Stackelberg Game Analysis of Green Design and Coordination in a Retailer-Led Supply Chain with Altruistic Preferences

Abstract

Green design by manufacturers is essential for achieving supply chain sustainability, and large retailers may exhibit altruistic preferences to incentivize such efforts. Accordingly, this study develops three game-theoretic models of a two-echelon supply chain composed of a manufacturer and a dominant retailer, with and without altruistic preferences, to examine how altruism and green design affect firms’ optimal decisions and environmental impact. In addition, two coordination mechanisms—green design cost-sharing and two-part tariff contracts—are proposed under altruistic preferences. We find that the dominant retailer’s altruistic preference can motivate the manufacturer to improve the green design level and increase system profit. Although the dominant retailer has altruistic preference, they cannot always lower the total environmental impact of products, so it is helpful to motivate the manufacturer to reduce the environmental adverse impact by increasing investments in green design. Both the two contracts designed in this paper can achieve incentive compatibility and perfect coordination of supply chain. However, with the retailer’s altruistic preference enhancement, the feasible range of the two contracts will be reduced.

1. Introduction

As the global economy grows rapidly, the problems of environmental pollution and resource shortages caused by the processes of industrialization have become more and more serious [1,2]. How to effectively build an environmentally responsible supply chain system, break the traditional extensive economic growth mode of “pollution first, treatment afterwards”, and minimize the negative environmental impact of manufacturing activities from the source has become a major problem faced by enterprises [3,4]. In this situation, green design, also known as environmental design—as a viable technique for lowering manufacturing resource consumption and environmental impact from the source through continuous design and innovation—has become one of the best choices for enterprises in fulfilling their environmental responsibilities [5,6,7].

Governments around the world have begun guiding and encouraging companies to implement green design practices and produce green products in order to develop a green low-carbon economy and improve the ecological environment [8,9]. In addition, growing environmental awareness among consumers has become a key market driver for manufacturing enterprises to adopt green design strategies [5,7]. Existing studies show that more and more consumers are purchasing ecologically friendly products and are prepared to pay greater costs to help the green sector flourish faster [10,11]. Driven by the above two factors (government and market), more manufacturers begin to integrate the green design concept into the product design and manufacturing process [9,12]. For example, Apple’s 2020 Environmental Progress Report highlights that its green design initiatives have improved material utilization while reducing resource consumption and carbon emissions. Huawei, HP, and many other well-known enterprises integrate green designs into their processes of product design and manufacturing; this not only effectively reduces energy consumption but also provides energy-saving and ecologically friendly goods to customers [12,13].

However, green is never free. Manufacturing enterprises bear huge cost pressures to carry out green design processes, which require continuous R&D (research and development) investments [10,14]. Moreover, green design also has the “dual external effects” of knowledge and environmental spillover, which makes it difficult for many manufacturing enterprises to maintain the motivation to carry out green design processes [7,15]. Simultaneously, with the wide application of information technologies, such as big data, many retail enterprises begin to understand the needs of consumers more and more. Retail enterprises represented by Wal Mart, Taobao, and JD.com (two very famous Chinese online shopping retail platforms) can rise rapidly and become the dominant supply chain, which further weakens the competitiveness of manufacturing enterprises in supply chains [16]. In this situation, manufacturers that implement green design practices struggle to survive in supply chains that are dominated by large retailers [17,18].

In the context of the growing green and low-carbon economy, the environmental impact and sustainability of supply chains have become a significant index for evaluating the success of supply chain management [5]. Most large retailers have begun to implement environmentally responsible supply chain strategies in response to attention from all sectors of society on green and low-carbon developments; this has resulted in many manufacturers bearing huge cost pressures for greening measures [18]. Therefore, while enjoying the advantages brought by manufacturers’ green design practices, numerous large retailers have also started paying attention to the survival and interests of manufacturers who implement green design practices, with the goal of better realizing their own sustainable development strategies [19,20]. For instance, Gome directly benefits Haier and other green manufacturers by canceling the entry fee. Gome and Haier also signed a three-year 50 billion cooperation agreement. As Britain’s largest retailer, Marks & Spencer has direct investment in the green design projects of their manufacturers and has obtained long-term and stable cooperation agreements because of its fair treatment of manufacturers [8]. Walmart supports green supplier development through sustainable supply chain financing plans and adding environmental labels to green products [5]. As an example of a contrast, Alibaba ignored the interests of its manufacturers and forced them to choose between it and other retailers; this led to Alibaba being boycotted by its manufacturers and being fined up to CNY 18.228 billion by relevant departments. These practical examples show that whether one seeks to maintain enterprise partnerships in the supply chain or seeks to construct a green and low-carbon socioeconomic system, dominant retailers who are benefiting from promoting green design products should focus on the interests of their manufacturers who are implementing green design practices, i.e., it is in their best interests to maintain a certain degree of altruistic preference [16].

Although prior studies have investigated green design strategies, altruistic preferences, and coordination contracts in supply chains, research that integrates these three elements is still scarce, particularly in retailer-led contexts where large retailers exert dominant market power. This gap is critical because the success of green transformation depends not only on manufacturers’ investment decisions and contractual mechanisms, but also on whether dominant retailers are willing to internalize manufacturers’ interests through altruistic behavior. While existing research confirms that incentive and cooperation contracts play a vital role in supporting manufacturers’ green transformation, little is known about how a retailer’s altruistic preference jointly affects green design decisions, supply chain performance, and environmental outcomes, or how coordination contracts should be structured under this dual influence. Moreover, analytical studies addressing these interactions from the perspective of environmental responsibility remain largely absent, underscoring the necessity of the present research.

Based on this, our research questions are: Firstly, how does the retailer’s altruistic preferences and supply chain decision mode affect the manufacturer’s green design decision? Secondly, do the retailer’s altruistic preferences always contribute to improving supply chain performance and reducing product environmental impact? Thirdly, how to realize the supply chain effective coordination considering altruistic preference and green design at the same time?

To answer the above questions, we construct decentralized and centralized green design decision models of environmental responsibility supply chains for retailers without and with altruistic preferences, and we derive and compare the equilibrium results under different models. Firstly, we focus on the effect of the dominant retailer’s altruistic preferences on the manufacturer’s green design decisions, supply chain optimal operations, and environment. Second, the impacts of green-design-related parameters on the supply chain’s optimal operation and environment are investigated. Finally, the coordination differences between green design cost-sharing contracts and two-part tariff contracts under the conditions of a dominant retailer’s altruistic preferences are compared.

This study makes contributions to the previous research from three aspects. Firstly, differently from traditional green supply chain research, we integrate altruistic preferences and green designs into the retailer-led environmental responsibility supply chain; here, we consider the three functions (cost, demand, and environment) through which a manufacturer implements green design practices in the models, and we analyze the interactions between altruistic preferences and green design practices. Secondly, we theoretically and numerically analyze the impacts of altruism preferences and green-design-related parameters on supply chain operation and environment. In addition, we also clarify the conditions that are required for a supply chain to achieve balanced economic and environmental development from the perspective of environmental responsibility. Finally, we design a green design cost-sharing contract and a two-part tariff contract under the altruistic preference of a dominant retailer to achieve Pareto improvements among supply chain members; then, we discuss the impacts of altruistic preferences on coordination contracts.

The rest of this paper is organized as follows. In Section 2, we provide a related literature review. In Section 3, we introduce the problem and models. In Section 4, we discuss the equilibrium results. In Section 5, we design the coordination mechanism under altruistic preference. Section 6 examines the findings by numerical simulation. Finally, we summarize the conclusions and discuss the future research directions in Section 7. For the sake of clarity and readability, the proofs of Propositions are provided in Appendix A.

2. Literature Review

This study is primarily related to two streams of research: green design/green investment strategies in supply chains and the altruistic preferences of supply chains. The first stream focuses on how manufacturers implement green design practices to reduce resource consumption and environmental impact, and how such strategies affect costs, demand, and overall supply chain performance. The second stream investigates altruistic preferences, which refer to circumstances in which decision makers consider not only their own profit but also the profit of another party. In this study, altruistic preference is attributed exclusively to the dominant retailer, who may incorporate the manufacturer’s profit into their utility in order to promote green design practices and to enhance supply chain sustainability. Furthermore, since the interaction between the dominant retailer and the manufacturer follows a hierarchical decision-making structure, this study also relates to the stream of research employing Stackelberg games in supply chains, which provides a natural framework for analyzing such leader–follower relationships.

2.1. Green Design/Green Investment Strategies in Supply Chain

An environmentally responsible supply chain requires its members to have certain environmentally responsible behaviors, the details of which have become a new research field [21]. The existing literature shows that a lot of research has been conducted based on green behaviors, such as green technology investments or the green innovation of enterprises [1,2,8]. This kind of research mainly discusses the relevant driving factors of enterprises’ green behavior under market-driven mechanisms or government environmental regulation policies [22,23]. Consumer environmental awareness (CEA) is continuously strengthening; accordingly, the impacts of CEA on the sales of green products and the green behaviors of enterprises are also increasing [6,24]. More and more scholars are discussing CEA as an important variable in their research frameworks for investigating green supply chain management [17,25]. Some studies have focused on the impact of CEA on supply chain operation coordination and green decision-making, such as Ghosh et al. [26] and Peng et al. [27].

Moreover, some researchers have considered the impact of enterprise competition or cooperation on supply chain greening development. Yu et al. [28] analyzed the impact of different cooperation contracts between enterprises on green technology inputs. Wang et al. [17] discussed the impact of government subsidies and channel power on green decisions and performances in the supply chain. Guan et al. [25] discussed ways of coordinating the green inputs of manufacturers and the service inputs of retailers through profit-sharing contracts. Li et al. [29] analyzed the impact differences in different types of cost-sharing contracts and revenue-sharing contract on manufacturers’ green designs, retailers’ market effort levels, and supply chain performances. Heydari et al. [30] investigated the impact of whether the retailer implements green marketing on the competition between green and non-green products, and designed a new coordination contract to alleviate channel conflict. Some scholars also investigated the impact of government subsidies, taxes, and other policies, such as Bai et al. [31]. The above research focuses on analyzing the impact of enterprise green behavior on market demand, while ignoring the multiple impacts of green design on demand, cost, and environment.

At present, some researchers have discussed the significant advantages of green design practices through qualitative research [32]. Raz et al. [33] introduced the concept of green design practices into the newsboy model and pointed out that enterprises could reduce the production cost and environmental impact of product units through green design practices. Yao et al. [7] explored the issue of choosing green design models for sustainable supply chains under different channel power structures. Yenipazarli [18] compared the impacts of cost-sharing contracts and revenue-sharing contracts on improving the green design level and system profits. Cai et al. [34] discussed manufacturer green design decision-making under environmental tax, showing that zero tax and linear tax are more conducive to improving the green design level than fixed tax.

However, the existing studies have focused on how companies can improve supply chain performance through green investment from the economic level, assuming that the supply chain decision makers are completely rational, that is, they believe that decision makers use maximizing own profits as their decision criteria. Therefore, the paper focuses on the impact of green design on supply chain optimization decisions and environment, and considers the altruistic preferences of the dominant retailer, especially the impact of altruistic preferences on coordination contracts and environment.

2.2. Altruistic Preferences in Supply Chains

A large number of empirical studies in behavioral economics show that enterprises do not only consider their own interests when making actual decisions; they also consider their social preferences, such as fairness and altruism [35,36]. Fairness preferences have been extensively investigated; for example, Cui et al. [37] introduced fairness preference into their supply chain operation optimization models and analyzed the coordination contracts of supply chains under retailer fairness preference. Liu et al. [38] discussed the effects of fairness preferences on profit distribution and product greenness among green supply chain members and designed corresponding coordination contracts. Singh et al. [39] analyzed the impact of enterprises’ fair concern behaviors on the pricing and green decision-making of the supply chain under different competition modes. Wu et al. [40] explored the issue of subsidies provided by retailers to financially constrain green manufacturers, considering whether retailers have concerns about fairness.

Through the existing research on supply chain operations with fairness preferences, it can be found that subordinate enterprises are more likely to have fairness preferences, and fairness preferences are detrimental to the long-term stability of the operations of dominant enterprises and supply chains [41,42]. Therefore, many dominant enterprises will avoid subordinate enterprises with fairness preferences by actively transferring their profits—that is, dominant enterprises have a certain altruistic preference [43].

In recent years, altruistic preference, as an effective strategy for supply chain leaders to care about the interests of supported formulas for social pressure, long-term development and cooperation, corporate social responsibility, or other strategic needs [16], has captured the attention of many scholars. Loch and Wu [35] show early consideration of the impact of altruistic preference on supply chain optimization decisions and showed that enterprises will reflect their enterprise value through altruistic behavior to a certain extent. Ge et al. [44] constructed a newsboy model considering altruistic preferences and proved that the altruistic preferences of enterprises can effectively improve the supply chain’s operational efficiency. Feng et al. [41] studied the joint replenishment problem of retailers under the carbon cap-and-trade mechanism and retailers having altruistic preference, and designed a supply chain profits distribution mechanism. Lin et al. [45] investigated the operation optimization problem of supply chains under altruistic preference considering two competitive retailers. Ma et al. [46] introduced altruistic preference into a product-service supply chain optimization model and studied the quality and service decision-making problems of supply chains. Wang et al. [16] analyzed the impact of retailers’ altruistic preferences on low-carbon supply chain decision-making and coordination. Wu et al. [19] studied the impact of retailers’ altruistic preferences on manufacturers’ green investment decisions in competitive supply chains under carbon tax policies.

Most existing studies on altruistic preferences focus on how firms’ altruistic behavior influences supply chain decisions and performance, while few have examined the impact of altruistic preferences on firms’ green and low-carbon practices as well as on supply chain coordination. The majority of research on green and low-carbon supply chain development and coordination contract design assumes that firms are rational profit-maximizing agents, without considering the role of altruistic behavior. Although Wang et al. [16] analyzed the effect of retailer altruistic preferences on low-carbon supply chain decisions and coordination, their study did not account for the multiple impacts of green design, nor did it investigate the differences in coordination contracts under altruistic preferences. By integrating green design, altruistic preferences, and coordination contracts within a retailer-led supply chain framework, this paper addresses these gaps and contributes to the literature on sustainable supply chain management.

2.3. Stackelberg Games in Supply Chains

The Stackelberg game, characterized by a leader–follower decision sequence, has become a fundamental analytical tool in supply chain research [4,47]. Its hierarchical structure is particularly suitable for modeling interactions between dominant and subordinate firms, as it reflects the reality that one party often has the power to move first, while the other optimizes decisions in response [10,11]. In two-echelon supply chains, the retailer or manufacturer may assume the leader role, while the other acts as the follower. This framework captures strategic asymmetries that cannot be represented by simultaneous-move games [5,6].

A rich body of research has applied Stackelberg games to examine various supply chain issues [5,6,7,8,9,10]. For example, they have been used to analyze wholesale pricing contracts, green investment, channel coordination, and information sharing [7,15,48]. In particular, when the retailer is the dominant party—as is common in industries such as consumer electronics, large-scale retailing, and e-commerce platforms—the Stackelberg game framework has been widely adopted to capture the retailer’s leadership in setting prices or contract terms [16,18]. Similarly, when the manufacturer is the dominant party, Stackelberg games have been employed to study product quality improvements, technology adoption, and emission-reduction decisions [1,9,49]. These applications confirm the flexibility of Stackelberg games in analyzing sequential decision-making within supply chains.

Similarly to the above studies, this study also adopts the Stackelberg game approach for modeling and analysis. The difference is that our framework simultaneously incorporates the multiple effects of green design practices, the altruistic preferences of the dominant retailer, and CEA. We construct corresponding decision models based on the Stackelberg game and derive optimal equilibrium solutions for different scenarios using backward induction. Through equilibrium analysis, we further reveal how altruistic preferences influence the manufacturer’s green design decisions, supply chain coordination, and environmental performance.

2.4. Research Gaps

The analysis of the relevant literature reveals three research gaps. First, the existing literature provides an in-depth discussion of the problems of green investment, altruistic preferences, or channel coordination. However, as far as we know, there is no research that has combined the three elements for exploration, let alone research which has conducted an analysis of the balance between environmental responsibility and economic aspects. Secondly, although Wang et al. [16] analyzed the impact of retailer altruistic preferences on manufacturer low-carbon investments, they did not consider the multiple impacts of green design practices, nor did they compare or analyze the differences in coordination mechanisms under the interaction between altruistic preferences and green design practices. Finally, the coordination effectiveness of the two-part tariff contract and cost-sharing contract under the influence of altruistic preference and green design practices has not been studied. Therefore, we integrate the impact of green design practices on demand, cost, and environment, as well as altruistic preference, into the decision-making model of enterprises, and design a green design cost-sharing contract and a two-part tariff contract. On the one hand, our research enriches the literature on green investment decision-making and the coordination of the environmental responsibility supply chain; on the other hand, it provides management insights for supply chain members in collaboration and performance of environmental responsibilities.

3. Models Construction and Solution

3.1. Problem Description and Assumptions

In recent years, governments have implemented increasingly stringent environmental regulations, while consumers have become more conscious of the environmental impact of products. As a result, manufacturers are expected to incorporate environmental considerations into the early stages of production and actively adopt green design. Green design refers to reducing resource consumption and pollutant emissions through environmentally friendly production processes and product improvements.

We consider an environmental responsibility supply chain to consist of a manufacturer and a dominant retailer. The two parties interact in a two-echelon Stackelberg game under complete information. The manufacturer determines the level of green design investment at the beginning of production, while the retailer is responsible for selling products to consumers. The green design decision not only affects production costs but also influences consumer demand by improving product environmental performance.

In practice, large retailers often recognize the long-term benefits of sustainability and may exhibit altruistic preferences toward their upstream manufacturers. Such altruistic behavior implies that, beyond maximizing their own profits, retailers also consider the manufacturer’s profit in their utility. This mechanism can encourage manufacturers to adopt higher levels of green design and contribute to sustainable supply chain development. For instance, Walmart has introduced strict green packaging and product design standards for its suppliers to reduce resource consumption and environmental impact. Similarly, Apple’s annual Environmental Progress Report documents substantial investments in green design, aiming to lower carbon emissions and enhance consumer recognition. These practices illustrate that manufacturers often face high upfront costs for green investments, and that dominant retailers may adopt incentive mechanisms, including altruistic preferences, to encourage sustainable supply chain operations.

Accordingly, we construct green design decision-making models of the retailer-dominated supply chain both without and with altruistic preference. These models allow us to analyze the effects of key factors—including the retailer’s altruistic preference coefficient, the manufacturer’s green design cost parameter, and CEA—on the manufacturer’s green design decisions, overall supply chain performance, and environmental impact.

For clarity, we present all symbols and their definitions in

Table 1. Notation’s description.

Notation	Description
$c$	The production cost of a product unit when a manufacturer does not implement green design practices.
$\varphi$	Environmental impact of a product unit when a manufacturer does not implement green design practices.
$r$	The degree of reduction in product unition cost caused by green design level, $0<r<1$.
$\lambda$	Reduction degree of environmental impact of a product unit caused by green design level, $0<\lambda <1$.
$c(e)$	The product unition cost when a manufacturer implements green design practices.
$\varphi (e)$	Environmental impact of a product unit when a manufacturer implements green design practices.
$\theta$	The dominant retailer’s altruistic preference coefficient.
$a$	Potential market size.
$b$	Consumers’ price sensitivity, $b>0$.
$\beta$	CEA level (consumer sensitivity to manufacturer green design level), $\beta >0$.
$q$	Market demand.
$k$	Green design investment cost coefficient, $k>0$.
$E$	Total environmental impact of products.
${\pi }_X^i$	The profits of supply chain members or whole, $i=\{C,D,A\}$, represents the centralized decision model and the decentralized decision model for retailers without/with altruistic preferences; $X=\{M,R,S\}$ represents the manufacturer, retailer, and supply chain system.
Endogenous variables
$w$	Wholesale price.
$p$	Retail price.
$m$	Retailer profit margin.
$e$	Manufacturer green design level.

. And the following relevant assumptions were introduced as the basis for subsequent analysis.

Assumption 1.

In line with Yenipazarli [18], the product market demand function under a manufacturer’s green design practices is $q(p,e)=a-bp+\beta e$.

The adoption of a linear demand function is justified for three reasons. First, it captures the empirical regularity that product demand decreases with price while increasing with environmental quality, which is consistent with observed practices of green design adoption in industry [5,6]. Second, the linear specification has been widely used in supply chain and operations management research, providing analytical tractability and allowing closed-form solutions to be derived [7,18]. Third, although alternative nonlinear demand forms could also be considered, prior studies have shown that the qualitative insights regarding green investment and consumer awareness remain robust across different specifications [17,24]. Therefore, this assumption strikes a balance between empirical plausibility and analytical convenience, ensuring that the model is both interpretable and applicable to real-world supply chain contexts.

Assumption 2.

When a manufacturer implements green design practices, the production cost of a product unit is $c(e)=(1-re)c$; the environmental impact degree of the product unit is $\varphi (e)=(1-\lambda e)\varphi$.

This assumption captures a practical pattern whereby firms reduce resource consumption and environmental impact through investment in green design practices. For example, BYD has continuously invested in green design practices, which has reduced the production costs of new energy vehicles by 30% and has improved energy efficiency and lowered pollutant emissions during both production and usage. Similarly, Gree’s award-winning, green-designed air conditioners save 241 kWh of electricity per unit annually. These cases demonstrate that green design practices can effectively reduce product unit costs and the environmental impact of products. Moreover, this assumption is consistent with the works of Raz et al. [33] and Yao et al. [7].

Assumption 3.

Referring to [15,24], we assume that the manufacturer’s investment cost of implementing green design is quadratic, i.e., $h(e)=k{e}^2$. The quadratic form is widely adopted in the literature as it captures the realistic feature that the marginal cost of green investment increases with the level of greenness. To ensure the concavity of the profit function and the uniqueness of the equilibrium solution, the green design investment cost coefficient must satisfy $k>{\displaystyle \frac{(a-bc)(bcr+\beta )+{(bcr+\beta )}^2}{4b}}$.

In fact, the lower bound of the green design investment cost coefficient $k$ is derived from the negative definiteness condition of the Hessian matrices across all decision models in this study. From a modeling and solution perspective, this condition ensures that all profit functions are concave with respect to the endogenous variables and that a unique optimal solution exists. Economically, it guarantees that the marginal benefit of green design cannot indefinitely exceed its marginal cost; otherwise, the manufacturer would unrealistically choose an infinitely high level of green investment. In practice, this inequality reflects the reality that beyond a certain point, additional green design efforts require disproportionately higher investment, which is consistent with actual supply chain scenarios.

3.2. Research Method

In this study, we adopt a Stackelberg game framework to model the interaction between the dominant retailer and the manufacturer. In this setting, the retailer acts as the leader, making decisions first, while the manufacturer acts as the follower, responding optimally to the retailer’s decisions. This hierarchical structure captures the reality of retailer-led supply chains, where large retailers often possess greater market power. Based on this framework, we construct the corresponding decision models under different scenarios of altruistic preference and green design. The equilibrium analysis is then conducted by applying backward induction, which allows us to solve the game sequentially from the follower’s decision to the leader’s optimal strategy.

To derive the equilibrium solutions, we further employ unconstrained nonlinear optimization techniques. Specifically, the first-order conditions of the profit functions with respect to the decision variables are solved to obtain optimal candidate solutions. The sufficiency and uniqueness of these solutions are then established by verifying the second-order conditions, i.e., confirming that the Hessian matrices are negative definite. This combined approach of Stackelberg modeling, backward induction, and optimization methods is widely applied in supply chain game-theoretic research and ensures the robustness and interpretability of the equilibrium results.

3.3. Centralized Decision Model (Model $C$)

In Model C, the supply chain is coordinated as a unified entity, and both the green design level $e$ and the retail price $p$ are determined jointly to maximize the overall system profit. The profit function of the supply chain consists of two components: (1) revenue, which equals the retail price $p$ minus the unit production cost multiplied by the market demand $q$; (2) green design cost, captured by a quadratic function $k{e}^2$ to reflect increasing marginal investment. Bringing these elements together, the profit function of the centralized supply chain system is formulated as follows:

$${\pi }_S^C(p,e)=(p-(1-re)c)(a-bp+\beta e)-k{e}^2$$

(1)

Theorem 1.

In Model $C$, the optimal green design level is $e^{C\ast }={\displaystyle \frac{(a-bc)(bcr+\beta )}{4kb-{(bcr+\beta )}^2}}$, the optimal retail price and market demand are $p^{C\ast }={\displaystyle \frac{2k(a+bc)-c(ar+\beta )(bcr+\beta )}{4kb-{(bcr+\beta )}^2}}$ and $q^{C\ast }={\displaystyle \frac{2kb(a-bc)}{4kb-{(bcr+\beta )}^2}}$, and the overall profit of the supply chain system is ${\pi }_S^{C\ast }={\displaystyle \frac{k{(a-bc)}^2}{4kb-{(bcr+\beta )}^2}}$.

Firstly, according to Equation (1), the Hessian matrix of ${\pi }_S^C(p,e)$ is $H^C=\left[\begin{array}{ll}-2b& \beta -bcr \\ \beta -bcr& 2\beta cr-2k\end{array}\right]$, it is easy to verify when $k>{\displaystyle \frac{{(bcr+\beta )}^2}{4b}}$, the $H^C$ is negative definite, which guarantees concavity of the system profit function and ensures the uniqueness of the solutions. This second-order condition ensures the existence of equilibrium solutions. At this point, setting the first-order derivatives with respect to $p$ and $e$, ${\displaystyle \frac{𝜕{\pi }_S^C(p,e)}{𝜕p}}=0$, ${\displaystyle \frac{𝜕{\pi }_S^C(p,e)}{𝜕e}}=0$, the first-order condition of ${\pi }_S^C(p,e)$ yields the optimal $e^{C\ast }$ and $p^{C\ast }$. Furthermore, according to $q(p,e)$ and Equation (1), we can obtain the maximum market demand $q^{C\ast }$ and ${\pi }_S^{C\ast }$.

3.4. Decentralized Model When the Dominant Retailer Is Without Altruistic Preference (Model $D$)

In model $D$, the decision-making sequence is such that the dominant retailer, acting as the Stackelberg leader, first determines the unit sales profit $m$, after which the manufacturer, as the follower, chooses the wholesale price $w$ and the green design level $e$. The manufacturer’s profit function consists of wholesale revenue, given by the unit margin ($w-(1-re)c$) multiplied by the market demand ($a-bw-bm+\beta e$), minus the quadratic green design investment cost $k{e}^2$. The retailer’s profit function consists of her per-unit profit margin $m$ multiplied by the same market demand. Thus, the profit functions of the manufacturer and the retailer are expressed as follows:

$${\pi }_M^D(w,e)=(w-(1-re)c)(a-bw-bm+\beta e)-k{e}^2$$

(2)

$${\pi }_R^D(m)=m(a-bw-bm+\beta e)$$

(3)

Theorem 2.

In Model $D$, the retailer’s optimal unit profit and products retail prices are $m^{D\ast }={\displaystyle \frac{a-bc}{2b}}$ and $p^{D\ast }={\displaystyle \frac{2kb(3a+bc)-(bcr+\beta )(a(bcr+\beta )+bc(ar+\beta ))}{2b(4kb-{(bcr+\beta )}^2)}}$; the manufacturer’s optimal products wholesale prices and green design level are $w^{D\ast }={\displaystyle \frac{2k(a+3bc)-c(bcr+\beta )(ar+bcr+2\beta )}{2(4kb-{(bcr+\beta )}^2)}}$ and $e^{D\ast }={\displaystyle \frac{(a-bc)(bcr+\beta )}{2(4kb-{(bcr+\beta )}^2)}}$; the optimal market demand is $q^{D\ast }={\displaystyle \frac{kb(a-bc)}{4kb-{(bcr+\beta )}^2}}$. The profits of manufacturer, retailer, and supply chain system are ${\pi }_M^{D\ast }={\displaystyle \frac{k{(a-bc)}^2}{4(4kb-{(bcr+\beta )}^2)}}$, ${\pi }_R^{D\ast }={\displaystyle \frac{k{(a-bc)}^2}{2(4kb-{(bcr+\beta )}^2)}}$, and ${\pi }_S^{D\ast }={\displaystyle \frac{3k{(a-bc)}^2}{4(4kb-{(bcr+\beta )}^2)}}$.

We employ the backward induction method to derive the equilibrium. Therefore, although the dominant retailer is the leader and makes her decision first in the Stackelberg structure, the equilibrium derivation follows a reverse order through backward induction. Specifically, we first derive the manufacturer’s best-response functions conditional on the retailer’s decision variables, and then substitute these responses into the retailer’s optimization problem to obtain the final equilibrium outcomes.

Firstly, according to Equation (2), the Hessian matrix of ${\pi }_M^D(w,e)$ is $H^D=\left[\begin{array}{ll}-2b\beta & -bcr \\ \beta -bcr& \beta cr-2k\end{array}\right]$; this is easy to verify when $k>{\displaystyle \frac{{(bcr+\beta )}^2}{4b}}$. Here, the $H^D$ is negative definite, and ${\pi }_M^D(w,e)$ is concave in the variables $w,e$. This second-order condition ensures the existence of equilibrium solutions. The first-order conditions of the manufacturer yield the following feedback functions: $w^D=\frac{2k(a-bm+bc)-(bcr+\beta )(cr(a-bm)-\beta c)}{4kb-{(bcr+\beta )}^2}$ and $e^D=\frac{(bcr+\beta )(a-bm-bc)}{4kb-{(bcr+\beta )}^2}$. Furthermore, the optimal feedback functions, $w^D$ and $e^D$, are substituted into Equation (3), respectively. Here, we can verify ${\displaystyle \frac{{𝜕}^2{\pi }_R^D(m)}{𝜕m^2}}={\displaystyle \frac{-4k{b}^2}{4kb-{(bcr+\beta )}^2}}<0$. The negativity of the second derivative ensures that the retailer’s profit function with respect to the marginal profit is strictly concave, thereby guaranteeing the existence of a unique optimal solution. The first-order condition, ${\displaystyle \frac{𝜕{\pi }_R^D(m)}{𝜕m}}=0$, yields the retailer’s optimal unit profit $m^{D\ast }$. By substituting $m^{D\ast }$ into $w^D$ and $e^D$, the optimal $w^{D\ast }$ and $e^{D\ast }$ can be obtained. Furthermore, by substituting $w^{D\ast }$, $m^{D\ast }$, and $e^{D\ast }$ into $p=w+m$ and $q(p,e)$, the $p^{D\ast }$ and $q^{D\ast }$ can be obtained. Finally, according to Equations (2) and (3), ${\pi }_M^{D\ast }$, ${\pi }_R^{D\ast }$, and ${\pi }_S^{D\ast }$ can be obtained.

3.5. Decentralized Model When the Dominant Retailer Has Altruistic Preferences (Model $A$)

In model $A$, the dominant retailer exhibits altruistic preferences, meaning that her utility is not only determined by her own profit but also partially incorporates the manufacturer’s profit. This reflects real-world cases where large retailers may provide support to green manufacturers to ensure long-term cooperation and enhance supply chain sustainability. Specifically, the retailer’s utility is modeled as a weighted sum of her own profit and the manufacturer’s profit, with the altruism coefficient $\theta$ ($0<\theta <1$) representing the degree of concern for the manufacturer’s performance [16,37]. Although alternative utility specifications could be adopted, prior studies suggest that the qualitative insights regarding the role of altruism in incentivizing green investment and improving supply chain coordination remain robust across different formulations, ensuring both the theoretical validity and the practical relevance of this assumption [16,43]. Accordingly, the utility function of the retailer with altruistic preferences is defined as

$$U_R^A(m)={\pi }_R^A(m)+\theta {\pi }_M^A(w,e)$$

(4)

The manufacturer’s profit function consists of wholesale revenue, defined as the unit margin ($w-(1-re)c$) and multiplied by market demand ($a-bw-bm+\beta e$), minus the quadratic green design cost $k{e}^2$. The retailer’s profit function consists of their unit margin $m$, multiplied by the same market demand. The profit functions of the manufacturer and retailer are expressed as follows:

$${\pi }_M^A(w,e)=(w-(1-re)c)(a-bw-bm+\beta e)-k{e}^2$$

(5)

$${\pi }_R^A(m)=m(a-bw-bm+\beta e)$$

(6)

Theorem 3.

In Model $A$, the retailer’s optimal product retail prices and unit profit are $p^{A\ast }={\displaystyle \frac{(2kb-\beta bcr)(a(3-2\theta )+bc)-bc(abc{r}^2(2-\theta )+{\beta }^2)-a{\beta }^2(1-\theta )}{b(2-\theta )(4kb-{(bcr+\beta )}^2)}}$ and $m^{A\ast }={\displaystyle \frac{(a-bc)(1-\theta )}{b(2-\theta )}}$; the manufacturer’s optimal product wholesale prices and green design level are $w^{A\ast }={\displaystyle \frac{(2k-\beta cr)(a+bc(3-2\theta ))-b{c}^2{r}^2(a+bc(1-\theta ))-{\beta }^{2}c(2-\theta )}{(2-\theta )(4kb-{(bcr+\beta )}^2)}}$ and $e^{A\ast }={\displaystyle \frac{(a-bc)(bcr+\beta )}{(2-\theta )(4kb-{(bcr+\beta )}^2)}}$; the optimal market demand is $q^{A\ast }={\displaystyle \frac{2kb(a-bc)}{(2-\theta )(4kb-{(bcr+\beta )}^2)}}$. The manufacturer’s profit is ${\pi }_M^{A\ast }={\displaystyle \frac{k{(a-bc)}^2}{{(2-\theta )}^2(4kb-{(bcr+\beta )}^2)}}$; the retailer’s profit and utility are ${\pi }_R^{A\ast }={\displaystyle \frac{2k{(a-bc)}^2(1-\theta )}{{(2-\theta )}^2(4kb-{(bcr+\beta )}^2)}}$ and $U_R^{A\ast }={\displaystyle \frac{k{(a-bc)}^2}{(2-\theta )(4kb-{(bcr+\beta )}^2)}}$, and the overall profit of the supply chain system is ${\pi }_S^{A\ast }={\displaystyle \frac{k{(a-bc)}^2(3-2\theta )}{{(2-\theta )}^2(4kb-{(bcr+\beta )}^2)}}$.

We also use the backward induction method to solve it. Firstly, according to Equation (5), the Hessian matrix of ${\pi }_M^A(w,e)$ is $H^A=\left[\begin{array}{ll}-2b& \beta -bcr \\ \beta -bcr& \beta cr-2k\end{array}\right]$, it is easy to verify when $k>{\displaystyle \frac{{(bcr+\beta )}^2}{4b}}$, the $H^A$ is negative definite, and ${\pi }_M^A(w,e)$ is concave in the variables $w,e$. This second-order condition ensures the existence of equilibrium solutions. The first-order conditions of the manufacturer that yield the optimal feedback functions are $w^A=\frac{2k(a-bm+bc)-(bcr+\beta )(cr(a-bm)-\beta c)}{4kb-{(bcr+\beta )}^2}$ and $e^A=\frac{(bcr+\beta )(a-bm-bc)}{4kb-{(bcr+\beta )}^2}$. Further, the optimal feedback functions $w^A$ and $e^A$ are substituted into Equation (4), respectively; we can verify $U_R^A(m)$ is concave function of $m$, according to the first-order conditions of the retailer, the $m^{A\ast }$ can be obtained. By substituting $m^{A\ast }$ into $w^A$ and $e^A$, the optimal $w^{A\ast }$ and $e^{A\ast }$ of the manufacturer can be obtained. Furthermore, substituting $w^{A\ast }$, $m^{A\ast }$, $e^{A\ast }$ into $p=w+m$ and $q(p,e)=a-bp+\beta e$, the $p^{A\ast }$, $q^{A\ast }$ can be obtained. Finally, according to Equations (4)–(6), the ${\pi }_M^{A\ast }$, ${\pi }_R^{A\ast }$, $U_R^{A\ast }$, ${\pi }_S^{A\ast }$ can be obtained.

4. Equilibrium Result Analysis

Firstly, the effect of retailer’s altruistic preference on green design level, enterprise performance, and environment were analyzed. Secondly, the impact of CEA and green design cost parameters on operational performance of supply chains are investigated.

4.1. The Effect of Retailer’s Altruistic Preference on Enterprise Performance and Environment

Proposition 1.

In the retailer-led environmental responsibility supply chain, the equilibrium results for the retailer’s altruistic preference satisfy ${\displaystyle \frac{𝜕w^{A\ast }}{𝜕\theta }}>0$, ${\displaystyle \frac{𝜕p^{A\ast }}{𝜕\theta }}<0$, ${\displaystyle \frac{𝜕m^{A\ast }}{𝜕\theta }}<0$, ${\displaystyle \frac{𝜕e^{A\ast }}{𝜕\theta }}>0$, and ${\displaystyle \frac{𝜕q^{A\ast }}{𝜕\theta }}>0$.

Proposition 1 shows that with the enhancement of the dominant retailer’s altruistic preference degree, the manufacturer’s green design level, products wholesale price, and market demand will increase accordingly, but the retailer’s marginal profit and products retail price will decrease, since the increase in retailer’s altruistic preference degree means that it will focus more on the manufacturer’s income when making decisions. At this time, on one hand, the retailer will increase marginal revenue of the manufacturer by sacrificing part of the marginal revenue. On the other hand, it will stimulate consumers and expand market demand by reducing retail prices, so as to make up for her own loss of profit and further increase the profit of the manufacturer (that is, the so-called “small profit and quick turnover”). Simultaneously, the manufacturer will also increase the green design level to increase demand, which not only helps increase her own profit, but also responds to the retailer’s concession behavior, thereby forming good positive feedback.

Proposition 1 indicates that a higher degree of altruistic preference by the dominant retailer not only motivates the manufacturer to enhance its green design level, but also improves consumer welfare by increasing market demand and lowering the effective purchase price of products. A practical example can be found in the cooperation between Gree, a well-known Chinese air conditioner manufacturer, and JD.com, one of China’s largest self-operated e-commerce retailers. By providing technological, data, and service support for Gree’s R&D and sales, JD.com has helped to stimulate consumer demand. During the 618 shopping festival in 2021, JD.com further promoted sales through targeted logistics subsidies and consumer discounts (over 200 minus 30, etc.), enabling Gree’s green air conditioners to consistently rank among the top-selling brands.

Proposition 2.

In the retailer-led environmental responsibility supply chain, the optimal profit and utility about retailer’s altruistic preference satisfy ${\displaystyle \frac{𝜕{\pi }_M^{A\ast }}{𝜕\theta }}>0$, ${\displaystyle \frac{𝜕{\pi }_R^{A\ast }}{𝜕\theta }}<0$, ${\displaystyle \frac{𝜕U_R^{A\ast }}{𝜕\theta }}>0$, and ${\displaystyle \frac{𝜕{\pi }_S^{A\ast }}{𝜕\theta }}>0$.

Proposition 2 demonstrates that as the dominant retailer’s altruistic preference increases, her own profit declines, whereas the manufacturer’s profit, the retailer’s utility, and the overall supply chain performance all improve. This occurs because stronger altruism leads to higher wholesale prices and greater market demand, but also lower retail prices, which compresses the retailer’s margin. By forgoing part of her revenue, the retailer not only secures higher utility through enhanced goodwill and stronger partnerships, but also supports the manufacturer and improves supply chain performance. A practical illustration is Suning’s policies during the COVID-19 pandemic in 2020: the retailer reduced or waived rents and provided traffic exposure and financial support to suppliers. Although these measures reduced its short-term profits, they effectively relieved manufacturers’ financial pressures, enhanced goodwill, and reinforced stable supply chain partnerships.

Propositions 1 and 2 together suggest that stronger altruistic preferences from the dominant retailer stimulate the manufacturer’s investment in green design, expand market demand for eco-friendly products, increase the profits of both the manufacturer and the supply chain, and reinforce cooperation among supply chain members. In the context of the green economy, such preferences not only provide consumers with higher-quality green products at lower prices but also accelerate the low-carbon transformation of manufacturing firms while enhancing the retailer’s social reputation and long-term partnerships. Evidence can be seen in Marks & Spencer’s “Plan A” initiative, which funded suppliers’ green projects to reduce costs, boost demand, and build lasting collaboration, as well as in JD.com’s support for Gree through data-driven sales assistance and logistics subsidies during major promotions such as the 618 festival. Both cases illustrate how retailer altruism generates economic, environmental, and relational benefits in retailer-led supply chains.

Proposition 3.

In the retailer-led environmental responsibility supply chain, the equilibrium results under three decision modes satisfy $w^{A\ast }>w^{D\ast }$, $p^{D\ast }>p^{A\ast }>p^{C\ast }$, $e^{C\ast }>e^{A\ast }>e^{D\ast }$, and $q^{C\ast }>q^{A\ast }>q^{D\ast }$.

Proposition 3 shows that in increasing the green design level and market demand, and lowering the products price, the centralized decision mode is always best; the decision mode under the retailer with altruistic preference and is better than the retailer with no altruistic preference. In fact, when the retailer has altruistic preferences, she will increase the manufacturer’s revenue through two aspects: on the one hand, she allows the manufacturer to appropriately increase the wholesale price of products; on the other hand, she can improve product demand by reducing the retail price, and at the same time, she can also achieve the effect of encouraging the manufacturer to improve the green design level.

Taking China’s home appliance industry as an example, a series of government-led appliance upgrade policies have encouraged manufacturers to increase investment in green design. This has improved product performance, reduced energy consumption, and significantly enhanced environmental outcomes—for instance, Haier’s fluorine-free refrigerators—while simultaneously leading to higher product prices. As dominant retailers in the supply chain, JD.com and Suning have responded by introducing integrated preferential schemes such as platform subsidies, and old-for-new trade-in subsidies. These measures have effectively lowered the retail prices of eco-friendly products, stimulated market demand, and accelerated the green and low-carbon transition of manufacturers, thereby facilitating consumers’ shift toward environmentally friendly appliances.

Proposition 3 further indicates that when the dominant retailer exhibits altruistic preferences, it consistently enhances the manufacturer’s green design level, reduces retail prices, and expands demand. Accordingly, in addition to guiding the low-carbon transformation of manufacturing enterprises, the government, as a market regulator, may also encourage altruistic behavior by retailers through targeted incentive policies. Such policies would not only accelerate the green transformation of manufacturers but also help alleviate the persistent challenge of high prices for environmentally friendly products.

Proposition 4.

In the retailer-led environmental responsibility supply chain, the optimal profits and utilities under three decision modes satisfy the following conditions: (1) ${\pi }_M^{A\ast }>{\pi }_M^{D\ast }$, ${\pi }_R^{D\ast }>{\pi }_R^{A\ast }$, $U_R^{A\ast }>{\pi }_R^{D\ast }$, and ${\pi }_S^{C\ast }>{\pi }_S^{A\ast }>{\pi }_S^{D\ast }$; (2) ${\pi }_R^{D\ast }=2{\pi }_M^{D\ast }$ and $U_R^{A\ast }>{\pi }_M^{A\ast }$ when $0<\theta \le {\displaystyle \frac{1}{2}}$ and $2{\pi }_M^{A\ast }>{\pi }_R^{A\ast }\ge {\pi }_M^{A\ast }$, and when ${\displaystyle \frac{1}{2}}<\theta <1$ and ${\pi }_M^{A\ast }>{\pi }_R^{A\ast }$.

Proposition 4 shows that when the dominant retailer has no altruism preference, or she has a lower altruism preference ($0<\theta \le {\displaystyle \frac{1}{2}}$), the retailer can still make more profit than the manufacturer. When the retailer’s altruistic preference exceeds a certain level (${\displaystyle \frac{1}{2}}<\theta <1$), the retailer will be less profitable than the manufacturer. This is because under altruistic preference, the retailer will sacrifice part of her own profit to achieve the effect of improving the profits of the manufacturer and supply chain. Simultaneously, the altruistic preference of the retailer is usually not too high ($0<\theta \le {\displaystyle \frac{1}{2}}$); only when facing government policy regulations or external market environment pressure (such as dealing with fierce competition and improving her own reputation, etc.) will it have a high degree of altruistic preference (${\displaystyle \frac{1}{2}}<\theta <1$). For example, Pinduoduo (a Chinese e-commerce platform) quickly reached long-term cooperation with merchants and occupied the market by exempting merchants’ commissions and platform service fees, and became the second largest e-commerce platform in China. On the contrary, in 2013, the green manufacturer Gree stopped the cooperation with Gome because she was dissatisfied with Gome’s price reduction procurement and other behaviors [16].

Proposition 4 shows that although the dominant retailer’s altruistic behavior leads to a partial loss of her own profit, it plays a crucial role in sustaining long-term cooperation with manufacturers and enhancing the retailer’s reputation. Therefore, retailers should adopt a forward-looking perspective and, as leaders, use altruistic behaviors not only to encourage manufacturers to engage in green design and green production, thereby promoting sustainable development, but also to strengthen cooperative relationships among supply chain members and maintain system stability and long-term sustainability.

Proposition 5.

In the retailer-led environmental responsibility supply chain, the environmental impacts under different decision modes satisfy $E^{A\ast }\ge E^{D\ast }$ when $0<\lambda \le {\lambda }_1$; and satisfy $E^{D\ast }>E^{A\ast }$ when ${\lambda }_1<\lambda <1$.

Proposition 5 shows that, compared with the retailer without altruistic preference, in situations where the dominant retailer has altruistic preferences, the total environmental impact of products is not always minimal, but it is always conducive to motivating the manufacturer to enhance the green design level and reduce the unit product environmental impact degree. Specifically, only when the green design can greatly reduce the environmental impact of unit product (that is, ${\lambda }_1<\lambda <1$), the retailer’s altruistic preferences can significantly lower the total environmental impact of products. Further, the retailer’s altruistic preference helps the manufacturer to reduce the unit product environmental impact to a critical point ${\lambda }_1$. This is because the total environmental impact of products depends on two aspects: on the one hand, the sales volume of products ($q$), and on the other, the environmental impact degree of unit product under green design ($(1-\lambda e)\varphi$, the larger the $\lambda$, the smaller the environmental impact of unit product under green design). Therefore, when $\lambda$ is smaller, the product sales have a more significant effect on the overall environment impact of products; with the increase of $\lambda$, the environmental impact degree of unit product is getting smaller and smaller, and at this time, the effect of $\lambda$ on the total environmental impact of products becomes more significant.

Proposition 5 indicates that when green design only slightly reduces the environmental impact of a single product, the dominant retailer’s altruistic preference may not significantly lower the total environmental footprint. However, such preferences help manufacturers reach a critical threshold of unit-level environmental improvement, after which further investment yields substantial total impact reductions. By offering altruistic support and concessionary measures (e.g., subsidies or cost-sharing), retailers can therefore encourage green innovation, stimulate demand, and promote the joint advancement of economic performance and environmental sustainability. For example, Walmart’s Sustainable Packaging Initiative shows how retailer support enabled suppliers to move from minor per-unit reductions to significant aggregate improvements, while BYD’s collaboration with domestic retail partners demonstrates how sustained support for R&D helped achieve critical gains in energy efficiency and carbon reduction in electric vehicles.

4.2. The Impact of Green-Design-Related Parameters on Optimal Supply Chain Decisions

Proposition 6.

In the retailer-led environmental responsibility supply chain, the equilibrium results for CEA satisfy the following conditions: ${\displaystyle \frac{𝜕w^{A\ast }}{𝜕\beta }}>{\displaystyle \frac{𝜕w^{D\ast }}{𝜕\beta }}>0$, ${\displaystyle \frac{𝜕p^{A\ast }}{𝜕\beta }}>{\displaystyle \frac{𝜕p^{D\ast }}{𝜕\beta }}>0$, ${\displaystyle \frac{𝜕m^{A\ast }}{𝜕\beta }}={\displaystyle \frac{𝜕m^{D\ast }}{𝜕\beta }}=0$, ${\displaystyle \frac{𝜕e^{A\ast }}{𝜕\beta }}>{\displaystyle \frac{𝜕e^{D\ast }}{𝜕\beta }}>0$, ${\displaystyle \frac{𝜕q^{A\ast }}{𝜕\beta }}>{\displaystyle \frac{𝜕q^{D\ast }}{𝜕\beta }}>0$, ${\displaystyle \frac{𝜕{\pi }_M^{A\ast }}{𝜕\beta }}>{\displaystyle \frac{𝜕{\pi }_M^{D\ast }}{𝜕\beta }}>0$, ${\displaystyle \frac{𝜕{\pi }_R^{A\ast }}{𝜕\beta }}>{\displaystyle \frac{𝜕{\pi }_R^{D\ast }}{𝜕\beta }}>0$, and ${\displaystyle \frac{𝜕{\pi }_S^{A\ast }}{𝜕\beta }}>{\displaystyle \frac{𝜕{\pi }_S^{D\ast }}{𝜕\beta }}>0$.

Proposition 6 shows that whether the dominant retailer has altruistic preferences, such as the enhancement of CEA, the wholesale and retail prices, market demand and green design level, as well as the profits of supply chain members and system will increase; in addition, the increase extent will be greater when the retailer has altruistic preference. This is because no matter whether the retailer has altruistic preferences or not, with the enhancement of CEA, consumers care more about the green design level of products than the products prices. Consequently, the manufacturer will enhance the green design level to attract more consumers and obtain more profit. Combined with Propositions 3–4, the retailer’s altruistic preference helps to alleviate the manufacturer’s investment pressure engaged in green design and improve the manufacturer’s green design level and income. Therefore, the change range of green design level is greater when the retailer has altruistic preference. Meanwhile, because the increasing effect of green design is more than the decreasing effect of price rise on demand, the retailer will appropriately increase the products price to increase her profit, whether she has altruistic preference or not. Finally, the supply chain members and system will benefit from the increase in market demand.

Proposition 6 indicates that higher CEA consistently promotes improvements in green design, product demand, supply chain performance, and overall sustainability. From a policy perspective, governments can strengthen CEA by establishing and certifying green product standards and promoting green consumption through collaboration with enterprises, third-party certification bodies, and other social organizations, thereby cultivating consumers’ long-term green purchasing habits. For dominant retailers, recognizing the value of altruistic preferences in supporting manufacturers is critical. By sharing profits and leveraging the positive effects of rising CEA, they can further consolidate their supply chain advantages and accelerate the transition to green and low-carbon development. For manufacturers, active implementation of green design enhances competitiveness by shaping a strong green brand image. A practical example is Haier, which has long pursued green investment and production (e.g., fluorine-free refrigerators). Even when the home appliance market faced significant pressure in 2020, Suning signed a direct order of 30 billion RMB with Haier, thereby sustaining supply chain stability and reinforcing the benefits of consumer trust in green brands.

Proposition 7.

In the retailer-led environmental responsibility supply chain, when a dominant retailer does/does not have altruistic preferences, the equilibrium results for the scale parameter satisfy the following conditions: (1) ${\displaystyle \frac{𝜕w^{H\ast }}{𝜕k}}<0$ and ${\displaystyle \frac{𝜕p^{H\ast }}{𝜕k}}<0$, when $\beta >bcr$; ${\displaystyle \frac{𝜕w^{H\ast }}{𝜕k}}>0$ and ${\displaystyle \frac{𝜕p^{H\ast }}{𝜕k}}>0$, when $\beta <bcr$; (2) ${\displaystyle \frac{𝜕m^{H\ast }}{𝜕k}}=0$, ${\displaystyle \frac{𝜕e^{H\ast }}{𝜕k}}<0$, ${\displaystyle \frac{𝜕q^{H\ast }}{𝜕k}}<0$, ${\displaystyle \frac{𝜕{\pi }_M^{H\ast }}{𝜕k}}<0$, ${\displaystyle \frac{𝜕{\pi }_R^{H\ast }}{𝜕k}}<0$, and ${\displaystyle \frac{𝜕{\pi }_S^{H\ast }}{𝜕k}}<0$; here, $H=\{D,A\}$.

Proposition 7 shows that, regardless of whether a dominant retailer has altruistic preferences, as the cost coefficient increases for green design investment, the market demand, green design level, the profits of supply chain members, and overall profits all decline. However, counter-intuitively, wholesale and retail prices may not necessarily increase accordingly. In fact, as the green design investment cost coefficient increases, it directly reduces the manufacturer’s motivation to engage in green design practices and indirectly affects market demand. In addition, market demand is affected by both the green design level and product prices, and both the profits of manufacturers and retailers are relatively more dependent on product market demand. Therefore, when consumers are more concerned with the green design level, both manufacturers and retailers will use price-reduction strategies to reduce the loss of product market demand caused by the decline in the level of green design practices. Conversely, when environmental consciousness among consumers is relatively weak, the reduction in product market demand caused by the decline in green design level is limited. At this time, it is more beneficial for the manufacturer and retailer to increase product prices appropriately.

Proposition 7 reveals that, regardless of whether the dominant retailers have altruistic preferences, the increase in the green design investment cost is unfavorable to improving the green design level, expanding the market demand, and increasing corporate profits. Therefore, as the market regulator, the government should support dominant retailers to create a better environment for green design innovation among manufacturers. By encouraging manufacturers to improve their green design level, it is possible to improve the overall performance of the supply chain. When formulating product prices, companies should consider both their own investment costs in green design practices and the combination of the consumption preferences of target consumer groups. Accordingly, they should formulate corresponding price strategies in order to better cater to consumers, supporting their position in the market.

5. Coordination Mechanism Design Under Dominant Retailer Altruistic Preferences

Altruistic preferences among dominant retailers can help incentivize manufacturers to improve their green design level and the overall performance of the supply chain. However, we show that dominant retailers need to sacrifice part of their net profit and still cannot completely achieve a centralized decision situation. So, we can design corresponding coordination contracts, on the one hand, to make up for the dominant retailer’s pure profit lost due to altruistic preferences; on the other hand, these contracts could further effectively encourage manufacturers to increase their investments in green design practices and realize the balanced development of economy and environment. In this section, we will separately design a green design cost-sharing contract and a two-part tariff contract under the altruistic preferences of the dominant retailer. Additionally, we will analyze the coordination performances of the two contracts and discuss the effects of altruistic preferences on contractual achievement and coordination performance.

5.1. Green Design Cost-Sharing Contract (Model AS)

A dominant retailer’s altruistic preferences mainly lead them to relieve investment pressures for manufacturers engaged in green design practices. Cost-sharing contracts are widely used as effective coordination mechanisms to directly help member companies to relieve cost pressures from each other [29]. Therefore, a green design cost-sharing contract requires a dominant retailer with altruistic preferences to provide contracts to their manufacturers, promising to directly share part of the green design costs ($\mu k{e}^2$, $0<\mu <1$); meanwhile, the manufacturer should then correspondingly improve the green design level to stimulate consumption and reformulate the product unit wholesale price accordingly. The manufacturer’s profit therefore consists of wholesale revenue, expressed as the unit margin times market demand, minus the reduced green design cost $(1-\mu )k{e}^2$. The retailer’s profit consists of their unit margin multiplied by the same market demand, reaching the net of their share of the green design cost $\mu k{e}^2$. So, the profit functions and utility function of supply chain members are as follows:

$${\pi }_M^{AS}(w,e)=(w-(1-re)c)(a-bw-bm+\beta e)-(1-\mu )k{e}^2$$

(7)

$${\pi }_R^{AS}(m)=m(a-bw-bm+\beta e)-\mu k{e}^2$$

(8)

$$U_R^{AS}(m)={\pi }_R^{AS}+\theta {\pi }_M^{AS}$$

(9)

Theorem 4.

Under a green design cost-sharing contract, when $w^{AS\ast }={\displaystyle \frac{2k(a+bc)-4k\mu (a-bc)-c(bcr+\beta )(ar+\beta )}{4kb-{(bcr+\beta )}^2}}$, $\mu \in \left[{\mu }_1,{\mu }_2\right]$, the contract can support the coordination of supply chain, and the supply chain members can accept the contract. Furthermore, the manufacturer’s profit is ${\pi }_M^{AS\ast }={\displaystyle \frac{k{(a-bc)}^2(4kb(1-2\mu )-(1-\mu ){(bcr+\beta )}^2)}{{(4kb-{(bcr+\beta )}^2)}^2}}$, the profit and utility of dominant retailer are ${\pi }_R^{AS\ast }={\displaystyle \frac{k\mu {(a-bc)}^2(8kb-{(bcr+\beta )}^2)}{{(4kb-{(bcr+\beta )}^2)}^2}}$ and ${\displaystyle \frac{k\mu {(a-bc)}^2(8kb-{(bcr+\beta )}^2)+k\theta {(a-bc)}^2(4kb(1-2\mu )-(1-\mu ){(bcr+\beta )}^2)}{{(4kb-{(bcr+\beta )}^2)}^2}}$, and the overall profits of supply chain is ${\pi }_S^{AS\ast }={\displaystyle \frac{k{(a-bc)}^2}{4kb-{(bcr+\beta )}^2}}$. Here, ${\mu }_1={\displaystyle \frac{2(1-\theta )(4kb-{(bcr+\beta )}^2)}{{(2-\theta )}^2(8kb-{(bcr+\beta )}^2)}}$ and ${\mu }_2={\displaystyle \frac{(1-\theta )(3-\theta )(4kb-{(bcr+\beta )}^2)}{{(2-\theta )}^2(8kb-{(bcr+\beta )}^2)}}$.

The derivation processes is similar to Model D, according to the first-order conditions, ${\displaystyle \frac{𝜕{\pi }_M^{AS}}{𝜕w}}=0$ and ${\displaystyle \frac{𝜕{\pi }_M^{AS}}{𝜕e}}=0$, the best feedback functions are $w^{AS}=\frac{2k(1-\mu )(a-bm+bc)-(bcr+\beta )(cr(a-bm)-\beta c)}{4kb(1-\mu )-{(bcr+\beta )}^2}$ and $e^{AS}=\frac{(bcr+\beta )(a-bm-bc)}{4kb(1-\mu )-{(bcr+\beta )}^2}$.

To make the supply chain overall profits under the contract consistent with the centralized decision-making, need to meet $p^{AS\ast }=w^{AS}+m^{AS}=p^{C\ast }$, $e^{AS\ast }=e^{C\ast }$. From this, the wholesale price $w^{AS\ast }$ rescheduled by the manufacturer under the coordination contract can be obtained.

Further, we need to ensure that the profits and utility of the manufacturer and retailer after coordination are not lower than those before coordination. Therefore, by ${\pi }_M^{AS\ast }\ge {\pi }_M^{A\ast }$, we obtain ${\mu }_2={\displaystyle \frac{(1-\theta )(3-\theta )(4kb-{(bcr+\beta )}^2)}{{(2-\theta )}^2(8kb-{(bcr+\beta )}^2)}}$; by ${\pi }_R^{AS\ast }\ge {\pi }_R^{A\ast }$, we obtain ${\mu }_1={\displaystyle \frac{2(1-\theta )(4kb-{(bcr+\beta )}^2)}{{(2-\theta )}^2(8kb-{(bcr+\beta )}^2)}}$; by $U_R^{AS\ast }\ge U_R^{A\ast }$, we obtain ${\mu }_3={\displaystyle \frac{(1-\theta )(4kb-{(bcr+\beta )}^2)}{(2-\theta )(8kb-{(bcr+\beta )}^2)}}$. Again, due to ${\mu }_3<{\mu }_1<{\mu }_2$, so only when $\mu \in \left[{\mu }_1,{\mu }_2\right]$, can satisfy ${\pi }_M^{AS\ast }\ge {\pi }_M^{A\ast }$, ${\pi }_R^{AS\ast }\ge {\pi }_R^{A\ast }$, $U_R^{AS\ast }\ge U_R^{A\ast }$.

Theorem 4 shows that, in the case of considering altruistic preference and green design, the green design cost-sharing contract can achieve perfect coordination and can make all decision variables and profits reach the optimal level under centralized decision-making, effectively improving the profits and utility of the manufacturer and retailer. Therefore, in the supply chain dominated by retailers with altruistic preferences, retailers can take advantage of the “first mover” advantage to provide manufacturers with a green design cost-sharing contract, which will not only stimulate manufacturers to increase investment in green design, but is also conducive to increase products market demand, improving the profits of supply chain members and overall.

Theorem 4 shows that when altruistic preferences and green design are considered together, the green design cost-sharing contract can achieve perfect coordination, aligning all decision variables and profits with the centralized optimum, effectively improving both the manufacturer’s and the retailer’s payoffs and utility. From a managerial perspective, this finding implies that in retailer-led supply chains, dominant retailers can leverage their “first-mover” advantage to implement cost-sharing contracts as a strategic tool to incentivize manufacturers’ investment in green design. By doing so, retailers not only stimulate greater innovation and increase market demand for eco-friendly products, but also strengthen supply chain collaboration, enhance long-term partnerships, and improve overall system sustainability. In practice, such contracts provide a pathway for retailers to balance short-term profit sacrifices with long-term competitive advantages, including enhanced consumer trust, stronger supplier relationships, and reputational benefits associated with supporting green and low-carbon transformation.

Proposition 8.

In a retailer-led environmental responsibility supply chain, the green design cost-sharing contract, satisfies ${\displaystyle \frac{𝜕{\mu }_1}{𝜕\theta }}<0$, ${\displaystyle \frac{𝜕{\mu }_2}{𝜕\theta }}<0$, and ${\displaystyle \frac{𝜕({\mu }_2-{\mu }_1)}{𝜕\theta }}<0$.

The proof for Proposition 8 is provided in Appendix A.

Proposition 8 shows that the retailer’s altruistic preferences affect the feasible range of green design cost-sharing contracts. Specifically, with the increase in the retailer’s altruistic preference degree, the upper and lower limits of the green design cost-sharing ratio are tightening, and the feasible range of the contract also becomes smaller. In fact, the retailer has altruistic preference, and providing green design cost-sharing contracts are all concessionary behaviors to ease the cost pressure of green design manufacturers. Under the contract, the retailer bears a lower green design costs proportion, which is more beneficial to the manufacturer (${\displaystyle \frac{𝜕{\pi }_M^{AS\ast }}{𝜕\mu }}<0$). Therefore, with the increase in the retailer’s altruistic preference, she will choose to bear fewer green design costs to better reflect her profit-giving behavior to the manufacturer.

Proposition 8 reveals that although increasing the retailer’s altruistic preference reduces the feasible range of green design cost-sharing contracts, it also reflects the dominant retailer’s concession behavior. Therefore, by adjusting the degree of altruism preference and the green design cost-sharing ratio, retailers can not only effectively incentivize manufacturers to improve the level of green design, improve manufacturers and their own performance, but also help maintain the stable operation of supply chains.

5.2. Two-Part Tariff Contract (Model AT)

The dominant retailer’s altruistic preference has effectively increased the supply chain overall and other members’ profits, but her own net profit has been affected to a certain extent. Based on this, this section will explore when the manufacturer provides a fixed transfer payment to the retailer in response to the altruistic preference behavior of the retailer, whether the cooperation relationship between the manufacturer and retailer can be further improved, and achieve profits in Pareto improvement. Therefore, the two-part tariff contract requires the manufacturer to proactively provide contract to the retailer, by giving the retailer a fixed transfer payment fee to motivate the retailer to lower the retail price, and then the manufacturer will re-set the green design level and wholesale price. Under this contract, the manufacturer’s profit consists of wholesale revenue, defined as the unit margin times the market demand, minus the quadratic green design cost $k{e}^2$, and further reduced by the fixed transfer payment $F$. The retailer’s profit is composed of her unit margin, multiplied by market demand, plus the fixed fee $F$, received from the manufacturer. In the two-part tariff contract ($w^{AT},F$), the profit functions and utility function of the supply chain members are as follows:

$${\pi }_M^{AT}(w,e)=(w-(1-re)c)(a-bw-bm+\beta e)-k{e}^2-F$$

(10)

$${\pi }_R^{AT}(m)=m(a-bw-bm+\beta e)+F$$

(11)

$$U_R^{AT}(m)={\pi }_R^{AT}+\theta {\pi }_M^{AT}$$

(12)

Theorem 5.

In the retailer-led environmental responsibility supply chain, under the two-part tariff contract, when $w^{AT\ast }={\displaystyle \frac{2k(a+bc)-c(bcr+\beta )(ar+\beta )}{4kb-{(bcr+\beta )}^2}}$, $F\in \left[F_1,F_2\right]$, the two-part tariff contract can achieve perfect coordination, and the supply chain members can accept the coordination contract. Furthermore, the manufacturer’s profit is ${\pi }_M^{AT\ast }={\displaystyle \frac{k{(a-bc)}^2}{4kb-{(bcr+\beta )}^2}}-F$, the profit and utility of the retailer are ${\pi }_R^{AT\ast }=F$ and $U_R^{AT\ast }={\displaystyle \frac{k\theta {(a-bc)}^2}{4kb-{(bcr+\beta )}^2}}+(1-\theta )F$, and the overall profit of the supply chain is ${\pi }_S^{AT\ast }={\displaystyle \frac{k{(a-bc)}^2}{4kb-{(bcr+\beta )}^2}}$. Here, $F_1={\displaystyle \frac{2k(1-\theta ){(a-bc)}^2}{{(2-\theta )}^2(4kb-{(bcr+\beta )}^2)}}$ and $F_2={\displaystyle \frac{k(1-\theta )(3-\theta ){(a-bc)}^2}{{(2-\theta )}^2(4kb-{(bcr+\beta )}^2)}}$.

Similarly to the derivation processes of Model D, the first-order condition ${\displaystyle \frac{𝜕{\pi }_M^{AT}}{𝜕w}}=0$, ${\displaystyle \frac{𝜕{\pi }_M^{AT}}{𝜕e}}=0$, yield the best feedback functions are $w^{AT}=\frac{a-bm+\beta e+bc-bcre}{2b}$, $e^{AT}=\frac{acr-bcrw-bcrm+\beta w-\beta c}{2k-2\beta cr}$.

To make the supply chain overall profits under the contract consistent with the centralized decision-making, they need to meet $p^{AT\ast }=w^{AT}+m^{AT}=p^{C\ast }$, $e^{AT\ast }=e^{C\ast }$. From this, in the coordination contract, the wholesale price $w^{AT\ast }$ rescheduled by the manufacturer can be obtained.

Further, we need to ensure that the profits and utility of the manufacturer and retailer after coordination are not lower than those before coordination. Therefore, by ${\pi }_M^{AT\ast }\ge {\pi }_M^{A\ast }$, we obtain $F_2={\displaystyle \frac{k(1-\theta )(3-\theta ){(a-bc)}^2}{{(2-\theta )}^2(4kb-{(bcr+\beta )}^2)}}$; by ${\pi }_R^{AT\ast }\ge {\pi }_R^{A\ast }$, we obtain $F_1={\displaystyle \frac{2k(1-\theta ){(a-bc)}^2}{{(2-\theta )}^2(4kb-{(bcr+\beta )}^2)}}$; by $U_R^{AT\ast }\ge U_R^{A\ast }$, we obtain $F_3={\displaystyle \frac{k{(1-\theta )}^2{(a-bc)}^2}{(1-\theta )(2-\theta )(4kb-{(bcr+\beta )}^2)}}$. Again, due to $F_3<F_1<F_2$, so only when $F\in \left[F_1,F_2\right]$, can satisfy ${\pi }_M^{AF\ast }\ge {\pi }_M^{A\ast }$, ${\pi }_R^{AF\ast }\ge {\pi }_R^{A\ast }$, $U_R^{AF\ast }\ge U_R^{A\ast }$.

Proposition 9.

In the retailer-led environmental responsibility supply chain, under the two-part tariff contract, the following are satisfied: ${\displaystyle \frac{𝜕F_1}{𝜕\theta }}<0$, ${\displaystyle \frac{𝜕F_2}{𝜕\theta }}<0$, and ${\displaystyle \frac{𝜕(F_2-F_1)}{𝜕\theta }}<0$.

The proof for Proposition 9 is provided in Appendix A.

Proposition 9 shows that, in the two-part tariff contract, the size of the fixed fee transferred from the manufacturer to the retailer is related to the altruistic preference degree of the retailer. In a scenario with a higher altruism preference degree in the retailer, the upper and lower bounds of the fixed transfer fee are tighter; that is, the retailer will give more profit to the manufacturer by lowering the standard of the fixed fee. Under the contract, the manufacturer can respond to the concessionary behavior of the retailer through a transfer payment, and the retailer can affect the manufacturer’s transfer payment by adjusting their degree of altruistic preferences. The manufacturer and the retailer thus form a good interaction and positive cycle, creating an effectively improved cooperative relationship, and increasing the overall profits and the profits of the supply chain members.

From a managerial perspective, two-part tariff contracts provide a flexible tool to balance profit distribution and foster trust in retailer-led supply chains. By adjusting the fixed fee, altruistic retailers can encourage manufacturers to invest more in green design, while manufacturers benefit from higher returns and stronger partnerships. Such arrangements not only enhance supply chain profitability but also support long-term sustainability goals.

Table 2. Comparison of cost-sharing and two-part tariff contracts under altruistic preferences.

Aspect	Cost-Sharing Contract	Two-Part Tariff Contract
Feasibility range	Effective under small or moderate altruistic coefficients ($\theta$)	Remains feasible even when altruistic coefficient ($\theta$) is higher
Advantages	Achieves perfect coordination with centralized optimum; directly incentivizes manufacturer’s green investment	Provides flexible profit redistribution; strengthens cooperation by compensating retailers for altruistic concessions
Limitations	Less effective when altruism is high; increases retailer’s risk burden	Feasible bounds of fixed transfer fees narrow as altruism rises
Managerial insights	Best suited when the retailer seeks to strongly encourage green innovation and maximize system efficiency	Appropriate when balancing profit allocation, stabilizing long-term partnerships, and maintaining fairness

compares the cost-sharing and two-part tariff contracts under altruistic preference. The cost-sharing contract achieves perfect coordination when the altruistic coefficient is within a reasonable range, directly stimulating manufacturers’ green investment but increasing the retailer’s risk when altruism is high. By contrast, the two-part tariff contract offers greater flexibility across a wider range of altruistic preferences, balancing profit distribution through fixed transfers, though the feasible bounds narrow with higher altruism.

From a managerial perspective, these findings suggest that retailers can strategically select contract mechanisms depending on their altruistic stance and market conditions. For example, Walmart has often used cost-sharing schemes to co-finance suppliers’ sustainability initiatives, ensuring efficiency gains but assuming higher risk. Meanwhile, JD.com and Gree have experimented with subsidy-based and transfer-payment mechanisms, which resemble two-part tariff arrangements, allowing profit redistribution to strengthen long-term partnerships while promoting green innovation. These cases highlight that aligning contract choice with altruistic preferences not only improves supply chain coordination but also enhances competitiveness and sustainability outcomes.

6. Numerical Simulation Analysis

First, we analyze the impact of parameters such as retailer altruistic preferences, $\theta$, on green design decisions and the performance of supply chain. Next, we jointly examine the effects of $\lambda$ and $\theta$ on the environment. Finally, we verify the effectiveness of the two coordination contracts designed in this study. To enhance the practical relevance of this research, parameter values are assigned based on the existing literature, survey reports, and empirical evidence. According to the Research Report on the Value and Trends of Low-Carbon Green Home Appliances and the China Environmental Statistics Yearbook, 2021, the market potential for green products is large, and consumer environmental preferences are steadily increasing, with more than half of consumers willing to pay a premium for green products. Meanwhile, public disclosures from green home appliance companies such as Midea and Haier indicate that the cost of green design investment remains high, suggesting that the green design cost coefficient is relatively large. Based on the above analysis, and referring to the parameter settings of Wang et al. [16], we assume that $a=150$, $k=120$, $b=6$, $\beta =5$, $c=10$, $r=0.3$, and $\varphi =1$. It should be noted that this simulation is based on a stylized two-echelon supply chain with complete information and linear demand structures, similar to those commonly observed in electronics and home appliance supply chains. Therefore, our analysis and managerial implications are derived within this context. While these findings provide important theoretical insights, caution should be exercised when extending them to more complex environments, such as multi-retailer competitions or uncertain demand conditions.

6.1. The Influences of Related Parameters on the Green Design and Performances of Supply Chains

Figure 1, Figure 2, Figure 3 and Figure 4 illustrate that, compared with scenarios in which the retailer has no altruistic preferences, the presence of altruistic preferences by the dominant retailer consistently leads to higher levels of green design, greater product demand, and improved performance for both the manufacturer and the supply chain. Moreover, regardless of whether altruistic preferences are present, increases in production cost savings per unit product achieved through green design (i.e., higher values of $r$) not only raise the manufacturer’s green design level but also stimulate market demand and enhance the profits of all supply chain members. These findings indicate that retailer altruism and manufacturer innovation are mutually reinforcing: while the retailer’s concessions create favorable conditions for investment, the manufacturer’s proactive improvements ensure that such concessions translate into tangible market demand and profit gains.

From a managerial perspective, Figure 1 shows that altruistic preferences significantly increase the manufacturer’s green design level, suggesting that retailers can strategically use altruism (e.g., preferential financing or shelf space) to motivate suppliers to invest in greener technologies. Figure 2 demonstrates that altruism combined with cost-saving green design substantially boosts consumer demand, highlighting that subsidies and marketing initiatives—such as JD.com’s promotional support for green appliances—can successfully stimulate adoption of eco-friendly products. Figure 3 indicates that manufacturer profits improve under higher altruistic preferences and greater cost savings, which implies that manufacturers should invest in efficient green design, as illustrated by Apple’s reduction in steel use in the iPhone 11 Pro to cut both costs and emissions. Finally, Figure 4 reveals that overall supply chain performance improves when altruistic preferences and green design reinforce each other, echoing real-world practices such as Marks & Spencer’s “Plan A” initiative, which co-invested in suppliers’ green projects to enhance long-term partnerships and sustainability outcomes.

Collectively, these findings suggest that supply chains in industries such as electronics, appliances, and automobiles can benefit from a balanced approach in which dominant retailers provide altruistic support (e.g., subsidies, logistics assistance, preferential shelf space), while manufacturers adopt green design to lower production costs and strengthen their green brand reputation. Such coordinated actions not only improve financial outcomes but also accelerate the transition toward low-carbon supply chains.

Figure 5, Figure 6, Figure 7 and Figure 8 show that a reduction in consumer price sensitivity and an increase in CEA consistently lead to higher levels of green design, greater market demand, and improved overall supply chain profits, though they do not directly reduce the retail price. Moreover, compared with scenarios without altruistic preferences, the presence of retailer altruism results in lower retail prices, higher levels of green design, greater demand, and higher overall supply chain performance. These results suggest that when formulating optimal pricing strategies, companies should jointly consider consumers’ price sensitivity and environmental awareness to achieve more balanced and sustainable outcomes.

Figure 5, Figure 6, Figure 7 and Figure 8 collectively demonstrate that reductions in consumer price sensitivity and increases in CEA play a critical role in driving higher levels of green design, greater product demand, and improved overall supply chain performance, while retailer altruism further amplifies these effects by lowering retail prices and enhancing profitability. From a managerial perspective, this suggests that dominant retailers should not only provide altruistic concessions to manufacturers but also actively invest in promoting green consumption and cultivating consumer habits that strengthen CEA. For example, Wal-Mart’s practice of offering preferential procurement terms to sustainable suppliers, combined with prominent in-store promotion of eco-friendly products, illustrates how raising CEA can magnify the benefits of altruistic preferences. Ultimately, the joint consideration of consumer price sensitivity, environmental awareness, and retailer altruism enables supply chains to achieve both competitive and sustainable advantages.

6.2. The Effects of $\lambda ,\theta$ on the Environment

Figure 9 shows that the altruistic preference of the dominant retailer does not always reduce the total environmental impact of products, but it helps the supply chain approach the critical threshold where environmental performance improves. Specifically, only when green design significantly reduces the environmental impact of each unit product (i.e., when the reduction efficiency $\lambda$ is sufficiently large), can the retailer’s altruism effectively lower the overall environmental impact. In practice, while altruistic preferences are always beneficial to increasing market demand, the net environmental outcome depends on the trade-off between unit product impact and total demand. Thus, unless green design yields substantial unit-level improvements, higher demand could offset the environmental gains and lead to greater aggregate emissions.

From a managerial perspective, this highlights that retailers should not only provide altruistic support by easing manufacturers’ financial pressures but also encourage substantive green innovation, such as material-saving design, energy-efficient technologies, and eco-friendly production processes. For instance, Haier’s adoption of fluorine-free refrigerants and Midea’s development of high-efficiency air conditioners demonstrate how unit-level green design improvements can reduce per-unit environmental damage while meeting growing market demand. By combining altruistic preferences with genuine green innovation, retailers and manufacturers can jointly reduce the total environmental impact and achieve sustainable supply chain development.

6.3. Investigation of the Effectiveness of the Two Coordination Contracts

This section mainly investigates the effectiveness of the green design cost-sharing contract and the two-part tariff contract proposed in this study. The relevant parameters are outlined in Section 6.1. The green design cost-sharing parameter is $\mu ={\displaystyle \frac{{\mu }_1+{\mu }_2}{2}}=0.26$, and the fixed transfer payment fee is $F={\displaystyle \frac{F_1+F_2}{2}}=235.33$. To further validate the theoretical bounds derived in Theorems 4 and 5, we conduct numerical experiments using different values of the cost-sharing parameter (${\mu }_1=0.23, {\mu }_2=0.29$) and the fixed transfer payment fee ($F_1=200.28, F_2=270.38$).

Table 3. Equilibrium results under different models ($\mu ,F$).

Model	${\mathit{w}}^{*}$	${\mathit{p}}^{*}$	${\mathit{e}}^{*}$	${\mathit{q}}^{*}$	${\mathit{\pi }}_{\mathit{M}}^{*}$	${\mathit{\pi }}_{\mathit{R}}^{*}$	${\mathit{U}}_{\mathit{R}}^{*}$	${\mathit{\pi }}_{\mathit{S}}^{*}$
Model $A$	16.43	20.03	0.52	32.43	143.06	200.28	243.20	343.34
Model $AS$	11.77	16.55	0.88	55.13	174.26	239.18	291.46	413.44
Model $AT$	16.55	16.55	0.88	55.13	178.11	235.33	288.76	413.44
Model $C$	\	16.55	0.88	55.13	\	\	\	413.44

shows that, under both the green design cost-sharing contract and the two-part tariff contract, the retail price of products decreases, while the green design level, market demand, and the profits of supply chain members all increase. Moreover, the overall supply chain profit under these contracts aligns with the outcome of centralized decision-making. This indicates that the proposed contracts not only achieve perfect supply chain coordination but also realize a win-win outcome by enhancing both firm performance and the level of green design. In addition, the results presented in

Table 4. Equilibrium results under different models (${\mu }_1,F_1$).

Model	${\mathit{w}}^{*}$	${\mathit{p}}^{*}$	${\mathit{e}}^{*}$	${\mathit{q}}^{*}$	${\mathit{\pi }}_{\mathit{M}}^{*}$	${\mathit{\pi }}_{\mathit{R}}^{*}$	${\mathit{U}}_{\mathit{R}}^{*}$	${\mathit{\pi }}_{\mathit{S}}^{*}$
Model $A$	16.43	20.03	0.52	32.43	143.06	200.28	243.20	343.34
Model $AS$	12.32	16.55	0.88	55.13	201.86	211.58	272.14	413.44
Model $AT$	16.55	16.55	0.88	55.13	213.16	200.28	264.23	413.44
Model $C$	\	16.55	0.88	55.13	\	\	\	413.44

and

Table 5. Equilibrium results under different models (${\mu }_2,F_2$).

Model	${\mathit{w}}^{*}$	${\mathit{p}}^{*}$	${\mathit{e}}^{*}$	${\mathit{q}}^{*}$	${\mathit{\pi }}_{\mathit{M}}^{*}$	${\mathit{\pi }}_{\mathit{R}}^{*}$	${\mathit{U}}_{\mathit{R}}^{*}$	${\mathit{\pi }}_{\mathit{S}}^{*}$
Model $A$	16.43	20.03	0.52	32.43	143.06	200.28	243.20	343.34
Model $AS$	11.22	16.55	0.88	55.13	146.67	266.77	310.77	413.44
Model $AT$	16.55	16.55	0.88	55.13	143.06	270.38	313.30	413.44
Model $C$	\	16.55	0.88	55.13	\	\	\	413.44

further verify the upper and lower bounds of the cost-sharing parameter and the fixed transfer payment fee, confirming that coordination remains effective within the theoretically derived feasible ranges.

7. Conclusions

This study is based on a stylized two-echelon supply chain model with complete information, linear demand, and quadratic green design costs. Within this framework, we investigate a retailer-led supply chain under scenarios with and without altruistic preferences, and analyze how altruism, CEA, and green design costs jointly influence supply chain optimization, environmental outcomes, and coordination contracts. Although the analysis is specific in scope, the findings provide theoretical insights and practical guidance for industries such as electronics and home appliances, where dominant retailers and green design manufacturers closely interact.

The main conclusions are as follows:

(1) A dominant retailer’s altruistic preference motivates manufacturers to increase green design investment, reduce retail prices, expand product demand, and improve overall supply chain performance, while also fostering stronger cooperative relationships between members.

(2) Enhanced CEA consistently strengthens the positive effects of altruistic preferences, amplifying demand and investment incentives.

(3) An increase in the green design investment cost coefficient does not necessarily raise retail prices, but it reduces manufacturers’ willingness to invest in green design, thereby lowering overall supply chain profits.

(4) Altruistic preferences help manufacturers reduce the environmental impact of unit products, but they lower the total environmental impact only when green design achieves substantial per-unit improvements.

(5) Both cost-sharing contracts initiated by retailers and two-part tariff contracts initiated by manufacturers can improve green design levels and supply chain performance, though higher levels of altruistic preferences narrow the feasible ranges of these coordination contracts.

Based on the above conclusions, the management enlightenment is as follows: Firstly, the government as market regulator, in the process of promoting the green and low-carbon transformation of manufacturing enterprises, on the one hand, can guide retailers to enhance their altruistic preference for manufacturers and reduce the cost pressure of manufacturers engaged in green design from within the supply chain. On the other, it can strengthen the promotion of green consumption and other green life concepts to create a better market environment for manufacturing companies to implement green design. Secondly, when retailers are the leader, they should properly handle the competition and cooperation relationship with manufacturers, while safeguarding their own profits, pay more attention to the income of subordinate enterprises (appropriate altruistic preference) from the perspective of the system, and promote product sales while improving the cooperation relationship. Manufacturers should also actively respond to retailers, make more green investment in reducing the adverse environmental impact of products, actively participate in the design of coordination mechanism, and reach a mutually beneficial green development mode with retailers.

Despite its contributions, this study has several limitations. First, the analysis is based on a stylized two-echelon supply chain consisting of a single manufacturer and a single dominant retailer under conditions of complete information. In practice, information asymmetry, and multi-retailer competition are common and may significantly influence green design and coordination outcomes. Future research could extend the model to asymmetric information settings or competitive environments to better capture real-world complexities. Second, the current study focuses exclusively on the altruistic preference behavior of the retailer. Other types of social preferences—such as fairness concerns, reciprocity, or risk aversion—on the part of both retailers and manufacturers may also affect supply chain decisions and environmental outcomes. Exploring the interplay of multiple social preferences within supply chains therefore represents an important avenue for future research. Finally, the study assumes linear demand and quadratic green design costs, which facilitate analytical tractability but may not fully capture consumer heterogeneity or nonlinear cost dynamics. Future work could relax these assumptions and employ alternative demand and cost specifications, or even integrate empirical data, to test the robustness and generalizability of the findings.