Sustainable Supply Chains for Poverty Alleviation: Considering Branding and Nash Bargaining Fairness Concerns

Abstract

With economic development and shifting consumption trends, branding has become an important way to improve the efficiency of poverty alleviation supply chains (PASCs) in practice. However, academic research on this topic is limited. To fill this gap in the literature, we constructed a differential game of a PASC that examines how to build a sustainable poverty reduction model through branding, considering government subsidies and supplier’s Nash bargaining fairness concerns. Our findings show the following: (1) Government subsidies can improve the decision-making level and channel efficiency of leading enterprises (E) and poor suppliers (F). Government subsidies are necessary for a PASC to establish a sustainable poverty alleviation mechanism. (2) F’s Nash bargaining fairness concerns only reduce their level of production effort but do not affect the brand construction and corporate social responsibility levels of E. (3) As F’s bargaining power increases, Nash bargaining fairness concerns have a more significant effect on the PASC’s performance. While F’s fairness concerns can enhance their utility to some extent, it ultimately leads to more significant profit losses for both parties. (4) The proposed mixed cost-sharing and revenue-sharing contract can effectively align members’ incentives, enhancing profitability for both parties.

1. Introduction

Poverty remains one of the most pressing global challenges, making its alleviation a critical priority worldwide [1]. According to data from the United Nations Development Programme, 1.1 billion people are still living in poverty1. As the largest developing country in the world, China eliminated extreme poverty in 2020 through government investment, encouraging enterprises to participate in poverty alleviation and actively taking on social responsibility [2]. However, China will remain in relative poverty for the foreseeable future [3]. Thus, poverty alleviation will continue to be one of the key tasks of the Chinese government.

As poverty shifts from extreme to relative poverty, China’s poverty alleviation work has exposed many problems. Production in China’s poor areas and areas emerging from poverty is dominated by primary agricultural products, with low industrialization, imperfect product branding, weak and fragile poverty alleviation supply chains (PASCs), and a lack of competitive advantages. An effective approach is to establish branding of poverty alleviation products. For example, Apple Inc. created branded agricultural goods, such as kiwi and tea, in Sichuan Province, China, to help build a sustainable poverty alleviation model [4]. Another noteworthy example of poverty alleviation through branding is China Baifeng Trade Co. Ltd.’s creation of the famous brand, JD Chestnut, in Hebei Province, which established a development-oriented industrial poverty alleviation model2. Our work is motivated by the poverty alleviation branding practice of the Chinese government and companies.

However, poverty alleviation enterprises face many branding problems, such as insufficient funds and inadequate branding efforts. Thus, external support is needed to stimulate the intrinsic motivation of leading enterprises. Based on the experience of global poverty governance, government intervention has been widely used to regulate resource allocation. For example, in 2018, China’s Ministry of Agriculture and Rural Affairs introduced the “Strengthening Agriculture and Benefiting Agriculture Policy” to encourage leading enterprises to help farmers’ cooperatives, family farms, and other industrial poverty alleviation targets to develop advantageous and characteristic industries3. In 2021, the Ministry issued the “Priority and Preferential Support Policies for the Development of Agricultural Products Processing Enterprises”, supporting more than 220 leading enterprises in poverty-removing regions to implement brand construction4. Given the effectiveness and existential challenges of branding discussed above, we examine the role of corporate social responsibility (CSR) and brand building in the context of government subsidies for poverty alleviation enterprises.

Research and practice have identified inherent defects in the PASC. First, people living in poverty who are suppliers (i.e., farmers’ cooperatives, family farms, and other industrial poverty alleviation targets; hereafter, poor suppliers) often relinquish their rights to price their products, making them dominated by leading enterprises [5]. Second, poor suppliers may be subjected to unfair contracts when negotiating with leading enterprises, which can place a significant financial burden on them [5,6]. Finally, a poorly functioning contract farming system may allow leading enterprises to snatch most benefits [5,7]. A representative example is that in 2011, Shandong Liuhe Group Co. Ltd. leveraged its power advantage to absorb most of the benefits of the alleviation–poverty relationship with chicken farmers. Eventually, the farmers terminated their contracts [6]. Thus, poor suppliers in a vulnerable position in the PASC have sufficient motivation to consider fairness concerns. Driven by fairness concerns, poor suppliers aim to obtain appropriate returns for their production efforts rather than fixed returns. In the process of brand construction in the PASC, the investment in the production efforts of poor suppliers (e.g., technological upgrades, quality standardization protocols) and the investment in the brand construction of leading enterprises collectively shape market dynamics and influence the profits of all PASC participants. As poverty alleviation efforts continue, the contributions from both parties may also be evolving. To systematically model these complex interactions, we employ a Nash bargaining fairness framework to characterize the fairness concerns of poor suppliers.

This paper studies a PASC composed of a leading enterprise who undertakes CSR and brand construction and a poor supplier who carries out their production under government subsidies, taking goodwill and consumer-perceived value as the carrier. The supplier, who is in a follower position, has fairness concerns. Three decision-making models are established: two decentralized models without and with Nash bargaining fairness concerns and a centralized model. The impacts of fairness concerns on the optimal decisions and profits of both parties in the PASC are studied. After comparing the equilibrium results of these models, we propose a coordination mechanism to coordinate the PASC. This paper aims to answer the following questions:

(1)

What are the equilibrium decisions in differential game models?

(2)

How do Nash’s bargaining fairness concerns affect these equilibrium decisions?

(3)

How is a coordination mechanism designed to coordinate the Nash bargaining fairness concerns and improve PASC performance?

By answering the above questions, our work makes the following contributions:

First, this paper investigates how PASCs can build sustainable models through branding under government subsidies. Related studies [6,8] have studied the fairness concerns of poverty alleviation supply chains, but not in the context of branding. Therefore, this paper contributes to the literature on poverty alleviation. We provide new insights into how a leading enterprise adjusts optimal brand construction levels in response to government subsidies and the fairness concerns of poor suppliers in the poverty alleviation literature.

Second, this paper examines the impact of the supplier’s fairness concerns and bargaining power on PASC decisions and profits. Related studies [9,10,11] studied the impact of members’ fairness concerns on optimal decisions in coordinated supply chains but did not study the case in which members have bargaining power. Therefore, this paper complements research on the coordination of fairness concerns by examining Nash bargaining fairness concerns in the PASC. The results show that poor suppliers’ fairness concerns do not affect leading enterprises’ decisions but only decrease their production levels. Although the Nash bargaining fairness concerns can improve the utility of poor suppliers to a certain extent, fairness concerns will aggravate the double marginal effect of the PASC channel as suppliers’ bargaining power increases.

Third, we provide a coordination mechanism by a mixed cost-sharing and revenue-sharing contract to achieve long-term poverty reduction. Under certain conditions, this contract can transform poor suppliers’ Nash bargaining fairness concerns into the endogenous motivation to eliminate poverty and achieve coordination in the PASC.

The remainder of this paper is organized as follows: Section 2 reviews the related literature. Section 3 describes the model formulation. Section 4 analyzes different decision-making models and proposes a contract to coordinate the decentralized channel. Section 5 conducts a numerical analysis and discusses the results. Section 6 extends the model to discuss endogenous government subsidies and price decisions. Section 7 concludes the paper with a discussion of future work and presents managerial implications.

2. Literature Review

This section reviews relevant studies from three research streams: poverty alleviation, ingredient branding, and supply chain coordination with fairness concerns.

2.1. Poverty Alleviation

Our work builds on and contributes to poverty alleviation research. Poverty is a political, economic, and social issue. Governments and businesses must help people living in poverty break the cycle of poverty and become consumers in emerging markets [12].

Sodhi and Tang [13] reported that people living in poverty are embedded in the supply chain as suppliers or distributors to alleviate poverty and provided some seed models for supply chain poverty alleviation. Thereafter, many poverty alleviation studies have been published. Kang et al. [14] examined poverty alleviation practices in green supply chains. Specifically, manufacturers initiate the “greening” of products and provide microcredit to alleviate the financial constraints of poor raw material suppliers. They also analyzed the impact of cooperative mechanisms on supply chain members’ decisions and profits and offered a two-part pricing contract to improve supply chain profits. Shan and Yang [15] analyzed the behavioral evolution strategies of photovoltaic companies, poverty-stricken households, and the government in the context of the new energy industry. They demonstrated that a small amount of government supervision and performance subsidies can achieve a reasonable distribution of profits among members and ensure the sustainability of poverty alleviation measures. Kang et al. [8] studied the impact of government subsidies and CSR on poverty alleviation actions. The results showed that in most cases, the most effective mechanism for poverty alleviation combines government subsidies and market efforts. Wan and Qie [16] used the evolutionary game model to analyze the poverty alleviation model of intelligent supply chains under government financial subsidies. They suggested the transformation from blood transfusion-based poverty alleviation to hematopoietic poverty alleviation. Kang, Wang, and Luan [6] investigated the fairness concerns of poverty alleviation supply chains and gave an effective threshold range for government subsidies.

Our study is closely related to that of Kang, Wang, and Luan [6] but is also different in several important aspects. First, we focus on the long-term nature of poverty alleviation and branding, considering changes in enterprise goodwill and consumers’ perceived value of products. Second, we consider the contributions of both parties when portraying fairness concerns, which they did not consider.

2.2. Ingredient Branding

Our work also contributes to research on ingredient branding. In marketing theory, ingredient branding is defined as a strategy to enhance products’ value by highlighting their key components [17]. Norris [18] categorized ingredient branding motivations into improving consumer evaluation and creating brand recognition. Luczak [19] integrated these two motivations and proposed a new concept of ingredient branding. Intel’s success is a classic example of this concept in action [20]. Empirical research has validated the effectiveness of ingredient branding in improving market competitiveness through market research, statistical analyses, and experiments. Through market investigation, Helm and Özergin [21] researched intangible products’ branding and analyzed the internal relationship between customer preferences and services. Their results showed that brands can increase consumers’ willingness to buy and improve the competitiveness of products in the business-to-business market. Kanama and Nakazawa [22] conducted analyses on the effect of ingredient branding of foods in Japan. They found that branded products have higher sales volumes in the beverage market, with the agricultural product market showing a similar trend. Koschmann and Bowman [23] investigated the synergy between primary and secondary brands using market survey data on ingredient brand alliances. They proved the positive effect of component brands on alliance performance.

A few theoretical studies have studied branding from the perspective of operations management. Zhang et al. [24] constructed a secondary supply chain model composed of original equipment manufacturers and original equipment suppliers. They utilized a differential game model to study the suppliers’ ingredient branding strategy and their advertising cooperation with manufacturers. Additionally, they designed a contract aimed at achieving coordination within the supply chain.

From the quantitative and qualitative perspectives, these studies prove the role of brands in improving the competitiveness of the product market and provide a reference for our work to research brand construction in the PASC. To fill the research gap in branding for poverty alleviation, we employ a modeling method to analyze the PASC branding strategy and provide a methodology for implementing the PASC’s branding strategy to achieve long-term poverty reduction.

2.3. Coordination of Supply Chains with Fairness Concerns

This study is also closely related to the coordination of supply chains with fairness concerns. Cui, Raju, and Zhang [25] conducted a seminal study in this area. They considered others’ profit multiples as an outcome of fairness (without considering members’ bargaining power) and showed that wholesale price contracts could achieve supply chain coordination under certain conditions. Demirag, Chen, and Li [26] extended the research by Cui, Raju, and Zhang [25], showing that supply chain coordination is easier to achieve under an exponential demand function. Yang et al. [27] studied manufacturer–retailer advertising cooperation with fairness concerns and found that advertising cooperation can achieve supply chain coordination under certain conditions when unilateral fairness concerns exist. Nie and Du [9] studied the coordination between two fairness-concerned retailers and fairness-neutral manufacturers. They showed that combining a quantity discount contract and fixed fees could enable supply chain coordination. Niederhoff and Kouvelis [28] and Wang et al. [10] proposed revenue-sharing contracts and “cost-sharing joint commission” contracts to coordinate supply chains with fairness concerns. Hu et al. [11] investigated the impact of fairness concerns on decisions in a two-tier green supply chain in which the manufacturer and the retailer make green marketing efforts. The aforementioned coordinated research on fairness concerns does not consider the bargaining power of supply chain members. Du et al. [29] found that ordinary contracts do not coordinate the channels through which members have Nash bargaining fairness concerns.

The study by Guan, Ye, and Yin [30] is one of the first and few to examine the coordination of members with Nash bargaining fairness concerns. Their results show that a revenue- and cost-sharing contracts can coordinate conventional dyadic channels under certain conditions. Different from the Guan, Ye, and Yin’s [30] study, in a PASC, poor suppliers lose their pricing power. It is unclear how a PACS will be coordinated based on consideration of members’ bargaining power. This study complements research on the coordination of fairness concerns by examining the Nash bargaining fairness concerns in the PASC.

3. Model Formulation

Brand construction in the PASC is a time accumulation process of a joint investment by the leading enterprise (E, as the leader) and the poor supplier (F, as the follower) under government subsidies. We constructed a PASC model composed of E (referring to the enterprises that undertake CSR by incorporating the F into the supply chain and conducting brand construction) and F (referring to family farms, farmer cooperatives, or small agricultural organizations) under government subsidies. Specifically, F relies on local natural resources to grow agricultural products, and E is responsible for product purchase, brand construction, and product sales in the terminal market. We defined the production efforts level of F as $e_f(t)$ (interpreted as F purchasing new production equipment and planting technologies to improve the product quality and as F’s poverty elimination enthusiasm level), corresponding to its cost: $e_f^2(t)$. This definition is also widely used in operations management and marketing [5,24]. E undertakes CSR by including F in their supply chains, which can create economic value for the poor suppliers and enterprises [2,31]. To capture E’s CSR level, we define $e_r(t)$ to measure the CSR level and the associated cost $e_r^2(t)$ [6,32]. Focusing on the brand construction of E, we define $e_a(t)$ as the brand construction level (e.g., processing and publicity of agricultural products through investments in technology to improve the quality and popularity of agricultural products) and the corresponding cost $e_a^2(t)$ [33,34]. The government provides ${\epsilon }_1$ subsidies for F’s production efforts and ${\epsilon }_2$ subsidies for E’s brand construction level. These subsidies are designed to alleviate F’s production pressure and encourage E to invest in brand construction. Figure 1 shows the PASC structure.

Following Chintagunta [35]; Chakraborty, Chauhan, and Ouhimmou [34]; and Guan, Ye, and Yin [30], we modeled the demand level at time $t$, which depends on the consumer-perceived value and goodwill, as follows:

$$D(t)=\eta e(t)+\gamma s(t)$$

(1)

where $\eta$ and $\gamma$ represent the impact efficiency of consumer-perceived value and goodwill on market demand, respectively. The concept of goodwill captures two important facts. First, increasing customers’ awareness of the leading enterprise branding image takes time. Second, the supply chain members will consider their decisions’ current and future impacts on goodwill. Based on previous studies [36,37,38,39], we made the assumptions described below for our model.

Assumption 1. 

We modified the classic model by Nerlove and Arrow [36] to capture the impact of CSR and brand construction levels on goodwill as follows:

$$\stackrel{•}{s}(t)=\alpha e_r(t)+\beta e_a(t)-\sigma s(t), s(0)=s_0$$

(2)

where $s(t)$ denotes the accumulated goodwill of E over time $t$; $\alpha \ge 0$ measures the efficiency of CSR; $\beta \ge 0$ represents the efficiency of brand construction; and $\sigma \ge 0$ represents the diminishing level of goodwill due to consumers’ forgetful behavior, and $s_0$ is the initial goodwill.

Additionally, the consumer-perceived value of a product is a measure that accumulates over time. On the one hand, this perceived value is affected by the product’s branding. On the other hand, it is also affected by the level of production efforts, i.e., on F improving the quality of their products through production efforts.

Assumption 2. 

Following the study by Ma, Hu, and Yao [40], we assumed that the consumer-perceived value model is given by

$$\stackrel{•}{e}(t)=\lambda e_f(t)+\mu e_a(t)-\delta e(t), e(0)=e_0$$

(3)

where $\lambda$ and $\mu$ represent the strength of the impacts of production efforts and brand construction on the consumer-perceived value. $\delta \ge 0$ represents the diminishing level of consumer-perceived value that is attributable to consumers’ forgetful behavior, and $e_0$ is the initial consumer-perceived value of the product.

To focus more clearly on the brand construction studied in our work, we did not consider members’ pricing decisions in the main models and conducted research on endogenous price decisions in Section 6.2. ${\pi }_f$ and ${\pi }_e$ represent the marginal revenue per unit product of F and E, respectively. F, E, and the entire channel’s profit functions are, respectively, expressed as follows:

$$\begin{array}{l}{\mathrm{\Pi }}_F(t)={\pi }_{f}D(t)-(1-{\epsilon }_1)e_f^2(t)\\ {\mathrm{\Pi }}_E(t)={\pi }_{e}D(t)-(1-{\epsilon }_2)e_a^2(t)-e_r^2(t)\\ {\mathrm{\Pi }}_{SC}(t)=({\pi }_f+{\pi }_e)D(t)-(1-{\epsilon }_2)e_a^2(t)-e_r^2(t)\end{array}$$

(4)

4. Decision-Making Model Analysis

In this section, we analyze and compare the equilibrium results of decentralized models, both with and without Nash bargaining fairness concerns, against those of the centralized model. We further propose a mixed cost-sharing and revenue-sharing contract to coordinate the decentralized channel effectively.

4.1. Decentralized Model (Fairness-Neutral)

First, we establish a benchmark model (Model A), a fairness-neutral decentralized model under government subsidies, as a decision-making benchmark to assess the supplier’s Nash bargaining fairness concerns. In this model, both parties play a Stackelberg game over an infinite time horizon, with E as the leader, and make independent decisions to maximize their own profits. E decides the CSR and brand construction levels, and F decides the production effort level. Both F and E have the same discount coefficient, $\rho$. Then, the decision functions of F and E can be formulated as follows:

$$\left\{\begin{array}{l}\underset{e_r(t), e_a(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}{\mathrm{\Pi }}_E}{{\displaystyle |}}_{e_f(t)=e_f^{NG*}(t)}dt\\ e_f^{NG*}(t) are derived from solving the following problem\\ \underset{e_f(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}{\mathrm{\Pi }}_F(t)}dt\\ s.t.\left\{\begin{array}{l}\stackrel{•}{s}(t)=\alpha e_r(t)+\beta e_a(t)-\sigma s(t), s(0)=s_0\\ \stackrel{•}{e}(t)=\lambda e_f(t)+\mu e_r(t)-\delta e(t), e(0)=e_0\end{array}\right.\end{array}\right.$$

(5)

Lemma 1. 

In Model A, the equilibrium results of production effort, CSR, and brand construction are as follows:

$$e_r^{NG*}={\displaystyle \frac{{\pi }_e\gamma \alpha }{2(\rho +\sigma )}}, e_f^{NG*}={\displaystyle \frac{{\pi }_f\eta \lambda }{2(\delta +\rho )(1-{\epsilon }_1)}}, e_a^{NG*}={\displaystyle \frac{{\pi }_e(\beta \delta \gamma +\beta \gamma \rho +\eta \mu \rho +\eta \mu \sigma )}{2(1-{\epsilon }_2)(\rho +\sigma )(\delta +\rho )}}$$

(6)

Meanwhile, the trajectory for goodwill and consumer-perceived value are as follows:

$$\begin{array}{l}{s}^{NG*}(t)=(s_0-s_{\infty }^{NG})e^{-\sigma t}+s_{\infty }^{NG}, \\ e^{NG*}(t)=(e_0-e_{\infty }^{NG})e^{-\delta t}+e_{\infty }^{NG},\end{array}$$

(7)

and the present values of the monetary profits of F, E, and the entire channels are

$$\begin{array}{c}{V}_f^{NG*}(s_0,e_0)={\displaystyle \frac{{\pi }_f\gamma }{\rho +\sigma }}{s}_0+{\displaystyle \frac{{\pi }_f\eta }{\delta +\rho }}{e}_0+m_3^{NG}, \\ V_e^{NG*}(s_0,e_0)={\displaystyle \frac{{\pi }_e\gamma }{\rho +\sigma }}{s}_0+{\displaystyle \frac{{\pi }_e\eta }{\delta +\rho }}{e}_0+n_3^{NG}, \\ V_{SC}^{NG*}(s_0,e_0)={\displaystyle \frac{({\pi }_e+{\pi }_f)\gamma }{\rho +\sigma }}{s}_0+{\displaystyle \frac{({\pi }_e+{\pi }_f)\eta }{\delta +\rho }}{e}_0+n_3^{NG}+m_3^{NG},\end{array}$$

(8)

where $s_{\infty }^{NG}$ and $e_{\infty }^{NG}$, respectively, denote the steady state of accumulated goodwill and consumer-perceived value, with $m_3^{NG}$ and $n_3^{NG}$ representing a set of parameters. Because the parameters ($s_{\infty }^{NG}$, $e_{\infty }^{NG}$, $m_3^{NG}$, $n_3^{NG}$) are lengthy, detailed expressions of the parameters and all proofs are shown in the Supplementary File. From Lemma 1, we can observe that both the equilibrium results for production effort and brand construction increase with higher government subsidy amounts, while CSR remains independent of subsidies. This result also holds in the decentralized model with Nash bargaining fairness concerns and the centralized model under government subsidies (see Lemmas 3 and 4). This is because these subsidies are designed to alleviate the production pressure of F and encourage E to invest in brand building. We can also obtain the equilibrium results of the model without government subsidies, as stated in Lemma 2.

Lemma 2. 

In Model A, given that ${\epsilon }_1=0$ and  ${\epsilon }_2=0$, we obtain the equilibrium results of the model without government subsidies as follows:

$$e_r^{N*}={\displaystyle \frac{{\pi }_e\gamma \alpha }{2(\rho +\sigma )}}, e_f^{N*}={\displaystyle \frac{{\pi }_f\eta \lambda }{2(\delta +\rho )}}, e_a^{N*}={\displaystyle \frac{{\pi }_e(\beta \delta \gamma +\beta \gamma \rho +\eta \mu \rho +\eta \mu \sigma )}{2(\rho +\sigma )(\delta +\rho )}}$$

(9)

Meanwhile, the trajectories for goodwill and consumer-perceived value are

$$\begin{array}{l}{s}^{N*}(t)=(s_0-s_{\infty }^N)e^{-\sigma t}+s_{\infty }^N, \\ e^{N*}(t)=(e_0-e_{\infty }^N)e^{-\delta t}+e_{\infty }^N,\end{array}$$

(10)

and the present values of the monetary profits of F, E, and the entire channel are

$$\begin{array}{c}{V}_f^{N*}(s_0,e_0)={\displaystyle \frac{{\pi }_f\gamma }{\rho +\sigma }}{s}_0+{\displaystyle \frac{{\pi }_f\eta }{\delta +\rho }}{e}_0+m_3^N, \\ V_e^{N*}(s_0,e_0)={\displaystyle \frac{{\pi }_e\gamma }{\rho +\sigma }}{s}_0+{\displaystyle \frac{{\pi }_e\eta }{\delta +\rho }}{e}_0+n_3^N, \\ V_{SC}^{N*}(s_0,e_0)={\displaystyle \frac{({\pi }_e+{\pi }_f)\gamma }{\rho +\sigma }}{s}_0+{\displaystyle \frac{({\pi }_e+{\pi }_f)\eta }{\delta +\rho }}{e}_0+n_3^N+m_3^N.\end{array}$$

(11)

where $s_{\infty }^N$ and $e_{\infty }^N$ denote the steady state of accumulated goodwill and consumer-perceived value, respectively, with $m_3^N$ and $n_3^N$ representing a set of parameters. The detailed expressions of the parameters ($m_3^N$, $n_3^N$) are shown in the Supplementary Materials.

Proposition 1. 

(i) $e_r^{NG*}=e_r^{N*}$, $e_f^{NG*}>e_f^{N*}$, $e_a^{NG*}>e_a^{N*}$; (ii) $s^{NG*}>s^{N*}$, $e^{NG*}>e^{N*}$; (iii) $V_f^{NG*}(s_0, e_0)>V_f^{N*}(s_0, e_0)$, $V_e^{NG*}(s_0, e_0)>V_e^{N*}(s_0, e_0)$, $V_{SC}^{NG*}(s_0, e_0)>V_{SC}^{N*}(s_0, e_0)$.

Proposition 1 shows that government subsidies can effectively improve the production effort level of F and the brand construction level of E and improve the PASC performance. A study by Kang et al. [8] also verified this result. One may intuitively think that when the government subsidizes the branding efforts of E, it may create a synergistic effect to improve the CSR level. However, Lemma 1 and Proposition 1 show that government subsidies do not affect the CSR level but only increase E’s brand construction level, indicating that synergistic effects do not exist. The government can improve production efforts and brand construction through subsidies, thereby improving consumer-perceived value and goodwill and enhancing market demand. In practice, E needs to explore an appropriate CSR-sharing mechanism to improve their CSR level and enhance the performance of the PASC further.

4.2. Decentralized Model (Fairness-Concerned)

In this section, we establish a decentralized model with Nash bargaining fairness concerns under government subsidies (Model B) to examine the impact of the Nash bargaining fairness concerns of F in the branding process of the PASC. Fairness concerns have been extensively studied in a conventional dyadic channel as a behavioral factor affecting member decisions. Fehr and Schmidt [41] were the first to incorporate fairness concerns into operations management. Cui, Raju, and Zhang [25] integrated fairness concerns in the functional model in the context of supply chains. Subsequently, fairness concerns in supply chains have been studied extensively [42,43,44]. Du et al. [29] extended the research of Cui, Raju, and Zhang [25] by considering members’ power and contribution endogenously, proposing a Nash bargaining fairness concerns framework. In this paper, we adopt the Nash fairness concerns model of Du et al. [29] to describe the linear utility function of PASC members:

$$\begin{array}{l}{U}_f(t)={\mathrm{\Pi }}_F(t)+h_f\left[{\mathrm{\Pi }}_F(t)-{\overline{\mathrm{\Pi }}}_F(t)\right], \\ U_e(t)={\mathrm{\Pi }}_E(t)+h_e\left[{\mathrm{\Pi }}_E(t)-{\overline{\mathrm{\Pi }}}_E(t)\right],\end{array}$$

(12)

where $h_f$ and $h_e$ denote the level of fairness concerns of F and E, respectively; ${\mathrm{\Pi }}_F(t)$ and ${\mathrm{\Pi }}_E(t)$ denote the F and E profit functions, respectively; and ${\overline{\mathrm{\Pi }}}_F(t)$ and ${\overline{\mathrm{\Pi }}}_E(t)$ denote the fairness reference point of F and E, respectively. The reference point denotes each player’s psychological expectation that each player admits after considering their power and contribution endogenously. Thus, it should satisfy the Pareto efficiency axiom. Therefore, ${\overline{\mathrm{\Pi }}}_F(t)+{\overline{\mathrm{\Pi }}}_E(t)={\mathrm{\Pi }}_F(t)+{\mathrm{\Pi }}_E(t)={\mathrm{\Pi }}_{SC}(t)$ [9,10,29,30]. Based on the existing literature [7,30,45,46], the Nash bargaining solutions ${\overline{\mathrm{\Pi }}}_F(t)$ and ${\overline{\mathrm{\Pi }}}_E(t)$ are derived by maximizing the following model:

$$\begin{array}{c}\underset{{\mathrm{\Pi }}_f(t), {\mathrm{\Pi }}_e(t)}{\max }{U}_f^M(t)U_e^{1-M}(t)\\ s.t.\left\{\begin{array}{l}{\overline{\mathrm{\Pi }}}_F(t)+{\overline{\mathrm{\Pi }}}_E(t)={\mathrm{\Pi }}_{SC}(t)\\ {\mathrm{\Pi }}_F(t)+{\mathrm{\Pi }}_E(t)={\mathrm{\Pi }}_{SC}(t)\\ {\mathrm{\Pi }}_F(t)>0, {\mathrm{\Pi }}_E(t)>0\end{array}\right.\end{array}$$

(13)

where $M$ and $(1-M)$ denote the bargaining power of F and E, respectively. Subsequently, we can derive the Nash bargaining solutions as follows:

$$\left\{\begin{array}{l}{\overline{\mathrm{\Pi }}}_F(t)={\displaystyle \frac{M(1+h_f)}{1+M(h_f-h_e)+h_e}}{\mathrm{\Pi }}_{SC}(t)\\ {\overline{\mathrm{\Pi }}}_E(t)={\displaystyle \frac{(1-M)(1+h_e)}{1+M(h_f-h_e)+h_e}}{\mathrm{\Pi }}_{SC}(t)\end{array}\right.$$

(14)

In the Introduction, we explained the fairness concerns regarding F’s weaker position in the PASC branding process, as achieving a return on their contributions is challenging. Given that poor suppliers are in vulnerable positions in the PASC, we only consider the fairness concerns of F, i.e., $h_e=0$. Let $N$ denote F’s fairness concerns level ($N=h_f$); then, the linear utility function for both sides can be simplified as follows:

$$\left\{\begin{array}{l}{U}_f(t)={\displaystyle \frac{1+N}{1+MN}}{\mathrm{\Pi }}_F(t)-{\displaystyle \frac{MN(1+N)}{1+MN}}{\mathrm{\Pi }}_E(t)\\ U_e(t)={\mathrm{\Pi }}_E(t)\end{array}\right.$$

(15)

Then, the decision functions of F and E can be formulated as

$$\left\{\begin{array}{l}\underset{e_r(t), e_a(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}{\mathrm{\Pi }}_E}{{\displaystyle |}}_{e_f(t)=e_f^{FG*}(t)}dt\\ e_f^{FG*}(t) are derived from solving the following problem\\ \underset{e_f(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}\left\{(\frac{1+N}{1+NM}){\mathrm{\Pi }}_F-(\frac{MN(1+N)}{1+MN}){\mathrm{\Pi }}_E\right\}}dt\\ s.t.\left\{\begin{array}{l}\stackrel{•}{s}(t)=\alpha e_r(t)+\beta e_a(t)-\sigma s(t), s(0)=s_0\\ \stackrel{•}{e}(t)=\lambda e_f(t)+\mu e_r(t)-\delta e(t), e(0)=e_0\end{array}\right.\end{array}\right.$$

(16)

Lemma 3. 

In Model B, the equilibrium results of production efforts, CSR, and brand construction are as follows:

$$e_r^{FG*}={\displaystyle \frac{{\pi }_e\gamma \alpha }{2(\rho +\sigma )}}, e_f^{FG*}={\displaystyle \frac{({\pi }_f-{\pi }_{e}MN)\eta \lambda }{2(1-{\epsilon }_1)(\delta +\rho )}}, e_a^{FG*}={\displaystyle \frac{{\pi }_e(\beta \delta \gamma +\beta \gamma \rho +\eta \mu \rho +\eta \mu \sigma )}{2(\rho +\sigma )(\delta +\rho )(1-{\epsilon }_2)}}$$

(17)

While the trajectories for goodwill and consumer-perceived value are

$$\begin{array}{l}{s}^{FG*}(t)=(s_0-s_{\infty }^{FG})e^{-\sigma t}+s_{\infty }^{FG}, \\ e^{FG*}(t)=(e_0-e_{\infty }^{FG})e^{-\delta t}+e_{\infty }^{FG},\end{array}$$

(18)

and the present values of the utilities of F, E, and entire channel are

$$\begin{array}{l}{V}_{Uf}^{FG*}(s_0,e_0)=({\displaystyle \frac{1+N}{1+MN}}){\displaystyle \frac{({\pi }_f-{\pi }_{e}MN)\gamma }{\rho +\sigma }}{s}_0+({\displaystyle \frac{1+N}{1+MN}}){\displaystyle \frac{({\pi }_f-{\pi }_{e}MN)\eta }{\delta +\rho }}{e}_0+m_{U3}^{FG}, \\ V_{Ue}^{FG*}(s_0,e_0)={\displaystyle \frac{{\pi }_e\gamma }{(\rho +\sigma )}}{s}_0+{\displaystyle \frac{{\pi }_e\eta }{(\delta +\rho )}}{e}_0+n_3^{FG}, \\ V_{USC}^{FG*}(s_0,e_0)=\left[{\displaystyle \frac{({\pi }_f+{\pi }_e+{\pi }_{f}N-{\pi }_{e}M{N}^2)\gamma }{(1+MN)(\rho +\sigma )}}\right]s_0+\left[{\displaystyle \frac{({\pi }_f+{\pi }_e+{\pi }_{f}N-{\pi }_{e}M{N}^2)\eta }{(1+MN)(\delta +\rho )}}\right]e_0+m_{U3}^{FG}+n_3^{FG},\end{array}$$

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Further, the present values of the monetary profits of F, E, and the entire channel are

$$\begin{array}{l}{V}_e^{FG*}(s_0,e_0)={\displaystyle \frac{{\pi }_e\gamma }{(\rho +\sigma )}}{s}_0+{\displaystyle \frac{{\pi }_e\eta }{(\delta +\rho )}}{e}_0+n_3^{FG}\\ V_f^{FG*}(s_0,e_0)={\displaystyle \frac{{\pi }_f\gamma }{\rho +\sigma }}{s}_0+{\displaystyle \frac{{\pi }_f\eta }{\delta +\rho }}{e}_0+m_3^{FG}\\ V_{SC}^{FG*}(s_0,e_0)={\displaystyle \frac{({\pi }_f+{\pi }_e)\gamma }{(\rho +\sigma )}}{s}_0+{\displaystyle \frac{({\pi }_f+{\pi }_e)\eta }{(\delta +\rho )}}{e}_0+m_3^{FG}+n_3^{FG}\end{array}$$

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where $s_{\infty }^{FG}$ and $e_{\infty }^{FG}$ denote the steady state of accumulated goodwill and consumer-perceived value, while $m_3^{FG}$, $n_3^{FG}$, $m_{U3}^{FG}$, and $n_{U3}^{FG}$ represent a set of parameters, the detailed expressions of which are shown in the Supplementary Materials.

Proposition 2. 

$e_r^{FG*}$ and $e_a^{FG*}$ are independent of $N$, while $e_f^{FG*}$ decreases with $N$.

Extant research demonstrates that in a conventional dyadic channel, fairness concerns can affect the decision-making of supply chain members [25,47,48,49]. In contrast, Proposition 2 shows that in the branding process of the PASC, the Nash bargaining fairness concerns of F only reduce their production effort level but do not affect the brand construction and CSR levels of E. The possible reasons for this result are, firstly, that government interventions in PASCs through subsidies can effectively eliminate the marginal effect of Nash bargaining fairness concerns on the decision-making of E, thus keeping E’s decisions unchanged. Secondly, despite F having Nash bargaining fairness concerns, E is the leader in the PASC and may not change their decision-making due to E’s decision on the purchase price of F’s products (i.e., F loses the pricing power of their products). In the branding process of the PASC, E needs to ensure that the marginal returns for both parties are rational. To achieve this, E should design a corresponding cost-sharing mechanism to share the cost of F’s planting effort and reduce the motivation behind F’s fairness concerns, thereby improving the level of F’s production efforts. Next, we analyze the impact of Nash bargaining fairness concerns on goodwill, consumer-perceived value, and the present monetary values of F and E. The result is shown in Proposition 3.

Proposition 3. 

(i) $s^{FG*}$ is independent of $N$, while $e^{FG*}$ decreases with $N$; (ii) $V_f^{FG*}(s_0,e_0)$ and $V_e^{FG*}(s_0, e_0)$ decrease with $N$.

Based on Proposition 2, F’s Nash bargaining fairness concerns do not change E’s decision-making. Therefore, it does not affect E’s goodwill. Nash bargaining fairness concerns reduce the level of production effort and affect the consumer-perceived value, thus further reducing demand. The more F focuses on fairness concerns, the more significant the effects on demand are. Ultimately, as demand declines, the profitability also diminishes for both parties. Note that when F exhibits Nash bargaining fairness concerns, the degree of its influence on decisions and the profits of both members are no longer fixed but are influenced by F’s bargaining power ($M$). Along with the increase in $M$, F’s decision to reduce their production efforts level will be more aggressive (${\partial }^2{e}_f^{FG*}/\partial N\partial M<0$), expanding the double marginal effect of decentralized channels and further aggravating the loss of profits on both sides. It is foreseeable that with the improvement in the supplier’s bargaining power (i.e., their poverty level decreasing), Nash bargaining fairness concerns will gradually become an essential factor affecting the performance of the PASC. In practice, E needs to consider the dynamic impact of Nash bargaining fairness concerns and dynamically adjust the marginal revenue of both parties to ensure the reasonable distribution of profits between both sides, thereby reducing F’s motivation for fairness concerns and the double marginal effect that it brings.

4.3. Centralized Model

To measure the efficiency of a PASC, a centralized model (Model C) is proposed and used as a benchmark for the effectiveness of coordination contracts. In this model, E and F play a cooperative differential game over an infinite time horizon, aiming to maximize the total profit of the entire system. The decision function is formulated as

$$\left\{\begin{array}{l}\underset{e_f(t), e_r(t), e_a(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}\left[{\mathrm{\Pi }}_F(t)+{\mathrm{\Pi }}_E(t)\right]}dt\\ s.t.\left\{\begin{array}{l}\stackrel{•}{s}(t)=\alpha e_r(t)+\beta e_a(t)-\sigma s(t), s(0)=s_0\\ \stackrel{•}{e}(t)=\lambda e_f(t)+\mu e_r(t)-\delta e(t), e(0)=e_0\end{array}\right.\end{array}\right.$$

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Lemma 4. 

In Model C, the equilibrium results of production effort, CSR, and brand construction are as follows:

$$e_r^{CG*}(t)={\displaystyle \frac{({\pi }_e+{\pi }_f)\gamma \alpha }{2(\rho +\sigma )}}, e_f^{CG*}(t)={\displaystyle \frac{({\pi }_f+{\pi }_e)\eta \lambda }{2(\delta +\rho )(1-{\epsilon }_1)}}, e_a^{CG*}(t)={\displaystyle \frac{({\pi }_e+{\pi }_f)(\beta \delta \gamma +\beta \gamma \rho +\eta \mu \rho +\eta \mu \sigma )}{2(\rho +\sigma )(\delta +\rho )(1-{\epsilon }_2)}}$$

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Meanwhile, the trajectories for goodwill and consumer-perceived value are

$$\begin{array}{l}{s}^{CG*}(t)=(s_0-s_{\infty }^{CG})e^{-\sigma t}+s_{\infty }^{CG}, \\ e^{CG*}(t)=(e_0-e_{\infty }^{CG})e^{-\delta t}+e_{\infty }^{CG},\end{array}$$

(23)

and the present values of the monetary profit of the entire channel are

$$V_{SC}^{CG*}(s_0,e_0)={\displaystyle \frac{({\pi }_f+{\pi }_e)\gamma }{\rho +\sigma }}{s}_0+{\displaystyle \frac{({\pi }_f+{\pi }_e)\eta }{\delta +\rho }}{e}_0+h_3^{CG}$$

(24)

where $s_{\infty }^{CG}$ and $e_{\infty }^{CG}$, respectively, denote the steady state of accumulated goodwill and consumer-perceived value, while $h_3^{CG}$ represents a set of parameters ($s_{\infty }^{CG}$, $e_{\infty }^{CG}$, $h_3^{CG}$), the detailed expressions of which are shown in the Supplementary Materials.

4.4. Comparative Analysis

By comparing the equilibrium decisions, goodwill, and consumer-perceived value in different scenarios (Models A, B, C), we reached the following conclusion:

Conclusion 1. 

(1) $e_r^{NG*}=e_r^{FG*}<e_r^{CG*}$, $e_f^{FG*}<e_f^{NG*}<e_f^{CG*}$ , $e_a^{NG*}=e_a^{FG*}<e_a^{CG*}$ ;

(2) $s^{NG*}(t)=s^{FG*}(t)<s^{CG*}(t)$, $e^{FG*}(t)<e^{NG*}(t)<e^{CG*}(t)$;

(3) $V_f^{FG*}(s_0, e_0)<V_f^{NG*}(s_0, e_0)$, $V_e^{FG*}(s_0, e_0)<V_e^{NG*}(s_0, e_0)$,

$V_{SC}^{FG*}(s_0, e_0)<V_{SC}^{NG*}(s_0, e_0)<V_{SC}^{CG*}(s_0, e_0)$.

Conclusion 1 indicates that when Fs exhibit Nash bargaining fairness concerns, their production effort levels are always lower than when they are fairness-neutral. In the PASC, Fs lose the pricing power over their products and cannot ensure reasonable marginal benefits. As a result, Fs increase their utility by reducing their level of production efforts. The greater F’s concerns about fairness are, the more significant the reduction in effort will be. In the centralized model, both E and F aim at maximizing the overall monetary value of the PASC. They achieve this by establishing higher levels of brand construction, CSR, and production efforts, which enhance goodwill and the consumer-perceived value, ultimately boosting market demand. Furthermore, among the three scenarios, the centralized model is also the most profitable. Therefore, it is necessary for Es to design a reasonable contract mechanism that improves the decision-making level for both parties in the decentralized model, realizing Pareto improvements within the PASC.

4.5. Coordination Mechanism

To coordinate the decentralized channel with fairness concerns, many scholars have proposed various supply chain contracts, such as a quantity discount contract [9], a cost-sharing contract [30], a cost-sharing joint commission contract [10], a revenue-sharing contract [50], and a cost-sharing joint revenue-sharing contract [6]. In the previous analyses, we pointed out that Es need to design an appropriate mechanism to share the production effort costs of F and improve the level of CSR and brand construction. We referred to the “guarantee + share” method used by China Zhongxin Enterprise when establishing the “Pujiang Kiwifruit” brand, which essentially involves dynamically adjusting the marginal benefits for both parties. Additionally, we considered the cost-sharing contract designed by Kang, Wang, and Luan [6] in their poverty research. Based on these methods, we propose a mixed cost-sharing and revenue-sharing contract to coordinate the decentralized channel effectively. A successful case of adopting this contract is that the famous liquor brand Wuliangye helped poor farmers increase their income by co-building a dedicated grain base and sharing dividends.

In the mixed cost-sharing and revenue-sharing contract, we allow E to adjust the marginal revenue between both parties (${\pi }_f\to {\overline{\pi }}_f$, ${\pi }_e\to {\overline{\pi }}_e$) and share a part of the production costs of F (the ratio is ${\phi }_e$). Simultaneously, the contract requires F to share E’s costs of CSR and brand construction (the ratio is ${\phi }_f$) to improve the decision-making level of both parties. The decision functions are as follows:

$$\left\{\begin{array}{l}\underset{e_f(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}\left\{{\overline{\pi }}_{f}D(t)-(1-{\phi }_e)(1-{\epsilon }_1)e_f^2-{\phi }_f\left[(1-{\epsilon }_2)e_a^2+e_r^2\right]\right\}}dt\\ \underset{e_r(t),e_a(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}\left\{{\overline{\pi }}_{e}D(t)-(1-{\phi }_f)\left[(1-{\epsilon }_2)e_a^2+e_r^2\right]-{\phi }_e(1-{\epsilon }_1)e_f^2\right\}}{{\displaystyle |}}_{e_f(t)=e_f^{XFG*}(t)}dt\\ e_f^{XFG*}(t) are derived from solving the following problem\\ s.t.\left\{\begin{array}{l}\stackrel{•}{s}(t)=\alpha e_r(t)+\beta e_a(t)-\sigma s(t), s(0)=s_0\\ \stackrel{•}{e}(t)=\lambda e_f(t)+\mu e_r(t)-\delta e(t), e(0)=e_0\end{array}\right.\end{array}\right.$$

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Conclusion 2. 

The decentralized model can be coordinated through the mixed cost-sharing and revenue-sharing contract if the contract parameters satisfy the following conditions:

$$\begin{array}{l}{\phi }_f={\displaystyle \frac{{\overline{\pi }}_f}{{\pi }_f+{\pi }_e}}, {\phi }_e={\displaystyle \frac{{\overline{\pi }}_e}{{\pi }_f+{\pi }_e}}, \\ {\phi }_f+{\phi }_e=1, {\overline{\pi }}_e+{\overline{\pi }}_f={\pi }_f+{\pi }_e,\end{array}$$

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The corresponding present values of F and E’s profits are:

$$\left\{\begin{array}{l}{V}_f^{XG}(e_0,s_0)=\phi V_{SC}^{CG*}(e_0,s_0)\\ V_e^{XG}(e_0,s_0)=(1-\phi )V_{SC}^{CG*}(e_0,s_0)\end{array}\right.$$

(27)

where $\phi (0<\phi ={\phi }_f<1)$ represents the proportion of F in the total profit of the PASC after coordination, which depends on the strength and bargaining power of F. In the decentralized model with fairness concerns, both F and E accept the coordination mechanism, and they must ensure that the following conditions are satisfied:

$$\left\{\begin{array}{l}{V}_f^{XG*}(e_0,s_0)=\phi V_{SC}^{CG*}(e_0,s_0)\ge V_f^{FG*}(e_0,s_0)\\ V_e^{XG*}(e_0,s_0)=(1-\phi )V_{SC}^{CG*}(e_0,s_0)\ge V_e^{FG*}(e_0,s_0)\\ V_{Uf}^{XG*}(e_0,s_0)={\displaystyle \frac{(1+N)V_{SC}^{CG*}(e_0,s_0)}{1+MN}}\left[\left(1-MN\right)\phi -MN\right]\ge V_{Uf}^{FG*}(e_0,s_0)\end{array}\right.$$

(28)

Thus,

$${\displaystyle \frac{V_f^{FG*}(e_0,s_0)-MN{V}_e^{FG*}(e_0,s_0)}{(1+N)V_{SC}^{CG*}(e_0,s_0)}}+{\displaystyle \frac{MN}{1+MN}}\le \phi \le 1-{\displaystyle \frac{V_e^{FG*}(e_0,s_0)}{V_{SC}^{CG*}(e_0,s_0)}}$$

(29)

Further, we observe that $\phi$ is positively correlated with $N$. This implies that poor supplier profit will increase with any rise in the degree of Nash bargaining fairness concerns after coordination. In the decentralized model without fairness concerns, both F and E choose to accept the coordination mechanism when

$$\left\{\begin{array}{l}{V}_f^{XNG*}(e_0,s_0)=\phi V_{SC}^{CG*}(e_0,s_0)\ge V_f^{NG*}(e_0,s_0)\\ V_e^{XNG*}(e_0,s_0)=(1-\phi )V_{SC}^{CG*}(e_0,s_0)\ge V_e^{NG*}(e_0,s_0)\end{array}\right.$$

(30)

Thus,

$${\displaystyle \frac{V_f^{NG*}(e_0,s_0)}{V_{SC}^{CG*}(e_0,s_0)}}\le \phi \le 1-{\displaystyle \frac{V_e^{NG*}(e_0,s_0)}{V_{SC}^{CG*}(e_0,s_0)}}$$

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5. Numerical Analysis

In this section, we conduct a numerical analysis to illustrate the validity of the mixed cost-sharing and revenue-sharing contract and further gain management insights. Following existing studies [6,9,25,29,30], we consider parameters of $e_0=1$, $s_0=2$, $\rho =0.3$, $\alpha =0.4$, $\beta =0.3$, $\sigma =0.3$, $\lambda =0.4$, $\mu =0.3$, $\delta =0.3$, $\eta =0.5$, and $\gamma =0.5$. Let ${\epsilon }_1=0.3$, ${\epsilon }_2=0.2$, ${\pi }_f=0.2$, and ${\pi }_e=0.6$. According to the coordination threshold shown in Conclusion 2 under the decentralized model with fairness concerns, we have $\phi \in \left[{\phi }_{\min },{\phi }_{\max }\right]$, where ${\phi }_{\min }=(0.282MN+0.021M^2{N}^2+0.255)/(1+MN)$ and ${\phi }_{\max }=(0.282+0.041MN)$. By selecting ${\phi }_v=({\phi }_{f\min }+{\phi }_{f\max })/2$, we compare the present profit values and the utility values of pre-coordinated and post-coordinated supply chains by setting $M\in \left[0.1, 0.2\right]$ and $N\in \left[0, 1\right]$ as the independent variables. The results are shown in Figure 2 and Figure 3.

The results shown in Figure 2 and Figure 3 illustrate that the mixed cost-sharing and revenue-sharing contract can coordinate the decentralized channel effectively, thus achieving a “win–win” situation between the PASC members. In addition, we find that the larger the $N$ is, the higher the profit that F obtains after coordination is (see the left subfigure of Figure 2), implying that $N$ improves the profit threshold after F coordination. An interesting conclusion is that F does not increase its fairness concern levels indefinitely, because its utility is only increased in the non-green area depicted on the right side of Figure 3. We also observe that with the increase in $N$, the interval in which F obtained the utility increase from $N$ gradually narrowed. This finding also holds after coordination, meaning that appropriately raising the $M$ of F can effectively reduce its reliance on $N$. It also shows that when $M$ is small, F has a stronger motivation for improving its fairness concern levels, because it is easier to gain utility.

Next, we analyze other parameters’ effects on the coordination mechanism’s effectiveness. Under the parameter settings in Figure 2 and Figure 3, the relationship between the $\phi \in [{\phi }_{\min },{\phi }_{\max }]$ and $[M,N]$ is depicted in Figure 4. Figure 4 shows that as $M$ and $N$ increase, both the lower bound ${\phi }_{\min }$ and the upper bound ${\phi }_{\max }$ has become higher. Therefore, the increase of $M$ and $N$ is conducive to improving the profit after F coordination. In addition, the degree of change in the upper bound is more obvious than in the lower bound. This result shows that the double marginalization of $N$ has a more pronounced impact on E, and its degree of influence gradually increases with the increase of $M$ and $N$, which increases the negotiation space between E and F, and makes it easier for E and F to reach cooperation.

Let $M=0.2$, $N=0.3$, ${\pi }_e\in \left[0.55, 0.65\right]$, and ${\pi }_f+{\pi }_e=0.8$. Figure 5 illustrates the relationship between the $\phi \in [{\phi }_{\min },{\phi }_{\max }]$ and ${\pi }_e$. Figure 5 shows that the feasible condition of the coordination mechanism is negatively related to the marginal revenue (${\pi }_e$) of E, and the coordination interval increases with the increase in ${\pi }_e$. Combining this with Proposition 2, we come to an interesting conclusion. In general, an increase in ${\pi }_e$ will increase E’s profit. However, under the coordination mechanism, the increase in ${\pi }_e$ will reduce the proportion of branding and CSR costs that are shared by F, which in turn will increase the cost of E. In practice, the contract can improve the distribution of profits among members to a certain extent.

Let $M=0.2$, $N=0.3$, ${\pi }_f=0.2$, ${\pi }_e=0.6$, ${\epsilon }_1\in \left[0.25,0.35\right]$, and ${\epsilon }_2=\in \left[0.15,0.25\right]$. The relationship between the $\phi \in [{\phi }_{\min },{\phi }_{\max }]$ and $[{\epsilon }_1,{\epsilon }_2]$ is depicted in Figure 6. As can be seen from Figure 6, ${\phi }_{\min }$ is negatively correlated with ${\epsilon }_1$, and ${\phi }_{\max }$ is positively correlated with ${\epsilon }_1$. ${\phi }_{\min }$ and ${\phi }_{\max }$ are positively correlated with ${\epsilon }_2$. Appropriately increasing the proportion of government subsidies (${\epsilon }_1$) can reduce F’s fairness concern motivation to a certain extent. In addition, the size of the feasible interval $\left[{\phi }_{\min },{\phi }_{\max }\right]$ is positively correlated with ${\epsilon }_1$ and ${\epsilon }_2$. That is, with the increases in ${\epsilon }_1$ and ${\epsilon }_2$, the coordination interval increases. This means that the government can effectively promote cooperation between the two sides by increasing financial subsidies. However, more government subsidies are not always better, as they can increase the financial burden on the government. An appropriate subsidy approach is one that combines the marginal benefits of both parties (see the section Extensions).

6. Extensions

Our paper investigates the PASC’s performance with exogenous government subsidies and given marginal revenue. In this section, we further discuss the potential extensions of our problem setting, including endogenous government subsidies and sale price decisions.

6.1. Endogenous Government Subsidy

In this subsection, we relax the assumption of exogenous government subsidies and explore the optimal level of government subsidies in the fairness-neutral decentralized model. In the conventional supply chain, the objective function of government subsidies is often to maximize social welfare. The difference is that in the PASC brand construction process, government subsidies aim to improve the brand construction of E and the production efforts of F, thereby improving the market competitiveness of products. The government’s goal is to improve the efficiency of the PASC channel through financial subsidies. Thus, the government’s objective function is

$$\underset{{\epsilon }_1(t),{\epsilon }_2(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}}\left[{\mathrm{\Pi }}_F(t)+{\mathrm{\Pi }}_E(t)\right]dt$$

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In this scenario, the decision sequence in the PASC is as follows: First, the government decides the subsidy levels ${\epsilon }_1(t)$ for production efforts and ${\epsilon }_2(t)$ for brand construction. Second, E decides the level of CSR and brand construction. Third, F decides the level of production effort. The decision functions of the three parties are given by

$$\left\{\begin{array}{l}\underset{{\epsilon }_1(t),{\epsilon }_2(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}}\left[{\mathrm{\Pi }}_F(t)+{\mathrm{\Pi }}_E(t)\right]{{\displaystyle |}}_{e_f(t)=e_f^{EG*}(t), e_a(t)=e_a^{EG*}(t), e_r(t)=e_r^{EG*}(t)}dt\\ e_f^{EG*}(t), e_a^{EG*}(t), e_r^{EG*}(t) are derived from solving the following problem\\ \underset{e_r(t),e_a(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}}{\mathrm{\Pi }}_E(t){{\displaystyle |}}_{e_f(t)=e_f^{EG*}(t)}dt\\ e_f^{EG*}(t) are derived from solving the following problem\\ \underset{e_f(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}{\mathrm{\Pi }}_F(t)}dt\\ s.t.\left\{\begin{array}{l}\stackrel{•}{s}(t)=\alpha e_r(t)+\beta e_a(t)-\sigma s(t), s(0)=s_0\\ \stackrel{•}{e}(t)=\lambda e_f(t)+\mu e_r(t)-\delta e(t), e(0)=e_0\end{array}\right.\end{array}\right.$$

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Proposition 4. 

${\epsilon }_1^{EG*}$ increases with ${\pi }_e$ and decreases with ${\pi }_f$, while ${\epsilon }_2^{EG*}$ increases with ${\pi }_f$ and decreases with ${\pi }_e$.

Proposition 4 shows that the optimal level of government subsidies to F and E decreases as their marginal benefits increase, positively correlating to the marginal revenue of other supply chain members. In the case of endogenous government subsidies, E needs to increase F’s marginal revenue and avoid setting exploitative purchasing prices to obtain more subsidies. The method of providing subsidies combined with the marginal benefits of both parties can promote the reasonable distribution of profits among supply chain members to a certain extent, reduce the motivation of F’s fairness concerns, and ensure the sustainable operation of the poverty alleviation mechanism based on branding.

6.2. Endogenous Price

In this subsection, we relax our problem setting to consider E’s sale price decision $p(t)$ on a decentralized model with Nash bargaining fairness concerns under exogenous government subsidies. We adopt the same demand function in the study by Guan, Ye, and Yin [30]. For simplity, we assume the unit production cost is zero, which does not change the qualitative insight of the model. Let $w$ denote the wholesale price. The decision functions of the three parties are as follows:

$$\left\{\begin{array}{l}\underset{e_r(t),e_a(t),p(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}}\left[(p(t)-w)D(t)-(1-{\epsilon }_2)e_a^2(t)-e_r^2(t)\right]{{\displaystyle |}}_{e_f(t)=e_f^{WG*}(t)}dt\\ e_f^{WG*}(t) are derived from solving the following problem\\ \underset{e_f(t)}{\max }{\displaystyle \underset{0}{\overset{\infty }{\int }}{e}^{-\rho t}\left\{\begin{array}{l}\frac{1+N}{1+NM}\left[w(a-bp(t))(\eta e(t)+\gamma s(t))-(1-{\epsilon }_1)e_f^2(t)\right]\\ -\frac{MN(1+N)}{1+MN}\left[(p(t)-w)(\eta e(t)+\gamma s(t))-(1-{\epsilon }_2)e_a^2(t)-e_r^2(t)\right]\end{array}\right\}}dt\\ s.t.\left\{\begin{array}{l}\stackrel{•}{s}(t)=\alpha e_r(t)+\beta e_a(t)-\sigma s(t), s(0)=s_0\\ \stackrel{•}{e}(t)=\lambda e_f(t)+\mu e_r(t)-\delta e(t), e(0)=e_0\end{array}\right.\end{array}\right.$$

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Proposition 5. 

$p^{WF*}, e_r^{WF*}, e_a^{WF*}$ are independent of $N$, while $e_f^{WF*}$ decreases with $N$.

Consistent with Proposition 2, Proposition 5 illustrates that the existence of Nash bargaining fairness concerns reduces the production efforts of F but does not affect the decisions on the levels of CSR and brand construction of E. Interestingly, price decisions are also not affected by the Nash bargaining fairness concerns of F.

7. Conclusions

With economic globalization and the consumption paradigm shifting from commodity consumption to brand consumption, brand construction has become an important way to improve the efficiency of PASCs. Our work attempts to explain how to build a sustainable poverty alleviation mechanism through branding while considering government subsidies and the supplier’s Nash bargaining fairness concerns. We constructed a differential game model in which market demand is affected by goodwill and the consumer-perceived value. To coordinate the decentralized channel with fairness concerns, we designed a coordination mechanism with a mixed cost-sharing and revenue-sharing contract. Through a comparative analysis of the equilibrium results in the decentralized models (with or without Nash bargaining fairness concerns) versus the centralized model, we reveal the following critical findings:

First, government subsidies can effectively enhance the level of brand construction of the leading enterprise and production efforts of the poor supplier in the fairness-neutral decentralized model, thereby improving the channel efficiency of a PASC. However, it will not bring synergistic effects to improve the CSR level of the leading enterprise.

Second, different from the existing research conclusions regarding fairness concerns in a conventional supply chain [25,47,48,49,51], we find that the poor supplier’s fairness concerns only reduce their production efforts but do not affect the brand construction and CSR levels of the leading enterprise. Therefore, fairness concerns do not affect the goodwill of the leading enterprise but reduce the consumer-perceived value of products and further decrease market demand. The Nash bargaining fairness concerns of the poor supplier can improve their utility value but reduce the monetary profit values of both parties. Moreover, as the supplier’s bargaining power improves, fairness concerns will increasingly impact the profit performance of the PASC.

Third, the centralized model demonstrates superior performance compared with decentralized models with or without Nash bargaining fairness concerns. Our proposed mixed cost-sharing and revenue-sharing contract can effectively align members’ incentives, enhancing profitability for both parties.

Our findings provide managerial insights for enterprises and governments regarding the implementation of PASC. First, as brand equity increasingly dictates market competitiveness, the leading enterprise needs to carry out brand construction to cultivate goodwill and increase market demand, thereby enhancing the poverty alleviation efficiency of the PASC [4]. Second, we identify a channel inefficiency paradox arising from fairness considerations: while enhancing the utility perception of the disadvantaged party, these concerns simultaneously diminish monetary gains for all participants. To resolve this dilemma, the dominant enterprise should establish a cooperative contract that converts fairness concerns to an endogenous motivation to eliminate poverty. Third, brand development by leading enterprises requires financial support from the government. Government subsidies should be combined with the marginal revenues of both parties, which can effectively enhance the profit distribution among members and ensure the sustainability of the PASC’s poverty alleviation efforts [8].

Our work points to several directions for future research. First, our theoretical analysis only considered one behavioral factor: fairness concerns. In practice, both parties may have risk-averse behaviors due to agricultural output uncertainty and market demand [52]. Therefore, exploring how multiple behaviors influence supply chain members’ decisions would be helpful. Second, researchers can empirically test how supplier fairness concerns affect members’ decisions and the supply chain’s performance. Third, while our model emphasizes the role of branding on a PASC while considering government subsidies and the supplier’s Nash bargaining fairness concerns, the impact of CSR on branding in a PASC can be further investigated [53].