Evolutionary game theory originated from population biology. In contrast to classic game theory, it integrates dynamic evolution process analysis with bounded rationality among players. Evolutionary game theory concentrates on the evolutionary process and evolutionary stable states in the model. Given its alignment with real-world dynamics, it has become an important research tool for the study of dynamic game problems. It has been widely applied to studying various aspects of the supply chain. First, regarding the number of game subjects, evolutionary games in the supply chain are mainly studied as two- and three-party games. Xiong et al. (2023) used the evolutionary game model to analyze the stable evolutionary strategies of logistics enterprises in collaborative transportation applying blockchain technology [5]. Long et al. (2021) used a three-party evolutionary game model to study green sensitivity in the green supply chain [6]. Second, we focus on the use of evolutionary game for cooperation among supply chain members. Yu et al. (2022) built an evolutionary game model based on the relationship between agricultural product suppliers and urban residents in the financing system [7]. Gu et al. (2019) built an evolutionary game theory model to examine NREI company cooperation in reverse logistics operations [8]. Huang et al. (2023) constructed a tripartite evolutionary game model of government, dealers, and ginger farmers under asymmetric price transmission and explored the impact of the target price insurance on the stabilization strategy of the tripartite evolutionary game [9]. Third, we consider the case of government regulation in the study of supply chain evolutionary games. Sun et al. (2019) investigated a two-tier supply chain’s green investment plan for manufacturers and material suppliers under a government subsidy structure [10]. Mahmoudi, R. and Rasti-Barzoki, M. (2018) employed evolutionary game theory to simulate how supply chain participants might perform under various government scenarios [11]. Cheng and Cheng (2023) used prospect theory and mental accounting theory to analyze the decision-making behavior of the public and private sectors in PPP project supervision, revealing the impact of factors like perceived costs, penalties, reference points, and risk exposure on their proactive behavior [12].

There have been recent significant advances in digital supply chain innovations which have been driven by the rapid evolution of technologies such as artificial intelligence (AI), blockchain, the internet of things (IoT), and digital twins. These innovations have been extensively studied in high-impact journals, focusing on their potential to enhance supply chain resilience, sustainability, and operational efficiency. One major area of research has been the integration of AI and machine learning (ML) for predictive analytics and decision-making. For example, Zhang et al. (2024) demonstrated how AI-powered demand forecasting models could significantly reduce uncertainties in volatile markets, particularly in the post-pandemic era [13]. The adoption of digital twins has gained momentum, with researchers exploring their potential for simulating and optimizing supply chain operations. For instance, Ivanov et al. (2024) developed a digital twin-based model for supply chain risk management which allows firms to simulate disruptions and test mitigation strategies in a virtual environment [14]. Sustainability remains a critical theme, with studies focusing on how digital innovations can support green supply chain initiatives. A notable contribution by Kumar et al. (2024) examined the use of IoT and big data analytics to monitor and reduce the environmental impact of supply chain activities, particularly in the manufacturing sector [15]. Jacobides, M. G. et al. (2018) expanded existing research by analyzing ecosystem development mechanisms and their distinctions from traditional governance structures [16]. According to Ron Adner, the ecosystem is the multilateral coalition of parties necessary for a focal value offer to become a reality [17]. Business ecosystems serve as a strategic framework for interorganizational collaboration, driving competitive advantage and innovation [18]. At present, academic research on business ecosystems is gradually maturing, and more scholars are beginning to focus on the field of supply chain ecosystems. From a theoretical research perspective, David Jr and Ketchen J et al. (2014) described a supplier ecosystem as a collection of interdependent and coordinated businesses that face some of the same adaptive difficulties and work together to develop and maintain a sourcing base that gives them a competitive edge [19]. Letaifa, S. B. (2014) revealed the difficult transition from the supply chain to the ecosystem, using the multidimensional definition of value-ecosystemic value and employing lifecycle theory to identify the different stages of the evolution of value-creation and value-capture processes in an ecosystem [20]. Liu et al. (2022) converted evolutionary stable strategies (ESSs) into the ideal ESS by adjusting certain parameters, and they provided suggestions for the platform to induce its supplier to choose ecological cooperation [21]. From a practical application perspective, Liu et al. (2021) investigated ecological cooperation patterns between logistics platforms and suppliers through a business ecosystem lens, employing evolutionary game theory to model multi-period interactions [22]. Yan et al. (2022) examined the elements that impact the adoption of the circular supply chain in the smart logistics ecological chain using a case study approach with four chosen instances, identifying five such factors [23].

In summary, evolutionary game analysis has emerged as a powerful tool in supply chain research, offering insights into dynamic interactions and decision-making processes among various stakeholders. Depending on the research focus, evolutionary game models have been applied to study the behavior of suppliers, manufacturers, platforms, consumers, and governments. A significant portion of the reviewed literature explores cooperation mechanisms between suppliers and manufacturers, highlighting the importance of collaborative strategies in enhancing supply chain efficiency and sustainability. Additionally, several studies have incorporated the role of government policies, examining how regulatory interventions, subsidies, and incentives influence the strategic choices of supply chain participants.

In recent years, the concept of supply chain ecosystem has gained traction among scholars, reflecting a shift from traditional linear supply chain models to more interconnected and collaborative frameworks. Ecological cooperation, characterized by symbiotic relationships and value co-creation among ecosystem participants, has become a cornerstone of supply chain management in the digital economy. This form of cooperation introduces new dynamics such as shared resources, joint innovation, and collective resilience, which distinguish it from conventional inter-enterprise collaboration. Despite these theoretical advancements, the literature remains fragmented in systematically modeling ecological cooperation within these ecosystems.

To address this gap, this article employs a three-party evolutionary game model involving suppliers, manufacturers, and the government. This framework not only captures the dynamic interactions among these key stakeholders but also integrates the unique features of ecological cooperation, such as resource sharing, innovation synergy, and regulatory influence. By grounding the model in the theoretical foundations of supply chain ecosystems, this study aims to provide a nuanced understanding of how ecological cooperation can be fostered and sustained in the context of evolving market and regulatory environments. Furthermore, the inclusion of the government as a strategic player allows for an exploration of how policy interventions can shape the trajectory of ecological cooperation, offering valuable insights for both academia and practice.

This study investigates factors affecting ecological cooperation among supply chain enterprises and government supervision mechanisms, focusing on a two-tiered supply chain composed of upstream suppliers and downstream manufacturers. The government will supervise cooperation due to data security and the stable operation of the market. The two-tiered supply chain comprises populations of upstream suppliers and downstream manufacturers, alongside local governments with finite regulatory capacity. Evolutionary game theory analyzes time-dependent dynamics and incorporates players’ learning mechanisms in strategic interactions. Building on evolutionary game theory, this study investigates the interaction mechanisms of tripartite behavioral strategies.

Assumption 1

The three participants—government, upstream suppliers, and downstream manufacturers—are boundedly rational, learning from each other’s strategic decisions and gradually altering their behavioral patterns until reaching equilibrium.

To take advantage of open innovation opportunities, organizations are changing their strategy, emphasis, and competencies from firm centricity to ecosystems [24]. The behavior of firms transforms from traditional competitive to more social and ecosystemic [20]. In this study, suppliers and manufacturers can choose to engage in ecological cooperation or not. If the suppliers and manufacturers both choose “non-ecological cooperation”, the profits of the suppliers and manufacturers are U 1 and U 2 , respectively. When the suppliers and manufacturers choose “ecological cooperation,” they need to pay extra costs ( C i ,1: suppliers 2: manufacturers) because of the adjustment of the company’s own business due to the cooperation, and these costs will cut their final profits. Enterprises face both opportunities (e.g., technological innovations) and risks (e.g., market volatility) in ecological cooperation. The net benefits comprise two components: (1) innovation gains from intra-supply chain collaboration and (2) risk-adjusted returns from enhanced market competitiveness. We assume that the total generated ecological resources are N (including sharing data, information, technology, and others) when enterprises choose “eco-cooperation.” The innovation benefits will be affected by the ecological sensitivity of enterprises ( a i ,1: suppliers 2: manufacturers), which represents the ability of companies to transform shared resources to their benefit through ecological cooperation. The risk-based returns ( U ) will be shared by the suppliers and manufacturers, and the allocation coefficient is δ .

If only one party (either suppliers or manufacturers) actively engages in ecological cooperation, the passive party may obtain speculative gains through free-riding but is contractually obligated to compensate the active party (amount F) for cost subsidies.

Assumption 2

We assume that the party not cooperating ecologically has access to all the data resources shared by the other party at the time of cooperation, but the speculative gain is determined by the speculative coefficient due to limitations in resources, technology, hardware equipment, etc. The cumulative gain is R i ( R i = r i N , 1: suppliers 2: manufacturers) and r 1 < a 1 , r 2 < a 2 .

The two pure tactics available to governments are supervision and non-supervision. In the case of supervision, governments set a subsidy coefficient ( π , 0 ≤ π ≤ 1 ) for the extra costs incurred by enterprises’ eco-cooperation and an integrated penalty ( D ) for speculative data theft and information leakage, which is also widely used in the literature [12, 25]. These need to pay a certain supervision cost ( C g ) by making policies. In return, supervision can bring extra benefits ( S ) to governments, including economic benefits and social reputation.

Assumption 3

Eco-collaboration is characterized by joint value creation and aims at maximizing overall benefits, although, in practice, a firm’s emphasis on value capture may hinder ecosystemic value creation [17]. This study assumes that enterprises aim to maximize their revenues. Governments pursue social and economic benefits, including green development and industrial upgrading.

Table 1 lists the corresponding payoff parameters for the three parties, and the interactive behavioral strategies and game relationships among the three parties are illustrated in Figure 1.

The assumptions in this study encapsulate key characteristics of contemporary supply chain ecological cooperation: the bounded rationality of participants mirrors the gradual, trial-and-error strategic adjustments observed in industries undergoing sustainability transitions (e.g., automotive manufacturers phasing in circular economy initiatives); the cost-sharing and speculative penalty mechanisms align with practical arrangements in sectors like electronics, where supply chain contracts enforce environmental cost allocation; the government’s hybrid subsidy–penalty framework reflects common structures in global green manufacturing incentive programs (e.g., proportional subsidies for eco-innovation coupled with tiered penalties for regulatory violations); the differentiation in ecological sensitivity coefficients captures real-world disparities in technological absorption capacity across industries (e.g., varying efficiency in adopting digital green technologies between high-tech and traditional manufacturing). These design elements enable the model to balance theoretical abstraction with empirical relevance, particularly in addressing modern challenges such as collaborative innovation and data security governance in digitally-driven supply chains.

We let x 0 ≤ x ≤ 1 and 1 − x represent the percentages of the suppliers that adopt the “ecological cooperation” strategy and the “non-ecological cooperation” strategy, respectively. Similarly, the proportions of manufacturers adopting the “ecological cooperation” strategy and the “non-ecological cooperation” strategy are y 0 ≤ y ≤ 1 and 1 − y , respectively. In addition, z 0 ≤ z ≤ 1 and 1 − z are the proportions of the governments that choose supervision and non-supervision, respectively.

According to these descriptions, there are eight strategy profiles; Table 2 displays a reward matrix for all players using various strategies.

The expected benefits of the suppliers adopting the “ecological cooperation” and “non-ecological cooperation” strategies are set as V x (Equation 1) and V 1 − x (Equation 2), respectively, and the average expected payoff is set as V x ¯ (Equation 3). V x = y z U 1 + a 1   N + δ U − C 1 + π C 1 + 1 − z U 1 + a 1   N + δ U − C 1 + 1 − y z U 1 + F − C 1 + π C 1 + 1 − z U 1 + F − C 1 (1) V 1 − x = y z U 1 − F + r 1 N − D + 1 − z U 1 − F + r 1 N + 1 − y × U 1 z + U 1 1 − z (2) V x ¯ = x V x + 1 − x V 1 − x (3)

Similarly, the expected payoffs when the manufacturers choose the ecological cooperation and the non-ecological cooperation strategies are set as V y (Equation 4) and V 1 − y (Equation 5), respectively, and the average expected payoff is set as V y ¯ (Equation 6). V y = x z U 2 + a 2   N + 1 − δ U − C 2 + π C 2 + 1 − z × U 2 + a 2   N + 1 − δ U − C 2 + 1 − x z U 2 + F − C 2 + π C 2 + 1 − z U 2 + F − C 2 (4) V 1 − y = x z U 2 − F + r 2 N − D + 1 − z U 2 − F + r 2 N + 1 − x × U 2 z + U 2 1 − z (5) V y ¯ = y V y + 1 − y V 1 − y (6)

In addition, the expected payoffs of the governments selecting the “supervision” and “nonshortision” strategies are set as V z (Equation 7) and V 1 − z (Equation 8), respectively, and the average expected payoff is set as V z ¯ (Equation 9). V z = x y W 1 + S − C g − π C 1 − π C 2 + 1 − y W 2 + S − C g − π C 1 + D + 1 − x y W 3 + S − C g − π C 2 + D + 1 − y W 4 + S − C g (7) V 1 − z = x W 1 y + W 2 1 − y + 1 − x W 3 y + W 4 1 − y (8) V z ¯ = z V z + 1 − z V 1 − z (9)

According to Assumption 1, the chances x , y , and z of the suppliers, manufacturers and governments adopting the “ecological cooperation,” “ecological cooperation,” and “supervision” strategies change dynamically over time t . As a result, the derivative of their respective timing probability can be used to mathematically define the growth rate of the three strategies— F x , F y , F z . The replicator dynamics equations of the suppliers, manufacturers, and the government are given as follows (Equations 10–12): F x = d x d t = x V x − V x ¯ = x 1 − x V x − V 1 − x = x 1 − x F − C 1 − r 1 N y + a 1   N y + δ U y + D y z + π C 1 z (10) F y = d y d t = y V y − V y ¯ = y 1 − y V y − V 1 − y = y 1 − y F − C 2 − r 2 N x + a 2   N x + 1 − δ U x + D x z + π C 2 z (11) F z = d z d t = z V z − V z ¯ = z 1 − z V z − V 1 − z = z 1 − z S − C g + D x + D y − π C 1 x − π C 2 y − 2 D x y (12)