Research on Consumer Behavior-Driven Collaborative Mechanism of Green Supply Chain and Its Performance Optimization

Abstract

As a crucial vehicle for advancing the transition to a green low-carbon economy, the green supply chain plays a pivotal role in alleviating pollution pressures and facilitating the green transformation of products. Existing studies mainly focus on static optimization and cost coordination in green supply chains, with limited attention to the dynamic impact of consumer behavior on green production and channel coordination. Based on consumer green preferences and the evolution of reference prices, we developed a differential game model for a two-tier green supply chain composed of a manufacturer and a retailer. The model incorporates green goodwill and consumer memory variables to capture the dynamic interaction among product greenness, sales effort, and consumer perception. By comparing the dynamic optimal response paths under integrated and non-integrated strategies, the study analyzes how reference price effects and goodwill accumulation influence decision-making and system performance. The results show that the stable reference price of green products is significantly higher than the actual selling price. When consumer environmental awareness is strong, cooperative strategies can markedly improve both green performance and supply chain profits, offering potential for Pareto improvement. This research enhances behavior-oriented modeling in green supply chains and provides theoretical and empirical support for designing collaboration mechanisms in green product promotion.

1. Introduction

The excessive consumption of natural resources and the increasing emission of pollutants have intensified global warming, threatening human survival and development. The continuous deterioration of environmental performance has led to a global focus on green and sustainable development. As global sustainability efforts progress, China has proactively implemented responsive measures [1]. Specifically, under its “Dual Carbon” goals, China’s carbon reduction effects exhibit significant spatial imbalance and dynamic evolution trends [2]. Non-governmental environmental organizations can promote green transformation in supply chains through information disclosure and social supervision [3]. Green supply chains, as an important vehicle for promoting the development of green low-carbon economies, play a key role in promoting the green transformation of products. Companies should incorporate environmental performance into their evaluation criteria [4].

Promoting green innovative production is a key measure for developing green supply chains and an important breakthrough for addressing environmental and pollution problems [5]. Typically, firms pursue green innovation in production by reducing carbon emissions through the manufacturer’s green production practices. This approach serves as an effective means of gaining a competitive edge in markets with similar products. As a result, most existing studies focus on intra-supply chain collaboration mechanisms—such as cost-sharing—to examine how coordination among supply chain members influences the outcomes of green innovation. In other words, prior research has primarily concentrated on internal coordination strategies that affect the level of green innovation efforts by suppliers and retailers. However, consumer behavior also plays a critical role in shaping the efficiency and sustainability of green production within supply chains. Variations in consumers’ low-carbon preferences, reference price perceptions, and awareness of green product attributes can all significantly influence the level of green production efforts undertaken by supply chain members.

In light of this, incorporating consumer behavior into the study of green supply chain coordination mechanisms is both necessary and valuable. Product green innovation is closely linked to consumers’ willingness to purchase. When firms engage in green innovation, the resulting increase in production costs often leads to higher product prices. However, consumers’ green preferences can raise their internal reference price for such products, partially offsetting the negative impact of price increases. Additionally, consumers accumulate green goodwill toward a product over time, shaping their expectations and perceptions of its value. When consumer purchase intentions are weak, green product labels can significantly increase purchasing intentions [6]. Moreover, for the manufacturing industry, green innovative production can help companies establish a premium brand image for green products, bringing good reputation and adding value to intangible assets [7]. The reference price is jointly influenced by product quality and marketing efforts, and in turn, it affects the accumulation of green goodwill. Therefore, firms must simultaneously strengthen both green production investment and sales effort to effectively enhance consumer perception and drive sustainable demand. For example, companies such as Costco and Uniqlo have cooperated with suppliers and increased their investment in green product research and development. However, they still face challenges such as insufficient recognition of green products and limited consumer willingness to pay a premium for them, which affects purchasing intentions [8]. The “2024 China Sustainable Consumption Research Report” indicates that nearly 70% of consumers (approximately 68.04%) have not heard of corporate green low-carbon product marketing campaigns. Therefore, promoting green products is not only the responsibility of manufacturers but also of retailers, who should engage in green product promotion and put in sales efforts. Specifically, manufacturers need to focus on enhancing product greenness—for example, automotive companies like Tesla have launched new energy vehicles as part of their commitment to green R&D [9]. For retailers, it is essential to strengthen green marketing, build a low-carbon brand image, and enhance goodwill through active advertising and promotion of the product’s environmental benefits, thereby attracting environmentally conscious consumers.

Given the influence of consumer behavioral preferences, it is necessary to re-examine coordination mechanisms among supply chain members in green supply chains by incorporating reference price effects. Coordination within the supply chain can fully realize the value of green innovation in production [10]. Accordingly, this study considers the reference price effect and the accumulation of green goodwill driven by consumer green preferences and investigates how these two factors influence the manufacturer’s green production and the retailer’s sales effort. Furthermore, the paper explores how supply chain members make strategic decisions under the impact of consumer behavior and how such decisions can enhance overall supply chain profitability.

In order to explore a low-pollution sustainable development economy, the international community has jointly launched green low-carbon development, actively guiding companies to undergo green transformation, realize green supply chain management, and promote green consumption [11]. Therefore, this paper focuses on a green supply chain consisting of a single manufacturer and retailer, constructing a dynamic cooperation model based on the dynamic changes in product green goodwill and reference prices. It is assumed that both product green goodwill and reference prices are influenced by the product’s green level and the retailer’s sales efforts. Given that product green goodwill and reference prices change over time, the study uses the Nerlove-Arrow framework for dynamic analysis, based on the theoretical frameworks of Chintagunta [12], Jørgensen [13], and Francisco J. [7]. The model assumes that the product’s green level, sales efforts, goodwill, and reference prices all positively affect sales. Using differential game theory and numerical simulation, this study explores green supply chain cooperation strategies, analyzing and comparing the optimal decisions of manufacturers and retailers regarding product green level and sales efforts under two different scenarios (integrated and non-integrated decision-making). This research has both theoretical and practical significance.

In terms of theoretical significance, this paper expands the scope of previous research on static supply chain optimization models and better reflects the long-term effects. Considering the impact of heterogeneous consumer preferences, reference price effects, and green goodwill on product demand, the study explores green supply chain development strategies from the multiple perspectives of supply chain members. By designing different contract coordination mechanisms, the paper investigates how companies can use green supply chains to promote the innovation and promotion of green products. In terms of practical significance, this research helps companies recognize consumer preferences for green products and understand the heterogeneous demands of consumers, helping to establish green consumption concepts. This study also helps companies achieve both cost-efficiency and environmental benefits, contributing to emission reduction and environmental governance.

The structure of this paper is as follows: Section 2 reviews the relevant literature. Section 3 constructs a dynamic collaboration model for the green supply chain considering the effects of green goodwill and reference prices, analyzing the optimal decisions of manufacturers and retailers under integrated and non-integrated decision-making structures. Building on the previous analysis, the paper further investigates whether a bilateral subsidy strategy can better coordinate the channel members. Section 4 conducts numerical analysis to derive further managerial insights. Section 5 concludes and provides managerial implications. The Appendix A and Appendix B provides proofs.

2. Literature Review

Research on green supply chain management has continuously evolved and can be broadly categorized into three streams: contract coordination under cooperative mechanisms; differential game models of green supply chains driven by consumer behavior; and dynamic modeling of green goodwill and reference prices.

2.1. Green Supply Chain Contract Coordination Research

In order to promote rapid economic growth and practice the concept of sustainable development, the green level of products has become one of the important factors to consider in product R&D. Additionally, with the growing awareness of environmental protection among the public, consumer willingness to purchase green products has significantly increased [14]. The use of environmentally friendly technologies to produce green products increases manufacturers’ cost burden; however, these incremental costs can be fully covered by reasonably adjusting product sales prices [15]. More importantly, collaboration among green supply chain members can also optimize supply chain profits and inject momentum into sustainable development. Research on coordination mechanisms in green supply chains has primarily focused on cost-sharing, profit allocation, and incentive contracts. For example, Wang et al. proposed that under the dual drivers of carbon trading and green consumer preferences, a bi-directional cooperation contract can enhance system profits [16]. Shen et al. analyzed the impact of different cost-sharing schemes on green performance and profitability using a two-tier green supply chain model [17]. Agi and Yan emphasized the dominant role of manufacturers in green cooperation games and highlighted their critical function in designing incentive mechanisms [18]. However, these studies often assume stable or linear demand and do not explicitly incorporate consumer behavior variables or their moderating effects on dynamic coordination strategies. Moreover, they generally lack long-term performance analysis of coordination mechanisms under the influence of reference price and green goodwill.

2.2. Consumer Behavior-Oriented Dynamic Modeling in Green Supply Chains

In recent years, incorporating consumer green preferences into supply chain modeling has become a research focus. Zu et al. [19] employed differential game methods to integrate consumer environmental awareness and channel coordination into the model, designing cost-sharing contracts to incentivize emission reduction among supply chain members. He et al. [20] developed a differential game model for green innovation in food supply chains based on consumer green preferences and reference price effects, revealing that consumer behavior significantly influences green investment levels and cooperation incentives. Ma et al. [21] further extended this line of research to an O2O product–service supply chain context, introducing service reference effects and supplier reciprocal altruism into the model to depict the interplay among quality, service level, and brand goodwill.

These studies provide valuable theoretical insights into how consumer behavior shapes green supply chain decision-making. However, two limitations remain. First, existing models often assume that reference effects influence only product quality or service benchmarks, without systematically capturing how consumer memory mechanisms drive the dynamic evolution of reference prices. Second, most cooperation mechanisms are designed around fixed forms of cost-sharing or reciprocal preferences, lacking explicit analysis of how collaborative strategies dynamically respond to the evolution of consumer behavior.

2.3. Dynamic Modeling of Green Goodwill and Reference Price Mechanisms

The reference price effect, as an important factor influencing market demand, can be traced back to research conducted in the 1980s. Lattin and Bucklin [22] demonstrated that the reference price theory framework is consistent with several psychological theories of consumer behavior and price perception. Existing studies show that consumers’ utility from purchasing a product is not only dependent on the current sales price but is also influenced by the reference price formed by historical prices [23,24]. When the sales price is higher than the reference price, consumers experience a sense of loss, whereas if the sales price is lower than the reference price, it brings a sense of gain, which leads to increased demand, i.e., the reference price effect [25,26,27]. The reference price effect has been empirically validated and widely accepted in academic research [28]. As the psychological basis of consumer purchasing decisions, reference price plays a crucial role in brand selection and pricing strategies. Existing studies, such as Lu [29], have explored how historical prices, marketing, and product attributes influence the evolution of reference price. Chen [30] and Wang [31] applied reference price effects to contexts of innovation investment and process improvement, revealing its dynamic impact on profitability and pricing strategies. Meanwhile, green goodwill has also been increasingly incorporated into supply chain models as a key asset reflecting firms’ environmental efforts [32,33]. Pnevmatikos [34] suggested that a retailer’s sales effort not only helps accumulate product goodwill but also enhances consumer surplus. However, most existing studies model reference price and goodwill separately, lacking an integrated framework that captures their co-evolution, and rarely connect these dynamics to channel coordination mechanisms or strategic collaboration analysis.

2.4. Research Gap

Based on the review and analysis of the aforementioned literature, we identified the studies highly relevant to this paper, as shown in Table 1, and examined the existing research gaps.

Table 1. Highly related studies.

Research Paper	Contract Coordination	Differential Game	Green Supply Chain	Reference Price	Green Goodwill
Wang (2023) [16]	√		√		√
Zu (2018) [19]	√	√	√
Lu (2016) [29]	√	√		√
Wang (2025) [31]	√			√
Taboubi (2019) [33]	√	√			√
Wang (2022) [32]	√	√	√		√
Our paper	√	√	√	√	√

Although existing studies have introduced consumer preferences and reference effects into green supply chain research or focused on contract-based incentive mechanisms, there remains a lack of an integrated dynamic game modeling framework that links “consumer behavior evolution–reference price dynamics–green goodwill accumulation–coordination mechanism optimization.” This paper makes the following extensions and innovations:

(1) It incorporates a consumer memory effect parameter into the decision variables to capture the evolution path of reference price and models its interactive influence on the accumulation of green goodwill, addressing the limitations of existing models in representing the endogenous evolution of consumer behavior;

(2) It introduces a dynamic bi-directional coordination contract based on product greenness and sales effort, and explores the dynamic optimal strategy paths of manufacturers and retailers under decentralized and centralized decision-making, thereby enriching the dimensions of coordination mechanism design;

(3) It integrates the above mechanisms into a unified differential game framework and conducts numerical simulations for comparative analysis, thus offering a clearer view of the dynamic impact of consumer behavior on green product promotion performance. Through structural comparison with representative studies such as He et al. [20] and Ma et al. [21], this paper clarifies its theoretical contribution in terms of variable design, mechanism integration, and analytical depth, providing a new modeling perspective and practical insights for consumer behavior-oriented green supply chain coordination research. Our paper establishes a dynamic cooperation model for green supply chain members that takes consumer purchasing behavior into account. It compares the decision-making of green supply chain members under different cooperation modes and analyzes the results to seek the optimal solution.

2.5. Comparative Analysis with Prior Differential Game Models

Although studies by He [20] and Ma [21] provide valuable insights into consumer preference-driven green supply chain games, the model in this paper extends their analytical scope. First, while He incorporates consumer green preferences and reference price effects, the focus is mainly on how consumer preferences moderate green investment levels in the food supply chain. In contrast, this paper analyzes dynamic green goodwill influenced by consumer reference prices in a two-tier supply chain and examines under which conditions cooperation among channel members can improve long-term green performance and supply chain profits.

Second, Ma [21] studies service reference effects and reciprocal altruism in O2O supply chains, exploring equilibrium decisions under reciprocity. Unlike this, our paper introduces a bilateral subsidy mechanism to coordinate product green levels and retailer sales effort, providing clearer theoretical guidance for achieving optimal integrated system decisions under decentralized green supply chain settings.

Finally, this study innovatively integrates reference price effects and green goodwill into a differential game framework, embedding dynamic reference prices into the goodwill evolution equation and focusing on consumer behavior impacts. This contrasts with previous models that treated the two separately. Through this approach, we reveal the dynamic cooperation between green investment and sales effort, offering a more detailed understanding of how consumer perception evolves over time and affects supply chain profitability. This highlights how cooperation, influenced by consumer behavior, can achieve Pareto improvements—an aspect not clearly captured in prior research.

3. Modeling Analysis

3.1. Problem Formulation

We consider a supply chain consisting of one manufacturer and one retailer. Assume that both members have complete information symmetry and are risk-neutral. Manufacturers fulfill their environmental responsibilities by investing in green design to provide green products to the market. Green products typically require stronger consumer guidance to boost sales. In addition to the manufacturer’s investment in green innovation, the retailer also exerts sales efforts, such as advertising expenditures. When the manufacturer shares a portion of the retailer’s sales effort cost, it can effectively motivate the retailer to engage in more active promotion, thereby expanding market share. During the process of promoting and selling green products, consumer-driven green goodwill accumulates over time, which in turn influences consumers’ reference prices. To further investigate how reference prices and green goodwill affect the supply chain and the profits of channel members, the following model is developed. The decision flowchart of the model is shown in Figure 1.

Figure 1. Decision-making Flowchart.

The notations are defined as shown in Table 2.

Table 2. Notations and explanations.

Notations	Explanations
$\mathrm{g}(t),s(t)$	The product green level and retailer sales effort at time $t$, $0\le g(t),s(t)\le M$
$G(t),r(t)$	The green goodwill and reference price at time $t$
$G_0,r_0$	Initial goodwill and reference price
$\theta ,\tau$	The influence coefficients of greenness level and sales effort on green goodwill, $\theta >0,\tau >0$
$\mu ,\upsilon$	The influence coefficients of greenness level and sales effort on reference price $\mu >0,\upsilon >0$
$\delta$	The goodwill diminishing rate, $\delta >0$
$\beta$	The sensitivity coefficient of consumers to the reference-actual price gap, $\beta >0$
$D(t)$	The market demand at time $t$
$p(t)$	The selling price at time $t$
$C_M,C_R$	The manufacturer’s green production cost and the retailer’s sales effort cost
$\alpha$	The influence coefficients of the impact of reference price on market demand
${\lambda }_1,{\lambda }_2$	The influence coefficients of greenness level and sales effort on market demand
$\eta$	The green cost coefficient, $\eta >0$
$k$	The sales cost coefficient, $k>0$
$\varphi$	The manufacturer’s cost-sharing ratio for sales cost, $\varphi >0$
${\pi }_M(t),{\pi }_R(t),\pi (t)$	Manufacturer’s profit, retailer’s profit, and total supply chain profit
$J_M,J_R,J$	Optimal profit

3.2. Model Development

We denote the manufacture’s green level of green products over time $t$ as $g(t)$, and the retailer’s sales effort level as $s(t)$.

In general, corporate image is influenced by information regarding a firm’s environmental behavior. A firm that achieves lower pollution levels than its regulatory targets will accumulate goodwill among consumers. The evolution of goodwill depends on factors such as green investment and advertising expenditures. From the perspective of goodwill, it is inherently dynamic. The evolution of goodwill is modeled following the Nerlove-Arrow framework [35], i.e.,

$$\dot{G}(t)=\theta g+\tau s+m(r-p)-\delta G,G(0)=G_0$$

(1)

Reference prices can accumulate into brand trust and long-term preferences through consumers’ psychological perception processes. Therefore, we introduce $m(r-p)$ in the green goodwill formulation to represent the positive impact of reference prices on the accumulation of green goodwill ($m>0$) where $G(t)$ denotes the accumulated goodwill over time $t$, and $G_0>0$ is the initial level of goodwill. The parameters $\theta$ and $\tau$ are positive constants that capture the respective contributions of the manufacturer’s green production and the retailer’s sales efforts to goodwill growth, and $\delta >0$ represents the decay rate of goodwill over time. The linear function can effectively capture the positive impact of sales effort on green goodwill, offers good interpretability, and facilitates mathematical treatment.

Additionally, the manufacturer’s green production and the retailer’s sales efforts can also influence the consumers’ reference price, the perceived reasonable price of a certain type of product. When making purchase decisions, consumers will compare the selling price of the product with their internal reference price. As noted by Mazumdar et al. [25], the reference price is affected by several factors, including the manufacturer’s green product level, the retailer’s sales effort level, and consumers’ recollection of historical prices. The reference price evolves over time $t$ and is denoted as $r(t)$, while the actual product price is denoted as $p(t)$. We assume that the evolution of the reference price is governed by the following equation:

$$\dot{r}(t)=\beta (p-r)+\mu g+\upsilon s,r(0)=r_0$$

(2)

where $r(0)=r_0$ is the initial reference price, and $\beta$, $\mu$ and $\upsilon$ are all constants. The term $\beta (p-r)$ in Equation (2) reflects consumers’ past purchasing experiences, where $\beta >0$ represents the memory effect, known as the “memory parameter.” A higher $\beta$ indicates that consumers have a short-term memory, meaning lower loyalty to the product. The items $\mu g$ and $\upsilon s$ in Equation (2) represent the impact of the manufacturer’s green product level and the retailer’s sales effort on the reference price respectively. Generally, investments in green production by the manufacturer and sales efforts by the retailer contribute to increasing product awareness and enhancing consumer evaluation of the product. Thus, we assume $\mu >0$ and $\upsilon >0$.

It should be noted that we assume that the retail price $p(t)$ in Equation (2) remains constant for several reasons. First, the core objective of this study is to examine how the manufacturer’s optimal green production and the retailer’s optimal sales efforts affect the evolution of consumers’ reference prices. Given that the study aims to investigate how reference price effects influence outcomes on green production and sales effort decisions, it is reasonable to keep the retail price fixed. Second, if an optimal retail price $p(t)$ were to be determined dynamically in our model, it would imply that the retailer needs to adjust the retail price day to day, which contradicts common business practices. Frequent promotions or price changes can influence consumer purchasing behavior, as customers accustomed to discounts may prefer waiting for promotions, thereby reducing the reference price. Lastly, when price $p(t)$ changes over time $t$ occur, the model can be recalculated to update optimal strategies for both the manufacturer and the retailer. Then the decisions can be easily changed.

In general, the manufacturer’s green product level, the retailer’s sales effort, goodwill, and consumers’ reference prices positively influence product demand. Hence, we assume that product demand $D(t)$ follows the equation:

$$D(t)=\alpha (r-p)+{\lambda }_{1}g+{\lambda }_{2}s+G$$

(3)

where $\alpha$, ${\lambda }_1$ and ${\lambda }_2$ are positive constants. The item $\alpha (r-p)$ in Equation (3) captures how the reference price influences demand. When $r>p$, the effect on demands is positive, whereas when $r<p$, demand decreases. A higher $\alpha$ reflects increased consumer responsiveness to the gap between the reference and actual selling prices. Additionally, the item $G$ implies that higher goodwill enhances demand, while ${\lambda }_{1}g$ and ${\lambda }_{2}s$ capture the direct and positive effects of green production level and sales effort on demand.

Following previous literature, the cost functions for green production and sales effort are assumed to follow a quadratic form, i.e.,

$$C_M={\displaystyle \frac{1}{2}}{g}^2$$

(4)

$$C_R={\displaystyle \frac{1}{2}}{s}^2$$

(5)

Disregarding the costs of green production and sales effort, we denote ${\rho }_M$ and ${\rho }_R$ be the marginal profits of the manufacturer and retailer respectively. Moreover, to motivate the retailer to invest in sales effort, the manufacturer partially shares the retailer’s sales effort cost. Denote $\varphi$ as the cost-sharing proportion borne by the manufacturer. Reference to Yu’s research [36], the manufacturer’s profit can be expressed as:

$${\pi }_M(t)={\rho }_{M}D-{\displaystyle \frac{1}{2}}{g}^2-{\displaystyle \frac{1}{2}}\varphi s^2$$

(6)

and the retailer’s profit is:

$${\pi }_R(t)={\rho }_{R}D-{\displaystyle \frac{1}{2}}(1-\varphi )s^2$$

(7)

Thus, the total supply chain profit is:

$$\pi (t)=({\rho }_M+{\rho }_R)D-{\displaystyle \frac{1}{2}}{g}^2-{\displaystyle \frac{1}{2}}{s}^2$$

(8)

We assume that $\varphi$ remains constant over time for two main reasons. First, dynamic cooperative sales effort plans are uncommon in practice due to their complexity. Implementing a time-varying advertising cost-sharing scheme would require firms to accurately monitor and respond to their partner’s day-to-day promotional expenditures, which is not a valid approach. Second, even if $\varphi$ varied with time, the resulting optimal strategies would also change accordingly. Since this study emphasizes the impact of consumer behavior on optimal strategies, rather than focusing on the participation rate itself, treating $\varphi$ as a constant is a reasonable simplification that facilitates analytical tractability.

The manufacturer and retailer aim to maximize their respective profits by determining the optimal green production level and sales effort respectively, i.e.,

$$\underset{g}{\max }{J}_M={\displaystyle {\int }_0^{+\infty }{e}^{-\rho t}}[{\rho }_{M}D(t)-{\displaystyle \frac{1}{2}}{g}^2-{\displaystyle \frac{1}{2}}\varphi s^2]dt$$

(9)

$$\underset{s}{\max }{J}_R={\displaystyle {\int }_0^{+\infty }{e}^{-\rho t}}[{\rho }_{R}D(t)-{\displaystyle \frac{1}{2}}(1-\varphi )s^2]dt$$

(10)

where $\rho$ is the discount rate. When the two channel members coordinate as a vertically integrated system, the entire supply chain’s objective is:

$$\underset{g,s}{\max }J={\displaystyle {\int }_0^{+\infty }{e}^{-\rho t}}[({\rho }_M+{\rho }_R)D(t)-{\displaystyle \frac{1}{2}}{g}^2-{\displaystyle \frac{1}{2}}{s}^2]dt$$

(11)

Due to diminishing marginal returns to green production and sales effort, the manufacturer and retailer will not increase these levels indefinitely. There exist upper bounds for both $g(t)$ and $s(t)$, denoted as:

$$0\le g(t),s(t)\le M$$

(12)

where $M$ is a sufficiently large constant.

In the following sections, we compute the manufacturer’s optimal green product level, the retailer’s optimal sales effort level, and the manufacturer’s optimal cost-sharing ratio based on supply chain coordination mechanisms. Furthermore, we analyze the corresponding coordination conditions within the coordination mechanism.

3.3. Non-Integrated Decision

When the manufacturer and retailer make decisions independently, the process follows a sequential order. First, the manufacturer announces the cost-sharing ratio $\varphi$. Based on this, both the manufacturer and retailer determine their respective green production and sales effort levels over time. Given the potential for these decisions to vary dynamically, we assume that the manufacturer and retailer make their decisions simultaneously. This structure forms a Stackelberg game framework, where the equilibrium levels of effort are derived for a given $\varphi$, followed by the calculation of the corresponding equilibrium profits. Since the present value of profits depends on the participation rate $\varphi$, the manufacturer selects the optimal $\varphi$ to maximize its profit. With $\varphi$ fixed, the manufacturer’s and retailer’s objective functions are represented by Equations (9) and (10), respectively. By incorporating the goodwill and reference price dynamics from Equations (1) and (2), the Hamiltonian functions for both the manufacturer and retailer can be formulated as follows, i.e.,

$$\begin{array}{c}{H}_M={\rho }_M[\alpha (r-p)+{\lambda }_{1}g+{\lambda }_{2}s+G]-{\displaystyle \frac{1}{2}}{g}^2-{\displaystyle \frac{1}{2}}\varphi s^2\\ +{\gamma }_{1M}[\beta (p-r)+\mu g+\upsilon s]+{\gamma }_{2M}[\tau s+\theta g+m(r-p)-\delta G]\end{array}$$

(13)

$$\begin{array}{c}{H}_R={\rho }_R[\alpha (r-p)+{\lambda }_{1}g+{\lambda }_{2}s+G]-{\displaystyle \frac{1}{2}}(1-\varphi )s^2\\ +{\gamma }_{1R}[\beta (p-r)+\mu g+\upsilon s]+{\gamma }_{2R}[\tau s+\theta g+m(r-p)-\delta G]\end{array}$$

(14)

where ${\gamma }_{1M}$, ${\gamma }_{2M}$ (${\gamma }_{1R}$, ${\gamma }_{2R}$) represent the co-state variables associated with the changes in the manufacturer’s (retailer’s) reference price and goodwill level, respectively.

From the Hamiltonian functions derived above, we obtained the manufacturer’s optimal green production level and the retailer’s optimal sales effort, which are formally presented in Proposition 1.

Proposition 1.

Given a fixed manufacturer’s participation $\varphi$, the equilibrium green production level of the manufacturer is

$$\overline{g}={\rho }_{M}A$$

(15)

and the sales effort of the retailer is

$$\overline{s}={\displaystyle \frac{{\rho }_R}{(1-\varphi )}}B$$

(16)

where $A={\lambda }_1+{\displaystyle \frac{\theta }{\rho +\delta }}+{\displaystyle \frac{\alpha \mu }{\rho +\beta }}+{\displaystyle \frac{m\mu }{(\rho +\delta )(\rho +\beta )}}$, $B={\lambda }_2+{\displaystyle \frac{\tau }{\rho +\delta }}+{\displaystyle \frac{\alpha \upsilon }{\rho +\beta }}+{\displaystyle \frac{m\upsilon }{(\rho +\delta )(\rho +\beta )}}$.

Proposition 1 provides the mathematical expressions for the optimal product greenness level and sales effort level under the manufacturer’s non-integrated decision-making. From Proposition 1, it can be seen that:

When $\varphi =0$, the retailer’s optimal sales effort level and the optimal product greenness level given in Equation (15) share similar structures. In Equation (15), ${\rho }_M{\lambda }_1$ and ${\rho }_M\theta /(\rho +\delta )$ represent the immediate and long-term effects of product greenness level on sales. ${\rho }_M\alpha \mu /(\rho +\beta )$ reflects the result of considering the reference price effect. When $\mu =0$, this component vanishes, indicating that product greenness level has no impact on sales. ${\rho }_{{\rm M}}m\upsilon /[(\rho +\delta )(\rho +\beta )]$ represents the compound effect through which the reference price indirectly promotes the accumulation of green goodwill. Since both product greenness level and retailer sales effort level typically exert positive influences on consumers’ reference prices (i.e., $\mu >0$ and $\upsilon >0$), this suggests that both manufacturers and retailers will appropriately enhance product greenness levels and sales effort levels when considering their effects on reference prices. The more sensitive consumers are to reference prices (i.e., the larger $\alpha$), the more consciously manufacturers and retailers will account for this influence. On the other hand, the larger $\beta$, the smaller the absolute value of ${\rho }_M\alpha \mu /(\rho +\beta )$ becomes, implying that when consumer product loyalty is lower, the reference price effect may be neglected.

By differentiating the expressions for $\overline{g}$ and $\overline{s}$ with respect to the manufacturer’s and retailer’s marginal profits, we obtain the following results: $\partial \overline{g}/\partial {\rho }_{{\rm M}}>0$, $\partial \overline{s}/\partial {\rho }_R>0$, $\partial \overline{g}/\partial {\rho }_R=0$, and $\partial \overline{s}/\partial {\rho }_{{\rm M}}>0$. The first two indicate that greater marginal profits motivate both the manufacturer and retailer to increase their respective investments in green production and sales effort. The third result suggests that the retailer’s marginal profit does not influence the manufacturer’s decision on product greenness. The fourth result implies a positive relationship between the manufacturer’s marginal profit and the retailer’s effort level. In practical terms, a higher marginal profit for the manufacturer often translates into greater subsidies offered to the retailer, thereby incentivizing increased sales efforts.

Specifically, when consumers are more sensitive to the difference between the reference price and the actual price, manufacturers should increase the product’s greenness level.

First, high consumer price sensitivity means that price deviations significantly affect purchasing decisions. When consumers exhibit strong responsiveness to discrepancies between the selling price and their reference price, they may easily abandon purchases if green products are perceived as too expensive compared to conventional ones. However, by enhancing the product’s greenness level (e.g., using renewable materials, energy-efficient designs, or lower carbon footprints), manufacturers signal higher value and ethical satisfaction to consumers. This makes consumers feel that “the higher price is justified,” thereby reducing resistance to price differences.

Second, a higher greenness level elevates consumers’ psychological “anchoring.” In reality, green attributes themselves contribute to consumers’ cognitive “reference price.” When a product’s greenness level is high, consumers recalibrate their mental “reasonable price range.” They associate “green” with “high value,” making them more accepting of prices exceeding expectations.

For example, when Tesla entered the market at prices far exceeding traditional cars, its positioning as not just an electric vehicle but also a symbol of low-carbon technology, intelligence, and sustainability offset consumer price sensitivity through perceived green-tech value. Similarly, while a regular mug priced at a few dozen yuan might seem expensive, Starbucks’ eco-friendly cups—emphasizing sustainability, recycled materials, and reprocessing techniques—are more readily accepted at premium prices.

From Proposition 1, we derive Lemma 1 to analyze the influencing factors of the optimal greenness level and sales effort level.

Proposition 1 proves that both the manufacturer’s product greenness level and the retailer’s sales effort are constant. Substituting $\overline{g}$ and $\overline{s}$ into Equations (9) and (10), the reference price of the product and the cumulative goodwill over time $t$ are obtained as follows.

Lemma 1.

Assuming that the green production level and sales effort level are both kept as constants $\overline{g}$ and $\overline{s}$ respectively, the reference price and the accumulated goodwill on green product over time are given by:

$$r{(t)}^D=r_0{e}^{-\beta t}+(1-e^{-\beta t})r_1^{*}$$

(17)

and

$$G{(t)}^D=C_1{e}^{-\delta t}+G_1^{*}+{\displaystyle \frac{m(r_0-r_1^{*})}{\delta -\beta }}{e}^{-\beta t}$$

(18)

where $G_1^{*}={\displaystyle \frac{\theta \overline{g}+\tau \overline{s}+m(r_1^{*}-p)}{\delta }}$, $r_1^{*}=p+{\displaystyle \frac{\mu \overline{g}+\upsilon \overline{s}}{\beta }}$, $C_1=G_0-G_1^{*}-{\displaystyle \frac{m(r_0-r_1^{*})}{\delta -\beta }}$.

The reference price in Equation (17) and the goodwill in Equation (18) reach steady states when $t\to +\infty$. At this point, the reference price becomes $p+(\mu \overline{g}+\upsilon \overline{s})/\beta$, which is mainly influenced by market price, product greenness level, and sales effort level. This implies that in the absence of greenness level and sales effort, the reference price would eventually equal the market price. However, since $\mu >0$ and $\upsilon >0$, the reference price generally increases with these influencing factors. Moreover, a smaller $\beta$ indicates deeper consumer memory of the product, leading to higher reference prices.

Similarly, analysis of the steady-state goodwill $[\theta \overline{g}+\tau \overline{s}+m(r_1^{*}-p)]/\delta$ reveals that higher product greenness levels and sales effort levels result in greater goodwill. That is, improving product greenness level and sales effort level can not only increase the reference price but also accumulate goodwill among consumers.

Substituting Equation (17) and Equation (18) into Equation (9) and Equation (10) respectively, the equilibrium profit values for the manufacturer and retailer under a fixed $\varphi$ are as follows:

$${\overline{J}}_M={\displaystyle \frac{{\rho }_M\alpha r_0}{\rho +\beta }}+{\displaystyle \frac{{\rho }_M\alpha \beta }{\rho (\rho +\beta )}}{r}_1^{*}-{\displaystyle \frac{{\rho }_M\alpha p}{\rho }}+{\displaystyle \frac{{\rho }_M}{\rho }}({\lambda }_1\overline{g}+{\lambda }_2\overline{s})+{\displaystyle \frac{{\rho }_M{C}_1}{\rho +\delta }}+{\displaystyle \frac{{\rho }_M{G}_1^{*}}{\rho }}-{\displaystyle \frac{{\overline{g}}^2}{2\rho }}-{\displaystyle \frac{\varphi {\overline{s}}^2}{2\rho }}$$

(19)

and

$${\overline{J}}_R={\displaystyle \frac{{\rho }_R\alpha r_0}{\rho +\beta }}+{\displaystyle \frac{{\rho }_R\alpha \beta }{\rho (\rho +\beta )}}{r}_1^{*}-{\displaystyle \frac{{\rho }_R\alpha p}{\rho }}+{\displaystyle \frac{{\rho }_R}{\rho }}({\lambda }_1\overline{g}+{\lambda }_2\overline{s})+{\displaystyle \frac{{\rho }_R{C}_1}{\rho +\delta }}+{\displaystyle \frac{{\rho }_R{G}_1^{*}}{\rho }}-{\displaystyle \frac{(1-\varphi ){\overline{s}}^2}{2\rho }}$$

(20)

Given that the manufacturer can evaluate its profit’s present value for any specified participation rate, it can strategically choose the rate that maximizes this value.

Lemma 2.

From this, the manufacturer determines the optimal participation rate $\varphi$ as: 

$$\overline{\varphi }=\left\{\begin{array}{cc}1-{\displaystyle \frac{2{\rho }_R}{2{\rho }_M+{\rho }_R}}& if 0<{\displaystyle \frac{{\rho }_R}{{\rho }_M}}\le 2\\ 0& else\end{array}\right.$$

(21)

When $0<{\rho }_R/{\rho }_M\le 2$, we obtain $\partial \overline{\varphi }/\partial {\rho }_{{\rm M}}>0$ and $\partial \overline{\varphi }/\partial {\rho }_R>0$, which means the higher the manufacturer’s marginal profit or the lower the retailer’s marginal profit, the greater the manufacturer’s subsidy to the retailer. When the manufacturer’s unit product profit is high (e.g., premium green products), the marginal benefit from sales growth is greater, making them willing to increase the subsidy ratio to incentivize retailers to enhance promotion efforts. Even with higher costs, they can still achieve net profit growth. Conversely, if the retailer’s marginal profit is low (i.e., retail price approaches wholesale price), the retailer lacks motivation to invest in sales efforts. To prevent insufficient market promotion leading to unsold green products, the manufacturer must increase subsidies to compensate for the retailer’s incentive gap.

By substituting Equation (21) into Equations (19) and (20), the optimal present values of profits for the manufacturer and retailer, ${\overline{J}}_M$ and ${\overline{J}}_R$, can be derived.

When the manufacturer holds greater profit dominance (high marginal profit or low retailer profit), they internalize the retailer’s sales externality through subsidies, promoting coordinated optimization of greenness level and sales effort. However, constrained by double marginalization and gaming losses in decentralized decision-making, the overall effect remains inferior to centralized decision-making.

3.4. Integrated Decision

In this section, we consider a vertically integrated supply chain, where the manufacturer and retailer operate as a unified entity aiming to maximize total system profit. Under this coordinated structure, the supply chain’s objective function is defined in Equation (11). By incorporating the goodwill and reference price dynamics from Equations (1) and (2), the present value Hamiltonian for the integrated supply chain is formulated as follows:

$$\begin{array}{c}H=({\rho }_M+{\rho }_R)[\alpha (r-p)+{\lambda }_{1}g+{\lambda }_{2}s+G]-{\displaystyle \frac{1}{2}}\eta g^2-{\displaystyle \frac{1}{2}}k{s}^2\\ +{\gamma }_1[\beta (p-r)+\mu g+\upsilon s]+{\gamma }_2[\tau s+\theta g+m(r-p)-\delta G]\end{array}$$

(22)

where ${\gamma }_1$ and ${\gamma }_2$ represent the co-state variables associated with the changes in consumer reference price and goodwill level for the entire supply chain. Based on the present value Hamiltonian derived from the above equations, the optimal manufacturer’s product greenness level and the optimal retailer’s sales effort are obtained, leading to Proposition 4.

Proposition 2.

When the manufacturer and the retailer coordinate as an integrated supply chain, both the optimal manufacturer’s product greenness level and the optimal retailer’s sales effort remain constant, i.e.,

$$\tilde{g}=({\rho }_M+{\rho }_R)A$$

(23)

$$\tilde{s}=({\rho }_M+{\rho }_R)B$$

(24)

Since the integrated manufacturer’s product greenness level significantly increases, the following equalities demonstrate that the retailer’s sales effort level has also improved. When $0<{\rho }_R/{\rho }_M\le 2$, according to Equation (21), we obtain $\overline{\varphi }=1-2{\rho }_R/(2{\rho }_M+{\rho }_R)$, and thus Equation (16) can be rewritten as:

$$\overline{s}=({\rho }_M+{\displaystyle \frac{1}{2}}{\rho }_R)B$$

(25)

When ${\rho }_R/{\rho }_M>2$, then Equation (16) can be rewritten as:

$$\overline{s}={\rho }_{R}B$$

(26)

Comparing the optimal product greenness levels and sales effort levels under integrated and non-integrated decision-making, it can be observed that both improve through coordination. Assuming $\Delta g=\tilde{g}-\overline{g}$, $\Delta s=\tilde{s}-\overline{s}$, we obtain:

$$\Delta g={\rho }_{R}A>0$$

(27)

When $0<{\rho }_R/{\rho }_M\le 2$,

$$\Delta s=={\displaystyle \frac{{\rho }_R}{2}}B>0$$

(28)

When ${\rho }_R/{\rho }_M>2$,

$$\Delta s={\rho }_{M}B>0$$

(29)

Proposition 3.

From $\Delta g>0$ and $\Delta s>0$, it can be seen that compared with the optimal solution under non-integrated decision-making, both the manufacturer’s product greenness level and the retailer’s sales effort level are improved under integrated decision-making.

Under non-integrated decision-making, the manufacturer and retailer each pursue their own profit maximization. Although the manufacturer guides the retailer’s behavior by setting participation rates, concerns about “free-riding” prevent the system from achieving optimal greenness and sales effort levels. In contrast, under integrated decision-making, the manufacturer and retailer jointly maximize supply chain profits as a whole, where improving greenness and sales efforts become mutually reinforcing strategies that enable unified planning and coordinated investments. For example, in Apple’s vertically integrated system, continuous improvements in product greenness (e.g., eco-friendly materials, carbon neutrality initiatives) are complemented by substantial investments in physical retail stores and digital marketing, creating a virtuous cycle that significantly enhances overall profitability.

Furthermore, Proposition 2 proves that both the manufacturer’s product greenness level $\tilde{g}$ and the retailer’s sales effort $\tilde{s}$ are constants. Substituting $\tilde{g}$ and $\tilde{s}$ into Equations (1) and (2) yields the reference price and accumulated goodwill as functions of time $t$:

$$r{(t)}^C=r_0{e}^{-\beta t}+(1-e^{-\beta t})r_2^{*}$$

(30)

$$G{(t)}^C=C_2{e}^{-\delta t}+G_2^{*}+{\displaystyle \frac{m(r_0-r_2^{*})}{\delta -\beta }}{e}^{-\beta t}$$

(31)

where $G_2^{*}={\displaystyle \frac{\theta \tilde{g}+\tau \tilde{s}+m(r_2^{*}-p)}{\delta }}$$r_2^{*}=p+{\displaystyle \frac{\mu \tilde{g}+\upsilon \tilde{s}}{\beta }}$, $C_2=G_0-G_2^{*}-{\displaystyle \frac{m(r_0-r_2^{*})}{\delta -\beta }}$.

Comparing these results with Lemma 1 shows that when two channel members coordinate as an integrated supply chain system, both the stable reference price and goodwill increase due to improvements in the manufacturer’s greenness level and retailer’s sales effort level. Substituting Equations (30) and (31) into (11) gives the present value of total supply chain profits:

$$\tilde{J}=({\rho }_M+{\rho }_R)[{\displaystyle \frac{\alpha r_0}{\rho +\beta }}+{\displaystyle \frac{\alpha \beta }{\rho (\rho +\beta )}}{r}_2^{*}-{\displaystyle \frac{\alpha p}{\rho }}+{\displaystyle \frac{{\lambda }_1\tilde{g}+{\lambda }_2\tilde{s}}{\rho }}+{\displaystyle \frac{C_2}{\rho +\delta }}+{\displaystyle \frac{G_2^{*}}{\rho }}]-{\displaystyle \frac{{\tilde{g}}^2}{2\rho }}-{\displaystyle \frac{{\tilde{s}}^2}{2\rho }}$$

(32)

Taking the differences between corresponding profit functions under non-integrated and integrated decision-making yields $\Delta J$, $\Delta J_M$, and $\Delta J_R$:

$$\Delta J=\left\{\begin{array}{cc}{\displaystyle \frac{{{\rho }_R}^2}{2\rho }}{A}^2+{\displaystyle \frac{{{\rho }_R}^2}{8\rho }}{B}^2,& {\displaystyle \frac{{\rho }_{{\rm M}}}{{\rho }_R}}>{\displaystyle \frac{1}{2}}\\ {\displaystyle \frac{{{\rho }_R}^2}{2\rho }}{A}^2+{\displaystyle \frac{{{\rho }_{{\rm M}}}^2}{2\rho }}{B}^2,& else\end{array}\right.$$

(33)

3.5. Bilateral Subsidy Strategy

In the previous chapter, we found that the optimal product greenness level for the manufacturer and the sales effort level for the retailer is higher under the integrated decision-making scenario. Since the supply chain profit is higher in the cooperative game structure, it is necessary to establish a contract between the manufacturer and the retailer, so that both channel members will choose decisions that maximize the supply chain profit, even when making independent decisions. The bilateral subsidy policy can achieve this coordination. The bilateral subsidy policy means that the manufacturer not only shares part of the retailer’s sales effort costs based on the participation rate, but the retailer also shares part of the manufacturer’s green production costs based on the participation rate. Under the bilateral subsidy policy, the profits of the manufacturer and retailer are as follows:

$${\pi }_M(t)={\rho }_{M}D-{\displaystyle \frac{1}{2}}(1-{\varphi }_2)g^2-{\displaystyle \frac{1}{2}}{\varphi }_1{s}^2$$

(34)

$${\pi }_R(t)={\rho }_{R}D-{\displaystyle \frac{1}{2}}{\varphi }_2{g}^2-{\displaystyle \frac{1}{2}}(1-{\varphi }_1)s^2$$

(35)

The present value Hamiltonian for the manufacturer and retailer is as follows:

$$\begin{array}{c}{H}_M={\rho }_{{\rm M}}[\alpha (r-p)+{\lambda }_{1}g+{\lambda }_{2}s+G]-{\displaystyle \frac{1}{2}}(1-{\varphi }_2)g^2-{\displaystyle \frac{1}{2}}{\varphi }_1{s}^2\\ +{\gamma }_{5M}[\beta (p-r)+\mu g+\upsilon s]+{\gamma }_{6M}[\tau s+\theta g+m(r-p)-\delta G]\end{array}$$

(36)

$$\begin{array}{c}{H}_R={\rho }_R[\alpha (r-p)+{\lambda }_{1}g+{\lambda }_{2}s+G]-{\displaystyle \frac{1}{2}}{\varphi }_2{g}^2-{\displaystyle \frac{1}{2}}(1-{\varphi }_1)s^2\\ +{\gamma }_{5R}[\beta (p-r)+\mu g+\upsilon s]+{\gamma }_{6R}[\tau s+\theta g+m(r-p)-\delta G]\end{array}$$

(37)

When the participation rates ${\varphi }_1$ and ${\varphi }_2$ are fixed, the optimal product greenness level for the manufacturer and the optimal sales effort level for the retailer can be derived as follows.

Proposition 4.

Under the bilateral subsidy policy, assuming that the participation rates ${\varphi }_1$ and ${\varphi }_2$ are fixed, the optimal product greenness level for the manufacturer and the optimal sales effort level for the retailer are as follows:

$$\widehat{g}={\displaystyle \frac{{\rho }_{{\rm M}}}{1-{\varphi }_2}}A$$

(38)

$$\widehat{s}={\displaystyle \frac{{\rho }_R}{1-{\varphi }_1}}B$$

(39)

There exist fixed participation rates ${\varphi }_1$ and ${\varphi }_2$ such that $\widehat{g}=\tilde{g}$ and $\widehat{s}=\tilde{s}$ hold true. That is, the equilibrium product greenness level of the manufacturer and the equilibrium sales effort level of the retailer are the same as the equilibrium solution of the entire supply chain.

Proposition 5.

When the manufacturer and retailer take fixed participation rates ${\varphi }_1$ and ${\varphi }_2$, we have

$${\varphi }_1={\displaystyle \frac{{\rho }_M}{{\rho }_M+{\rho }_R}}$$

(40)

$${\varphi }_2={\displaystyle \frac{{\rho }_R}{{\rho }_M+{\rho }_R}}$$

(41)

It can be concluded that ${\varphi }_1>\varphi$ and ${\varphi }_2>0$ imply that under the bilateral subsidy policy, higher participation rates are required to coordinate the supply chain.

Based on the solution process outlined above, we can similarly obtain the profits of the manufacturer and retailer under the bilateral subsidy policy as follows:

$${\widehat{J}}_M={\rho }_M[{\displaystyle \frac{r_0\alpha }{\rho +\beta }}+{\displaystyle \frac{G_0}{\rho +\delta }}-{\displaystyle \frac{\alpha p}{\rho +\beta }}+{\displaystyle \frac{\alpha (\mu \widehat{g}+\upsilon \widehat{s})}{\rho (\rho +\beta )}}+{\displaystyle \frac{\theta \widehat{g}+\tau \widehat{s}}{\rho (\rho +\delta )}}+{\displaystyle \frac{{\lambda }_1\widehat{g}}{\rho }}+{\displaystyle \frac{{\lambda }_2\widehat{s}}{\rho }}]-{\displaystyle \frac{(1-{\varphi }_2){\widehat{g}}^2}{2\rho }}-{\displaystyle \frac{{\varphi }_1{\widehat{s}}^2}{2\rho }}$$

(42)

$${\widehat{J}}_R={\rho }_R[{\displaystyle \frac{r_0\alpha }{\rho +\beta }}+{\displaystyle \frac{G_0}{\rho +\delta }}-{\displaystyle \frac{\alpha p}{\rho +\beta }}+{\displaystyle \frac{\alpha (\mu \widehat{g}+\upsilon \widehat{s})}{\rho (\rho +\beta )}}+{\displaystyle \frac{\theta \widehat{g}+\tau \widehat{s}}{\rho (\rho +\delta )}}+{\displaystyle \frac{{\lambda }_1\widehat{g}}{\rho }}+{\displaystyle \frac{{\lambda }_2\widehat{s}}{\rho }}]-{\displaystyle \frac{{\varphi }_2{\widehat{g}}^2}{2\rho }}-{\displaystyle \frac{(1-{\varphi }_1){\widehat{s}}^2}{2\rho }}$$

(43)

Let $\Delta J_M={\widehat{J}}_M-{\overline{J}}_M$ and $\Delta J_R={\widehat{J}}_R-{\overline{J}}_R$. By comparing the profits under the bilateral subsidy strategy and non-integrated decision-making, we can conclude:

$$\Delta J_M=\left\{\begin{array}{cc}{\displaystyle \frac{{\rho }_{\mathrm{M}}{\rho }_R}{2\rho }}{A}^2-{\displaystyle \frac{{{\rho }_R}^2}{8\rho }}{B}^2,& {\displaystyle \frac{{\rho }_{{\rm M}}}{{\rho }_R}}>{\displaystyle \frac{1}{2}}\\ {\displaystyle \frac{{\rho }_{\mathrm{M}}{\rho }_R}{2\rho }}{A}^2+{\displaystyle \frac{{{\rho }_{{\rm M}}}^2-{\rho }_{{\rm M}}{\rho }_R}{2\rho }}{B}^2,& else\end{array}\right.$$

(44)

$$\Delta J_R=\left\{\begin{array}{cc}{\displaystyle \frac{{{\rho }_R}^2-{\rho }_{\mathrm{M}}{\rho }_R}{2\rho }}{A}^2+{\displaystyle \frac{{{\rho }_R}^2}{4\rho }}{B}^2,& {\displaystyle \frac{{\rho }_{{\rm M}}}{{\rho }_R}}>{\displaystyle \frac{1}{2}}\\ {\displaystyle \frac{{{\rho }_R}^2-{\rho }_{\mathrm{M}}{\rho }_R}{2\rho }}{A}^2+{\displaystyle \frac{{\rho }_{{\rm M}}{\rho }_R}{2\rho }}{B}^2,& else\end{array}\right.$$

(45)

From the above results, it can be concluded that $\Delta J_M>0$ and $\Delta J_R>0$ do not always hold, meaning that when the overall supply chain profit improves, one of the two channel members may experience a profit loss. By comparing the profit changes under bilateral subsidies and decentralized decision-making, it is found that an improvement in the overall supply chain profit does not necessarily guarantee simultaneous benefits for both the manufacturer and the retailer. Specifically, profit variations depend on the cost-sharing ratio ${\rho }_{\mathrm{{\rm M}}}/{\rho }_R$ between the two parties; for instance, the manufacturer’s profit may decline due to the retailer’s cost burden (e.g., $-({\rho }_R/8\rho k)B^2$). Conversely, if the retailer bears an excessive portion of the cost, its profit may also suffer. This indicates that although bilateral subsidies can enhance overall supply chain performance, an improperly designed profit allocation mechanism may lead to a decline in one party’s profit, thereby undermining the sustainability of cooperation. Therefore, supply chain members must carefully balance cost-sharing proportions when implementing subsidy strategies to ensure mutual benefit.

4. Numerical Example Analysis

To verify the dynamic properties of the proposed model and the differences in optimal strategies under different mechanisms, we conduct numerical simulations using multiple parameter settings. The parameter settings are based on the study by Zu et al. [37]. The simulations cover various aspects, including the dynamic evolution of green levels and sales efforts, the impact of price sensitivity, the coordination effect of subsidy strategies, and profit responses. These results further reveal the underlying mechanisms of green supply chain systems under different cooperation structures.

The numerical settings refer to previous studies and publicly available survey data. According to the 2024 China Sustainable Consumption Research Report, over 80% (82.36%) of respondents indicated that seeing low-carbon consumption information influences their daily purchasing choices, allowing us to quantify the carbon reduction contribution in the consumption process. Most consumers (68.58%) are more willing to purchase products when they learn positive sustainability information, and 60.37% of consumers do not perceive a significant price difference for low-carbon products. Based on this, the parameters of the demand function are set as: ${\lambda }_1=0.8$, ${\lambda }_2=0.7$, $\alpha =0.4$. In addition, the remaining parameters are set with reference to previous studies [19]: $\delta =1$, $\theta =12$, $\tau =2$, $\mu =2$, $\upsilon =2$, $\beta =2$.

4.1. Dynamic Evolution of Reference Prices and Green Goodwill

4.1.1. Evolution of Green Goodwill Under Reference Price Effects

Figure 2 uses the ode45 model to dynamically simulate the system of differential equations, focusing on the intrinsic mechanism of green goodwill $G(t)$ evolution under different initial conditions of reference price $r(t)$. As the reference price $r(t)$ gradually rises from a low initial level due to the firm’s green investment and sales effort, green goodwill $G(t)$ exhibits accelerated accumulation, driven by the positive feedback term $m(r-p)$ in the equation. Consumer recognition of a product’s green attributes strengthens as the reference price increases, further promoting brand goodwill accumulation. When the system approaches a steady state, the reference price stabilizes at $r^{*}$, and green goodwill reaches its equilibrium value $G^{*}$, confirming the global stability of the system of differential equations.

Figure 2. Evolution of Green Goodwill with Reference Price under Different Initial Values. Note: This figure shows the dynamic trajectories of green goodwill $G(t)$ with changes in reference price $r(t)$ under different initial reference prices $r_0$ and initial green goodwill $G_0$. All trajectories eventually converge to the same steady-state point $(r^{*},G^{*})$. Managers should adopt a phased strategy: strengthen price awareness in the early stage and maintain goodwill through continuous innovation in the later stage.

This dynamic pattern reveals the formation process of consumer awareness of green products. During the market introduction phase, increases in reference price significantly enhance goodwill accumulation through the $m(r-p)$ effect. When the reference price nears its steady state, the accumulation of goodwill primarily relies on continued green investment and marketing effort by the firm. All trajectories eventually converge to the same steady-state point, and the steady-state reference price is noticeably higher than the actual price, providing a direct theoretical explanation for the market premium of green products.

The differences in trajectory shapes under varying initial conditions indicate that in markets with low initial reference prices, improving consumer awareness of a product’s green value can achieve higher efficiency in green goodwill accumulation. This provides a theoretical basis for firms to implement phased green marketing strategies: in new markets, resources should focus on building price awareness advantages, while in more mature markets, product innovation and brand development are needed to maintain goodwill stability. The dynamic patterns shown in the phase diagram closely match real-world performance of green products, validating the model’s effectiveness in capturing the interaction between consumer environmental perception and firm green investment.

4.1.2. Temporal Trends in Reference Price and Green Goodwill

Figure 3 and Figure 4 show the time evolution trajectories of product green goodwill $G(t)$ and reference prices $r(t)$ under three decision-making scenarios. Under non-integrated decisions, the steady-state levels of green goodwill and reference prices are significantly lower. In integrated decision-making and two-way subsidy decision-making, both $G(t)$ and $r(t)$ experience rapid growth and stabilize consistently in the mid-term. The two-way subsidy decision can approximate the synergistic effects of green investment and brand accumulation achieved by the integrated strategy under non-integrated conditions.

Figure 3. Temporal Evolution of Reference Price under Three Decision Modes. Note: This figure compares the changes in reference price $r(t)$ over time under three decision modes: non-integrated, integrated, and bilateral subsidy. Under the integrated and bilateral subsidy strategies, the reference price reaches a higher steady-state value more quickly. Firms can simulate integration effects through contract design to enhance market acceptance of the green premium.

Figure 4. Convergence of Green Goodwill to Steady-State under Three Decision Modes. Note: Green goodwill $G(t)$ is significantly higher under the integrated and bilateral subsidy strategies compared to the non-integrated strategy, and it reaches the steady state more quickly. Managers should recognize that green goodwill serves as a key link between a firm’s environmental actions and market returns, and its maximization requires coordinated internal and external efforts.

4.2. Consumer Behavior Effects

4.2.1. Impact of Consumer Price Sensitivity on Optimal Effort Level

As shown in Figure 5 and Figure 6, when consumer reference price sensitivity $\alpha$ increases, both the optimal green level $g$ of the manufacturer and the optimal sales effort level $s$ of the retailer increase. As reference price sensitivity $\alpha$ rises, consumers become more sensitive to the difference between the reference price and the actual price, prompting firms to enhance product green levels and sales efforts to improve the reference anchor. Both manufacturers and retailers are more inclined to persuade consumers to accept a premium for green products by increasing the green level $g$ and sales efforts $s$. The effort levels under non-integrated decision-making are generally lower than those under integrated decision-making, indicating that in the absence of coordination mechanisms, there are issues of free-riding and incentive asymmetry between channel members. Furthermore, we can observe that the product’s green level is more sensitive to changes in reference price $\alpha$; the greater the impact of the reference price, the more manufacturers should focus on improving the product’s greenness to meet consumer demand.

Figure 5. Product Green Level Response to Reference Price Sensitivity under Integrated and Non-Integrated Decisions. Note: As consumer sensitivity to price differences $\alpha$ increases, the manufacturer’s optimal green level $g$ rises under both integrated and non-integrated strategies, with a larger increase under the integrated strategy. Firms should enhance green levels to raise the reference price and mitigate resistance to the green premium.

Figure 6. Sales Effort Response to Reference Price Sensitivity under Integrated and Non-Integrated Decisions. Note: Sales effort $s$ is consistently higher under the integrated strategy than under the non-integrated strategy. This indicates that in markets with high price sensitivity, retailers need to strengthen green promotion to shape consumer perception and elevate the reference price.

4.2.2. The Impact of Consumer Behavior Effects on Profit

Figure 7 illustrates how consumer behavior, specifically memory effect $\beta$ and green goodwill decay rate $\delta$, influences the profit differentials of supply chain members under cooperative versus non-cooperative decision-making. As $\beta$ increases, indicating shorter consumer memory, the manufacturer’s profit improvement $\Delta J_M$ declines sharply. This is because short-term memory undermines the sustained influence of green investments on consumer reference prices and goodwill, thereby reducing the manufacturer’s incentive to collaborate. Similarly, a higher $\delta$ implies faster dissipation of accumulated green goodwill, further weakening the long-term benefits of green production. In contrast, the retailer’s profit differential $\Delta J_R$ is less sensitive to changes in $\beta$ and $\delta$, as sales efforts have a more immediate but shorter-lived impact on consumer perception. Overall, the total supply chain profit improvement $\Delta J$ follows a similar trend to $\Delta J_M$, confirming that green cooperation is most effective in markets where consumers exhibit strong green memory (low $\beta$) and goodwill persists over time (low $\delta$). These findings highlight the critical role of consumer behavior in shaping the viability and profitability of green supply chain collaboration strategies.

Figure 7. Impact of Consumer Memory and Green Goodwill Decay on Profit Optimization under Bilateral Subsidy Strategy. Note: This figure illustrates how the consumer memory parameter $\beta$ and the green goodwill decay rate $\delta$ affect cooperative profit gains. When $\beta$ is low or $\delta$ is low, the profit gains from cooperation are significant. In markets with high consumer loyalty and easily maintained green image, cooperative mechanisms are more likely to succeed. Firms should enhance consumer memory and slow down goodwill decay through brand building, repeat-purchase incentives, and other strategies.

4.3. The Effect of Decay Rate on the Steady-State Value of Green Goodwill

As shown in Figure 8, the steady-state level of green goodwill decreases rapidly as the decay rate $\delta$ increases, exhibiting a typical inverse relationship. When the decay rate $\delta$ is low, enhanced consumer memory allows green goodwill to accumulate quickly, even if green investment and marketing efforts remain constant. In contrast, a high decay rate $\delta$ leads to a rapid loss of green goodwill, requiring channel members to continuously increase their efforts to maintain goodwill and stabilize the green product market.

Figure 8. Effect of Decay Rate on the Steady-State Value of Green Goodwill. Note: The steady-state value of green goodwill $G^{*}$ declines rapidly as the decay rate $\delta$ increases, showing a significant negative correlation. Firms should establish sustainable green communication mechanisms to maintain continuous consumer recognition of green attributes.

4.4. The Effect of Marginal Profit on the Payoffs and Behavior of Channel Members

Figure 9 illustrates the profit evolution trajectories of the manufacturer and retailer under different cost-sharing ratios ${\varphi }_2$. Both manufacturer and retailer profits rise rapidly in the initial stage and then stabilize. At the beginning, high green production costs compress short-term profits. Over time, green goodwill $G(t)$ and reference price $r(t)$ gradually increase, consumers increasingly accept the green premium, and profits grow, eventually converging to stable values. As the cost-sharing ratio ${\varphi }_2$ increases, the manufacturer’s profit clearly rises while the retailer’s profit decreases, consistent with the redistribution of profits between channel members under bilateral subsidies. When the retailer bears a higher share of costs, it should receive compensatory transfers to maintain incentive compatibility; otherwise, its profit may fall below the non-cooperative level, leading it to reject the contract with the manufacturer.

Figure 9. Temporal Evolution of Channel Member Profits under Different Cost-Sharing Ratios. Note: This figure shows how manufacturer and retailer profits change over time under different cost-sharing ratios ${\varphi }_2$. If the retailer’s profit falls below the non-cooperative level, transfers or dynamic adjustment mechanisms are needed to maintain its willingness to cooperate. Contract design should balance incentive compatibility with fair profit distribution.

4.5. Profit Allocation and Risk Analysis of the Bidirectional Subsidy Mechanism

Figure 10 analyzes the impact of the bidirectional subsidy mechanism on manufacturer profit $J_M$, retailer profit $J_R$, and overall supply chain profit $J$ by defining different cost-sharing ratio $\kappa ={\rho }_{{\rm M}}/({\rho }_{{\rm M}}+{\rho }_R)$. $\kappa$ represents the marginal profit margin of the manufacturer within the entire supply chain, meaning that the larger $\kappa$, the more profit the manufacturer captures. As shown in Figure 6, both manufacturer and overall supply chain profits increase under the bidirectional subsidy decision. However, when $\kappa \to 1$, retailer profit margins are very low, and profits are even lower than under non-integrated decision-making. In this case, the retailer is unwilling to enter into a contract with the supplier. This indicates that while cooperation can enhance supply chain system profits, improper subsidy contract design may lead to profit losses for one channel member.

Figure 10. Profit Optimization and Risk Analysis under the Bilateral Subsidy Mechanism. Note: This figure analyzes changes in manufacturer, retailer, and total system profits under different marginal profit-sharing ratios $\kappa$. When the manufacturer’s share is high, total system profit increases, but the retailer’s profit may fall below the non-cooperative level, causing it to reject cooperation. This indicates that while cooperation can improve system efficiency, unreasonable profit distribution can still lead to failure.

4.6. Experimental Trend Comparison and Result Validation

To validate the practical applicability and rationality of the model’s predictions, this paper compares the numerical simulation results with existing empirical studies. For example, Trong Nguyen et al. [38], based on a structural equation model constructed from 231 consumer survey data in Vietnam, found that consumer green purchasing behavior is significantly influenced by factors such as attitudes, social norms, and environmental concern, with environmental concern being a key driver of green purchasing behavior. This aligns closely with the mechanism in this model, where green preferences drive the accumulation of green goodwill, influencing reference price and market demand.

Furthermore, Lee et al. [39], through consumer surveys and structural equation modeling, discovered that although consumers hold positive attitudes toward green supply chain management, actual purchasing behavior is more influenced by subjective norms and perceived behavioral control. This is especially true when products feature credible green labels and product information disclosure, making consumers more willing to accept higher green premiums. This paper’s model provides a dynamic mechanism explanation: under integrated decision-making, the retailer strengthens green information disclosure (corresponding to sales efforts), and the manufacturer increases green design investment. The combined effect accelerates the formation and updating of consumers’ reference prices, raising the reference anchor, thereby reducing consumers’ sensitivity to high prices and facilitating acceptance of higher green premiums. This causal mechanism mirrors the path in Lee et al.’s [39] empirical findings of “improved internal green supply chain mechanisms—enhanced reference expectations—stronger purchase willingness.”

In conclusion, the model presented in this paper not only aligns with the trend results of the aforementioned empirical studies but also provides a mechanistic explanation of how consumers dynamically adjust their purchase willingness based on green cognition and price memory. This enhances the model’s explanatory power and real-world applicability, providing theoretical support for firms to develop differentiated green marketing and collaboration strategies.

5. Conclusions and Managerial Implications

In the context of the global green transition, the sustainable development of supply chains requires balancing both economic and environmental benefits. Supply chain managers face not only internal cost control issues but also the need to precisely respond to consumer green preferences and behavioral psychology. This paper, based on differential game theory, constructs a dynamic coordination model for green supply chains that takes consumer behavior into account, revealing the impact mechanisms of reference price effects and green goodwill on supply chain member decisions. Through theoretical analysis and numerical simulation, this paper provides the following structured practical recommendations for green supply chain managers to optimize collaboration strategies and resource allocation under different market conditions.

This study finds that improvements in product greenness and sales effort can enhance both consumers’ reference prices and green goodwill, thereby increasing product acceptance and willingness to pay a premium. These effects ultimately contribute to higher overall supply chain profits. When consumers are more sensitive to price differences, manufacturers should place greater emphasis on improving product greenness, as this more effectively raises consumers’ reference prices and boosts their acceptance of green price premiums. However, given the practical challenges of achieving full vertical integration, this paper proposes a bilateral subsidy strategy as a feasible alternative. Under this mechanism, manufacturers subsidize retailers’ sales effort costs, while retailers share part of the manufacturers’ green investment costs. This mutual cost-sharing enables both parties to achieve a near-optimal outcome even under decentralized decision-making. Our findings indicate that when retailers are not overburdened by green cost-sharing, the dual subsidy strategy significantly improves profits for both parties and outperforms full integration; when the retailer’s cost burden becomes too high, transfer payments can be introduced to maintain incentive alignment.

As shown in Table 3, to make the managerial insights of this study more actionable, we develop a systematic decision-making framework based on the above simulations and analysis. This framework uses key market and consumer behavior characteristics as decision criteria and provides corresponding strategic priorities and recommendations for designing cooperation mechanisms. It aims to guide managers in formulating precise green supply chain collaboration strategies under different market scenarios.

Table 3. Decision-Making Framework Table.

Consumer Behavior Traits	Strategic Focus and Objectives	Cooperation Mechanisms and Strategic Recommendations
High Price Sensitivity ($\alpha$ High)	Rapidly raise consumers’ reference price to reduce premium resistance.	Manufacturer: Prioritize increasing product green level. Retailer: Strengthen communication of long-term benefits of green attributes. Use bilateral subsidy contracts; jointly invest in enhancing perceived value
Low Price Sensitivity ($\alpha$ Low)	Drive purchases through non-price factors (e.g., convenience, functionality).	Manufacturer: Control green costs to avoid excessive investment leading to high prices. Retailer: Focus marketing on convenience and functionality. Lower need for cost-sharing; explore other joint marketing models
High Consumer Memory Retention ($\beta$ Low; $\delta$ Low)	Build long-term green brand assets to secure sustainable premium.	Manufacturer: Pursue long-term, cutting-edge green innovations; use iterative innovation to maintain market freshness. Retailer: Invest in brand story, loyalty programs, and repeated exposure to sustain brand goodwill. Form long-term strategic alliances to stabilize investment expectations
Low Consumer Memory Retention ($\beta$ High; $\delta$ High)	Reinforce short-term stimuli and repeated exposure to sustain brand goodwill.	Manufacturer: Use iterative innovation to keep the market engaged. Retailer: Promote frequently across multiple channels. Apply dynamic subsidy contracts; adjust cost-sharing in real time based on market feedback to maintain flexibility

Despite the comprehensive dynamic model developed in this study, several limitations remain. First, the model assumes information symmetry between supply chain members, whereas in practice, information asymmetry is common and may affect the efficiency of cooperation mechanisms. Second, the study focuses on a two-tier supply chain with a single manufacturer and a single retailer. Future research could extend the model to include multiple manufacturers and retailers, capturing horizontal competition and network dynamics. Third, the model assumes that consumers have strong environmental preferences, which significantly influence reference prices and purchasing behavior. However, in reality, consumer awareness of environmental issues varies. Incorporating heterogeneous preferences and consumer segmentation would improve the model’s practical relevance.