ratio, and risk sensitivity factor constitute the key variables. This section focuses on analyzing how these three factors influence the choice of financial institutions and enterprises to adopt the BF mode.

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System Usage Cost

The consortium blockchain platform, which integrates blockchain and federated learning technologies, requires financial institutions and enterprises to bear input costs encompassing model training, daily system operation, and technical maintenance. The simulation results (Figure 12) reveal a marked disparity in the sensitivity to usage costs between the two parties. Financial institutions exhibit greater cost tolerance than enterprises. Specifically, as system usage cost gradually increases from 0 to 5, 10, and 20, the proportion of financial institutions choosing the BF mode stays persistently high, whereas enterprises’ willingness to participate decreases continuously. When the usage cost reaches the threshold of 10, all enterprises entirely abandon the BF mode. This disparity stems from the asymmetry in the cost–benefit structures of the two parties. As the ultimate bearers of financing credit risk and direct beneficiaries of the consortium blockchain platform, financial institutions derive returns characterized by certainty and immediacy. In contrast, enterprises, as the primary providers of supply chain data, can only obtain indirect and contingent long-term financing convenience after joining the platform, while platform usage costs constitute direct, current, and fixed expenditures. Once comprehensive costs exceed the marginal revenue equilibrium point, the evolutionary stable strategies of both parties will fundamentally reverse. Therefore, in promoting digitally empowered green supply chain finance, differentiated cost-sharing and financial compensation mechanisms should be formulated for distinct types of participants.

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Reward Distribution Coefficient

Given enterprises’ higher cost sensitivity, this section examines the influence of varying reward distribution coefficients on their willingness to participate in the BF mode. As shown in Figure 13, under low usage cost (cost = 5) and a low reward distribution coefficient, the enterprise group fails to converge rapidly to the full-participation stable equilibrium. As the coefficient increases continuously, enterprises’ willingness to join the BF mode is significantly stimulated, indicating that positive incentive mechanisms remain a necessary condition for attracting enterprise participation even when platform usage costs are low. When platform usage cost is high (cost = 15) and the reward distribution coefficient remains low, enterprises quickly evolve to the complete non-participation equilibrium. However, once the coefficient exceeds the critical threshold, a subset of enterprises begins to select the BF mode, and the overall participation rate rises synchronously with the coefficient. This simulation result demonstrates that sufficient incentive distribution can offset the negative impact of high usage costs on enterprises’ participation willingness.

Furthermore, Figure 14 illustrates the combined effect of usage cost and reward distribution coefficient on enterprise BF mode participation rate. As shown in the figure, with the reward distribution coefficient held constant, the participation rate decreases monotonically as usage costs increase; conversely, when usage costs remain fixed, the participation rate shows a marginally increasing trend with a higher reward distribution coefficient. Moreover, the figure also reveals that the positive effect of reward distribution on enterprise BF mode participation rate varies with usage cost levels. As usage costs rise, the threshold reward distribution coefficient required to sustain enterprise participation increases correspondingly. This implies that if the platform attempts to offset the negative impact of rising usage costs on participation rates by increasing rewards, the requisite incentive cost escalates with the usage cost level. Specifically, once usage costs exceed a critical threshold (approximately 30), the incentive effect becomes constrained even as the reward distribution coefficient approaches its theoretical upper bound of 1, leaving limited scope for further improvement in enterprise participation rates. Consequently, when usage costs are excessively high, adjusting the reward distribution alone cannot effectively promote widespread enterprise adoption of the BF mode. Platform operators should therefore adopt governance strategies that integrate cost optimization with diversified incentive mechanisms.

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Privacy Risk Sensitivity Coefficient

Figure 15 illustrates how the risk sensitivity factor influences enterprises’ willingness to participate in the BF mode. As shown in the figure, once the data leakage risk sensitivity factor exceeds a certain threshold, enterprises’ willingness to participate in the BF mode declines significantly. This phenomenon stems from the fundamental principle of federated learning, namely that “data remains local while algorithms operate across institutions.” Although federated learning ensures that all raw data are stored locally by each participant, optimizing the global training model requires continuous exchanges of updated intermediate parameters, such as model gradients and weights, with the central server. These transmitted parameters implicitly contain statistical features of the original data, making it possible to reconstruct private information through model inversion, inference attacks, or similar techniques. Consequently, when the risk sensitivity factor exceeds the threshold, heightened privacy and security concerns suppress enterprises’ willingness to participate in the BF mode.

7. Discussion

By integrating theoretical analysis with numerical simulations, this study examined how the BF mode affects financial institutions’ credit decisions and enterprises’ compliance behavior, as well as its effectiveness in curbing greenwashing. Furthermore, this study also investigated how key parameters, including usage costs, reward allocation ratios, and risk sensitivity factors, influence participating agents’ financing mode choices. This section returns to the research questions raised in the introduction and discusses the corresponding conclusions.

Regarding the mitigating effect of the BF mode on financing constraints, the theoretical analysis in Proposition 1 demonstrates that the BF mode strengthens firms’ performance incentives through reputational constraints and digital credit-enhancement mechanisms. Improved corporate compliance behavior fosters a more trustworthy environment, raises financial institutions’ willingness to extend credit, and thereby alleviates financing constraints. Numerical simulations further reveal that under conditions of insufficient collateral and low greenwashing probability, the traditional mode results in complete credit denial by financial institutions, even when high-quality firms with genuine compliance willingness are present in the green credit market. In contrast, the BF mode can rapidly achieve a stable equilibrium of (lending, compliance). This finding aligns with the conclusions of Zhan et al. derived from tripartite evolutionary game theory; their simulations show that blockchain technology significantly reduces firms’ default tendency and improves financial institutions’ willingness to grant credit by recording SMEs’ default behaviors on the blockchain [33]. Nevertheless, Zhan et al. mainly focus on the reputational disciplinary effect of blockchain and do not incorporate federated learning into their analytical framework. The marginal contribution of this study lies in revealing that federated learning constructs dynamic digital credit profiles for firms via privacy-preserving multi-source data fusion, thus providing financial institutions with a quantifiable basis for credit assessment under collateral-deficient scenarios.

Regarding greenwashing governance, this study finds that the BF mode significantly enhances lending institutions’ sensitivity to environmental risks, effectively restricting financing access for greenwashing firms. Proposition 2 provides theoretical substantiation for this finding through marginal analysis. Simulation results further reveal that, under the traditional mode, when collateral value is sufficient and government regulatory intensity remains low, financial institutions tend to extend credit even when facing high greenwashing probabilities, generating a distorted equilibrium featuring accessible financing amid rampant greenwashing. In contrast, lending decisions under the BF mode show greater sensitivity to firms’ greenwashing probabilities; once the probability exceeds a critical threshold, the loan approval rate drops to zero. These findings are consistent with the conclusions reported by Xu & Tian and Li et al. [19,20]. Xu and Tian show that blockchain, via smart contracts, enables the automatic execution of penalties and ensures transparent on-chain data recording, thus curbing corporate defaults and greenwashing behavior more effectively than conventional penalty mechanisms. Using a tripartite evolutionary game framework, Li et al. demonstrate that blockchain-enabled reputation mechanisms can effectively regulate the behavior of firms and financial institutions in low-regulatory-intensity environments, prompting firms to voluntarily pursue green innovation through reputational deterrence. Nevertheless, existing literature has not yet elucidated the intrinsic mechanism by which financial institutions continue to provide financing to greenwashing firms under specific conditions. This study contributes by identifying the conditions that give rise to accommodation between financial institutions and greenwashing firms under the traditional mode: when collateral value sufficiently covers credit risk and government regulatory intensity is weak, such insufficient external oversight allows financial institutions’ performance pressures related to green credit to outweigh their incentives to avoid greenwashing risks. Consequently, they grant loans even when greenwashing probabilities are high. On this basis, this study further uncovers the core advantages of the BF mode for mitigating greenwashing. The federated learning-driven collaborative risk-control framework integrates multisource, heterogeneous supply chain data, markedly improving the accuracy of greenwashing identification. Meanwhile, the transparency of consortium blockchains and their penetrating regulatory mechanism subject financial institutions to reputational losses, substantially raising accommodation costs. As a result, the optimal strategy for financial institutions under the BF mode shifts toward loan rejection, which in turn effectively curbs greenwashing. This result offers a valuable complement to prior literature, which largely concentrates on blockchain’s disciplinary effects on the firm side. From the financial institution perspective, this study illustrates how technological empowerment reshapes lending institutions’ payoff structures. It demonstrates that the BF mode can effectively cut off greenwashing firms’ access to financing from the capital supply side.

Regarding the key factors that constrain and drive the adoption of the BF mode among various stakeholders, the simulation results reveal three significant findings. First, usage costs serve as a critical determinant of BF mode adoption. This finding is consistent with Zhang and Kou, who demonstrate that the diffusion of blockchain technology is constrained by adoption cost thresholds [11]. Furthermore, this study reveals an asymmetric effect of usage costs on enterprises and financial institutions: the former exhibit greater sensitivity to cost increases, whereas the latter display higher cost tolerance. This study also quantitatively examines the substitution relationship between usage costs and reward allocation ratios. The results indicate that increasing the reward allocation ratio can effectively offset the negative effect of rising costs on enterprises’ participation willingness. However, this substitution relationship is subject to a saturation effect: when costs exceed a critical level, even if the reward allocation ratio approaches one, the marginal improvement in enterprise participation rates diminishes substantially. Second, when the risk sensitivity factor exceeds a certain threshold, enterprises’ participation willingness declines significantly. This study posits that this phenomenon is primarily attributed to rising privacy protection costs. Wu et al. [34], in the context of differentially private federated learning, found that when privacy protection intensity exceeds a critical threshold, the model’s recognition performance for minority-class samples weakens, thereby reducing commercial utility. This finding, which reveals the adverse effects of excessive privacy protection from the perspective of model utility, provides a complementary explanation for the above phenomenon. Third, the analysis of heterogeneous agents indicates that although the three categories of entities differ significantly in their adoption rates of the BF mode, the long-term evolutionary equilibrium remains robust, and the system ultimately converges to a stable state where the BF mode dominates. Heterogeneity merely affects the convergence speed and transition trajectory. This finding is analogous to that of Han et al. regarding heterogeneous firm behavior in CCUS technology diffusion, where firms with different production capacities exhibit significant disparities in technology adoption rates. Nevertheless, the long-term direction of technology diffusion is determined by cost–benefit conditions, with heterogeneity primarily influencing convergence speed and transition trajectory rather than long-term equilibrium outcomes [35].

8. Conclusions and Implications

8.1. Main Conclusions

Grounded in the challenges that SMEs encounter in accessing green financing, this study examines the innovative application of federated learning and blockchain technology within green supply chain financing. Based on theoretical derivation and numerical simulation, the main conclusions are as follows:

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The BF financing mode, underpinned by federated learning and blockchain technology, can alleviate green financing constraints for SMEs. This mode enhances SMEs’ digital creditworthiness through federated joint modeling, while leveraging blockchain to establish a credible reputation mechanism. It mitigates information asymmetry and credit challenges between financial institutions and enterprises, fostering a virtuous cycle in which institutions are willing to lend and enterprises remain compliant.

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The BF mode is shown to mitigate corporate greenwashing through a collaborative risk management model, real-time look-through supervision, and strengthened reputation-based constraints. Unlike the traditional mode, which relies heavily on on-site inspection, this digital governance approach enhances both the integrity and efficacy of green financing.

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The financing mode selection by financial institutions and enterprises is, in essence, a rational decision-making process driven by the calculation of net participation benefits. Key determinants of each participant’s inclination toward the BF mode include the system usage cost, reward distribution coefficient, and risk sensitivity factor.

8.2. Management Implications

Based on the above research findings, this paper offers the following implications:

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Implement a differentiated, tiered promotion strategy. In real-world markets, agents exhibit substantial heterogeneity in risk preferences and digital capabilities. Simulation results demonstrate that although such heterogeneity does not alter the system’s long-run evolutionary equilibrium, it materially shapes strategy diffusion trajectories and convergence dynamics. Consequently, promotion of the BF mode should eschew a one-size-fits-all approach. Shoomal et al. emphasize that value creation via digital and intelligent technologies is highly contingent on diverse enabling conditions, including firms’ technological infrastructure, organizational talent endowments, and external compliance pressures [36]. Accordingly, in addition to strengthening policy advocacy to mitigate concerns over implementation costs and data privacy, governments can collaborate with industry institutions to develop tiered technology-readiness diagnostic guidelines tailored for green supply chain financing scenarios. Such guidelines allow firms at varying readiness levels to accurately identify their baseline positions, thus avoiding resource misallocation stemming from uninformed conformity.

Specifically, for technologically advanced anchor enterprises, policymakers can encourage the pioneering deployment of innovative applications within high-complexity scenarios. Targeted incentive instruments, such as fiscal subsidies and positive regulatory assessment credits, could be leveraged to fully harness these firms’ benchmark status and demonstration effects. Conversely, for SMEs with limited technological foundations, policy priorities should focus on building fundamental data-acquisition capabilities and rolling out standardized interfaces to lay a solid foundation for their digital transformation. By offering one-off transformation subsidies and managed technology services, governments can significantly lower barriers to technology adoption and prevent these enterprises from becoming the weakest link in the overall diffusion process. Ultimately, tiered policy implementation and gradual diffusion mechanisms that cascade from both leading and lagging firms to drive the middle segment can achieve universal coverage and the effective delivery of policy benefits.

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Establish a multi-stakeholder, equitable cost–benefit sharing mechanism. First, policymakers should focus on adoption bottlenecks at the enterprise level, particularly among small- and medium-sized enterprises (SMEs), and develop an inclusive cost-sharing mechanism. Simulation results indicate that enterprise compliance incentives and improvements in the credit environment are pivotal drivers of system evolution. As implementation costs escalate, enterprises exit the BF financing mode earlier than financial institutions. Consequently, it is advisable to place greater emphasis on fiscal incentives and implementation support for enterprises. Specific measures include providing SMEs with lightweight blockchain nodes to lower access barriers; granting targeted subsidies for green data collection and equipment retrofitting; and instituting special low-interest credit facilities for SME green digitalization. For financial institutions, policymakers can effectively reduce funding costs via instruments such as green relending, preferential risk weights on green assets, and bonus points in regulatory assessments. Simultaneously, core enterprises may be incentivized to absorb part of the access costs for upstream and downstream SMEs within demonstration projects. A layered cost-sharing arrangement combining government subsidies, concessions from core enterprises, platform fee reductions, and SME co-payments prevents enterprises from being forced out of the system due to prohibitively high costs.

Building on this, it would be beneficial to establish an intelligent incentive system that aligns contributions with returns to reinforce cooperative stability. Within the BF financing system, practitioners could design an algorithm to objectively quantify each participant’s computational resource input, model performance contribution, and data quality level. Its core logic is encoded into smart contracts, rendering incentive rules transparent and enforceable while automating rule execution. Real-time matching of contributions and returns strengthens incentives for long-term collaboration and consolidates the underlying mutual trust.

Second, the substitutability between cost subsidies and reward incentives deserves explicit recognition. When promoting the BF financing mode, governments can flexibly consider adjusting the mix of these two policy instruments under budgetary constraints to optimize the allocation of policy resources. Such a mixed strategy avoids the diminishing marginal returns arising from over-reliance on a single instrument and maximizes the effectiveness of policy funds.

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Expand investment in foundational R&D to enhance operational efficiency and bolster risk governance throughout the technology lifecycle. Lessons drawn from the BF mode’s practice against greenwashing show that reallocating regulatory resources away from high-intensity ex post inspections under traditional modes toward ex ante deployment of technical infrastructure and the formulation of platform governance rules delivers greater cost effectiveness for ex ante greenwashing prevention via technical solutions, compared with reliance on ex post penalties alone. Building on this finding, governments can promote industry–academia research collaboration through national R&D programs. First, they should scale up investment in foundational technologies including blockchain, intelligent data acquisition, and communication infrastructure to boost data collection and transmission efficiency and optimize the operational performance of federated learning systems. Second, priority should be given to frontier technologies such as differential privacy, homomorphic encryption, cross-chain interoperability, and Byzantine robust federated learning, so that technological innovation can consolidate security and trust foundations.

8.3. Limitations and Future Research

This study has limitations that warrant further exploration:

First, regarding the game structure, this paper constructs a bilateral sequential game model between financial institutions and enterprises, where the government is not incorporated as a player but influences both parties’ decisions through exogenous variables such as regulatory intensity and penalty severity. Future research may endogenize the government as a strategic player and extend the framework into a tripartite dynamic game model, further examining how regulatory intervention affects firms’ green transformation decisions and financial institutions’ financing strategy choices.

Second, regarding the information structure, this paper adopts the complete information assumption. Future studies may introduce an incomplete information game framework, enhancing the model’s explanatory power for real-world phenomena such as corporate greenwashing behavior and adverse selection by financial institutions through characterizing participants’ type spaces and belief updating mechanisms.

Finally, regarding empirical grounding, this study’s conclusions rest on theoretical derivation and numerical simulation. Although these methods substantiate the theoretical framework and its computational implementation, they fall short of reflecting real-world financing behavior. Additional empirical inquiry is warranted to ascertain whether enterprises and financial institutions in practice conform to the posited behavioral patterns. A promising direction for future research would be to conduct case studies of representative green supply chain pilot enterprises, gathering firsthand data on corporate carbon emissions, green credit ratings, and financing costs to empirically corroborate the present findings through econometric analysis.