Gaming strategies within a green supply chain considering consumers’ concern about the greenness and conformance quality of products

With the growing demand for green development, providing green and conformance quality improved products for sustainable growth and industrial upgrading is essential. However, the related literature rarely considers the improvement of product conformance quality in green supply chain management. This paper incorporates both into a framework for addressing the problem. We analyze the optimal strategies of a manufacturer responsible for conformance quality of product and greenness improvement and a retailer responsible for product marketing in a supply chain under four contracts: full cooperation, price-only contract, two-part tariff, and marketing cost-sharing. The results show that full cooperation and two-part tariffs lead to the same and highest product quality, greenness, overall profit, and social welfare, but full cooperation is difficult to achieve in the supply chain. For the profit-maximizing manufacturer and retailer, the manufacturer most prefers two-part tariff contracts, while the retailer prefers marketing cost-sharing because both achieve the highest profit in the preferred contract. In addition, under the price-only contract, the conformance quality of product and greenness is the lowest, and the profit levels for manufacturers and retailers are the lowest. In all four cases, increased environment and quality awareness contribute to improved product greenness and conformance quality, leading to higher profits for the manufacturer and retailer and higher social welfare.


Introduction
With the emergence of serious environmental problems such as global warming, ozone layer depletion, acid rain, energy shortage, and declining forest resources, human beings have become increasingly aware of the protection of the ecological environment, and the concept of green development and sustainable development has gradually gained popularity. Furthermore, the impact of supply chain operations on the environment is also getting more and more attention, and it is generally accepted that a green supply chain is the future developing direction (Liu 2019). Therefore, many enterprises are undergoing green transformation and upgrading driven by governments, society, and the public.
Environmental regulation is the main external driver for the green transformation of supply chains. Many countries and regions have enacted laws and regulations to promote sustainable supply chain management systems. This management system focuses on environmental issues, circular economy, and sustainable supply chain development through green product design, green manufacturing, green recycling, and reversed logistics (Ji et al. 2017;Li et al. 2021a;Chen and Hu 2018). Furthermore, many empirical studies have revealed that government environmental regulations significantly impact the green development of supply chains (Wang and Yu 2020).
Meanwhile, consumers' green awareness is an essential market driver that promotes sustainable and green supply chain development. According to a survey implemented by Accenture, more than 80% of respondents consider the greenness of a product when making a purchase (Hong and Guo 2019). Also, a survey report from the Carbon Trust implies that about 20% of customers prefer to buy green products, even if they are more expensive than regular products ). In addition to consumer concerns about environmental conditions, factors driving increased consumer awareness include government and environmental organizations' advocacy and green marketing by the supply chain (Ma et al. 2017). The supply chain needs to develop increasingly green products to demonstrate its social responsibility due to the pressure from governments and the public. Therefore, enhanced marketing of green products becomes an essential means of profiting from green products. Therefore, retailers often invest in green marketing alone or in partnership with manufacturers, such as flat-rate marketing and advertising. For example, Procter & Gamble has partnered with Walmart, one of the world's largest retailers, in a series of green product marketing efforts . As a result, more and more consumers prefer to buy green products that are non-polluting and environmentally friendly, resulting in more competitive green products than traditional products. Therefore, a supply chain has to introduce green products preferred by consumers to achieve growth continuously.
In addition to ensuring the green attributes of the products, the improvement of conformance quality of products, which refers to conformance and defect avoidance in the implementation of a function to achieve a target level, is a critical factor in the greening of the supply chain. In order to promote the improvement of product quality, the 2016 Action Plan for the Implementation of the Quality Development Program issued by the Chinese government included the improvement of product quality in the national action plan. The plan calls for organizing and implementing projects to improve the quality of consumer goods, focusing on consumer goods of common concern, such as air purifiers, rice cookers, intelligent toilet seats, smartphones, toys, children's and infant clothing, kitchenware, and furniture. At the same time, many industries are now using improved conformance quality as a potent competitive tool to meet consumer expectations (He et al. 2016;Lambertini 2018). Failure to meet this expectation of consumers may lead to a reduction in sales of related products and the loss of goodwill of the company, which in turn, has negative consequences for the manufacturers' ability to sustain its position in the market (Hendricks and Singhal 2003). For example, in 2011, the Ford brand dropped ten spots in Consumer Reports' annual automotive reliability survey due to deteriorating conformance quality. In order to change this situation, "quality" became Ford's "job number one" (Durbin and Krisher 2011). As a result, Ford moved up to fourth place in the 2012 annual rankings by focusing on quality, beating out BMW, Hyundai, and even Toyota. It is Ford's best position in the report's 31-year history (Chakraborty et al. 2019). This case of Ford shows that without the improvement of conformance quality of products only to improve the product's greenness, the product provided by the supply chain still cannot be favored by consumers, and this development model is inevitably unsustainable.
However, existing literature on green supply chains has focused on improving product greenness but rarely considered improving the conformance quality of products. Therefore, this paper incorporates both considerations for supply chain decisions into the same analytical framework, develops a leader-follower game model in a supply chain in which the manufacturer is the leader, and the retailer is the following leader. Moreover, applying the classic Stackelberg game analysis method of management to examine the equilibrium results of the game between manufacturers and retailers under different strategies such as full cooperation, price-only contracts, price discrimination, and marketing cost-sharing draws insightful management conclusions comparing the results between the four strategies. Our research can provide a more complete and reliable operation strategy for supply chain enterprises under low-carbon background. Applying this strategy, supply chain enterprises can maximize profits and protect the ecological environment, making sustainable growth and industry improvement a reality.
The remainder of the article is as follows. The second section reviews the relevant research. The materials and methods grow up in the third section, including the basic assumptions and the game's equilibrium results under the four cases. The fourth section shows the comparative analysis of the results. Finally, the fifth section summarizes the paper.

Literature review
This study is closely related to two research streams: green management in the supply chain and conformance quality of product management in the supply chain. We will review the research related to each research stream in the following sections. Moreover, we highlight the differences between this study and the existing literature.
The first research stream closely related to our paper is operational decision-making in green and sustainable supply chain management, which mainly includes sustainable product design, by-products generated during product use, and reversed logistics (Gaur et al. 2017;Yi et al. 2021a). An extensive literature has emerged in these areas, and our research focuses on sustainable product design.
Green and sustainable product design requires appropriately positioning the product's function, assessing the environmental impact in product production, consumption, and even post-consumption scenarios and weighing the economic benefits against the environmental costs (Gouda et al. 2016;Hong et al. 2017). Chen (2001) studies the environmental impact of green product development and concludes that strict environmental standards are unnecessary for environmental improvement. Gouda et al. (2016) proposes a composite environmental regulation to regulate automakers and finds that automakers could achieve economies of scale while delivering environmental benefits under the regulation. Hong et al. (2018) analyze the supply chain configuration of a green product family issue. The objective is to minimize the overall cost of the supply chain by optimizing service time and option selection decisions. Pakseresht et al. (2020) analyze how to optimize the development of the green products family in the supply chain by making the best choices for suppliers, manufacturers, assembly plants, distribution lefts, and retailers. Mehrbakhsh and Ghezavati (2020) develop a green supply chain model in which product recovery capacity and uncertainty for demand are taken into account. Parast et al. (2021) analyzed the green reverse supply chain network. Their study considered several issues, including the location, route, and inventory of pickup and delivery. By comparing the two models of manufacturer-led and retailer-led green product development, Li et al. (2021a) find that the greenness of the products and the profitability of the leaders are higher under the former model. Assuming that the manufacturer grants a credit period to the retailer or gives the retailer a discount on the sales price, Ghosh et al. (2021) develop a model of coordination between the manufacturer and the retailer regarding the reality of green products and analyze the payments made by each party under each model. Yi et al. (2021a, b) analyze the impact of post-consumer product regulation policies on the life cycle greenness of products provided by the supply chain under the extended producer responsibility (EPR). Cai et al. (2022) developed a green supply chain game model considering participants' attitudes to risk. The results show that risk aversion reduces the green level for a centralized supply chain, while for a decentralized supply chain, risk aversion may induce suppliers to improve the green level.
The second research stream relevant to our paper is the conformance quality of product management in the supply chain. Improving product quality is the most effective means for supply chains to achieve a competitive advantage, and it has received close attention from the academic community (Chen et al. 2017;Lambertini 2018). Much research has focused on the quality management of supply chain collaboration (Reyniers and Tapiero 1995;Lee et al. 2013;El and Kogan 2013;Lambertini 2018;Chakraborty et al. 2019). For example, El and Kogan (2013) believe that even though revenue-sharing contract contracts increase the commitment of suppliers to improve quality, such contracts do not entirely solve the coordination problem. While Chakraborty et al. (2019) argue that the cost-sharing model is an effective way of cooperation, and it has higher product quality and profit levels than price contracts. Lambertini (2018) analyzes the coordination of two firms belonging to the same supply chain that make joint R&D investments to improve product quality and finds that vertically integrated supply chains can effectively coordinate using a two-part tariff contract. Baiman et al. (2000) analyzed the relationship between product quality, cost of quality, and contractable information among supply chain participants. Gray et al. (2015) investigates the conformance quality benefits of combining production and R&D activities and finds that the closer the location of production and R&D activities is, the higher the conformance quality of products. Krishnan et al. (2000) believe that improved conformance quality of software products has a positive impact on product life cycle productivity, and good staff quality, deployment of product development resources, and improvement of the production process can guarantee improvement conformance quality of software products. Nandakumar et al. (1993) develop a dynamic programming model to evaluate the cost of conformance quality of products and show that it may not be optimal for quality improvement efforts to target products with the highest defective levels and the highest direct costs or consume the maximum capital resources. Thirumalai and Sinha (2011) finds that the conformance quality of medical products directly affects the probability of product recall, consumers' demand for the company's products, and even the company's reputation.
Although the existing literature has extensively studied green and product quality management in supply chains, these two issues rarely enter the same analytical framework, with a slight exception. Chen (2001) develops a qualitybased model to investigate green product development where the product quality and environmental consequences simultaneously enter the producer's decision function. Inspired by Chen (2001), in this paper, we extend Chen's (2001) precious work with the following four distinct differences: (1) We move decision-makers from a single manufacturer to a supply chain due to the development of management science; the strategic interaction between each main body of the supply chain is becoming more and more common in today's product supply side (Liu 2019;Li et al. 2021a).
(2) Concerning "product quality" in this paper, we focus on products' "conformance quality." The reasons are as follows: as far as we know, the quality of products can be subdivided into conformance quality, design quality, perceived quality, etc. Although the manufacturer is responsible for improving the quality mentioned above, it can also assign some responsibility to the designer or retailer in the supply chain. The perceived quality, for example, can be improved by retailers' increased marketing efforts, while the improvement of the conformance quality of the product can only be performed by the manufacturer alone. Therefore, to avoid confusion of responsibility, we limit the quality of the product improved by the manufacturer to "conformance quality" in this paper. (3) An entirely new demand function is developed in which, in addition to product price, product greenness, and conformance quality, marketing efforts jointly and positively affect product demand. (4) We analyze the best decisions of the manufacturer and retailer and their respective payments and social welfare under four scenarios, full cooperation, wholesale price contract, price discrimination, and marketing cost-sharing, and compare the equilibrium results of the game in the four scenarios to conclude the study.
We use Table 1 further to compare the differences between this paper and previous studies.

Problem description
Consider a two-echelon supply chain consisting of a manufacturer and a retailer. The manufacturer is responsible for producing a product of improved conformance quality and green. The retailer advertises and sells it. Consumers prefer good quality and green products. It competes for market share with traditional products that are functionally identical to those in the supply chain that we investigated and already existed in the marketplace.
As the leader in our leader-follower game, the manufacturer first determines the product's conformance quality, degree of greenness, and wholesale price. Then, as the game follower, the retailer assumes advertising effort and the product's retail price. We consider four ways that the manufacturer and retailer can choose to play the game: full channel coordination, a price-only contract, a two-part tariff contract, and a marketing cost-sharing contract. Moreover, we indicate them with "c," "d," "tt," and "cs," respectively, for notational convenience.

Fundamental assumption
To describe the model more clearly and conveniently, we summarize the symbols and definitions of the variables and parameters used in the model in Table 2.
To meet consumer demand and gain an advantage in the competitive marketplace, the manufacturer and retailer in the supply chain perform their roles.
On the one hand, the manufacturer is responsible for improving the conformance quality q (0 < q < 1) and greenness e (0 < e < 1) of the product. Consistent with related studies such as Lambertini (2018) and Chakraborty et al.
(2019) and Chen (2001), assume that to improve the product conformance quality of the product q costs the manufacturer an investment cost βq 2 . It is a convex increasing function in line with the basic view of microeconomics, where the constant β represents the difficulty factor of product quality improvement. Product greenness e indicates the percentage of emissions saved relative to conventional products. Its improvement depends on the development of green technologies of the manufacturer. Following Hong and Guo (2019) and Li et al. (2021a), we assume that the investment cost of the development of green technologies is αe 2 for obtaining the greenness e, where α is the cost rate of the green technology development.
On the other hand, the retailer is responsible for marketing the product. It promotes product sales through advertising efforts t. Usually, higher advertising efforts require more advertising costs and will result in more product sales. In agreement with Atasu et al. (2009) and Hong and Guo (2019), we assume the product marketing cost rate of the retailer is ϕ, and it suffer a convex and increasing advertising cost ϕt 2 . Now, let us investigate the consumption function. Firstly, as with recent research on green supply chains, consumers are environmentally conscious. Therefore, they are willing to pay higher prices for greener products or more quantity in demand at the same price (same below). Secondly, according to common perceptions, consumers are more willing to pay when faced with a higher quality product. In particular, Thirumalai and Sinha (2011) empirical research shows that the conformance quality of products positively impacts product demand. This idea is supported by relevant research such as Hendricks and Singhal (2003). Thirdly, as shown in recent studies such as Hong and Guo (2019), retailers' advertising efforts are a direct factor in increasing consumers' willingness to pay. Fourthly, as demand functions generally, there is an inverse relationship between the quantity demanded and the price, i.e., a higher price leads to a lower quantity demanded. Combining the above four factors, obtain our demand function as follows: where k 1 and k 2 are consumers' greenness preference and quality preference for the product, respectively. In addition, we unitize the market size and the marginal effect of price and advertising on the quantity demanded as 1, which is consistent with recent related studies such as Hong and Guo (2019).
In the following, we first investigate the form of full channel coordination as a benchmark for comparison. In this form, the manufacturer and retailer in the supply chain can be treated as one profit left from two independent profit lefts, and they choose the optimal strategy to maximize the profit of the entire consortium.

Game equilibrium under full channel coordination (c)
In the case of full channel coordination, the manufacturer and retailer make decisions from a holistic perspective. The decision-making order under full channel coordination is shown in Fig. 1.
Therefore, we can give their joint objective function as the following equation: According to the first-order and second-order conditions of Eq. (2), one can get the optimal strategies under the full channel coordination as described in Theorem 1.

Theorem 1.
Under the full channel coordination, the optimal equilibrium strategies for the manufacturer and the retailer are as follows: We put the proof of Theorem 1 in Appendix 1.
Substituting the optimal equilibrium strategies stated in Theorem 1 into Eq.
(2), we obtain the production and total profit of the supply chain: Consumers' greenness preference for the product k 2 Consumers' greenness preference for the product ε Conversion factor for converting pollution emission reductions to money Let us next employ Corollary 1 to investigate the effect of specific system parameters on the optimal decisions of the manufacturer and retailer.
Corollary 1. The optimal decisions under full channel coordination have the following properties: The higher cost of green technology development decreases optimal greenness investment, decreasing consumer demand and product prices. We also find a cascade of other responses by the consortium to higher green technology development costs: optimal marketing efforts, conformance quality improvement efforts, and even overall profits decline. From (2) and (3), we can see that the increase in marketing effort cost and conformance quality improvement cost has the same effect on each variable as the increase in product greenness improvement cost. This phenomenon reflects that conformance quality improvement, greenness improvement, and product marketing have a complementary relationship in the profit consortium of the supply chain. Improving one will improve the other two and improve demand, raise demand prices, and increase profits. We find from (4) and (5) that the increase in consumer preference for product greenness or quality motivates the profit consortium to invest in conformance quality of the product and greenness and enhance product marketing, resulting in an overall increase in profits.
The overall profit level of the supply chain may be substantial under full channel coordination. However, according to our analysis in Appendix 1, the optimal prices and marketing efforts must obey the following relationships to achieve full cooperation: If Eq. (3) is valid, then the wholesale price equals the manufacturer's marginal cost, i.e., w * = c. It makes the manufacturer cannot improve product quality and product greenness. Otherwise, it will incur a loss. Thus, the mode of the entire channel coordination is contrary to the assumptions of this paper. In other words, full channel coordination is not feasible in our model. Therefore, we next examine other feasible game strategies for them, including singleprice strategy, price discrimination strategy, and marketing cost-sharing strategy.
One can see the proof of Theorem 1, Corollary 1, and Eq.

Game equilibrium under single-price contract (d)
We apply the inverse induction method to investigate the supply chain decision under a price-only contract in a Stackelberg game framework. The manufacturer, as the leader, offers the product to the retailer at its optimal wholesale price. The retailer acts as a follower, buys the product from the manufacturer at the wholesale price determined by the manufacturer, and sells the product to the consumer at its We first analyze the optimal decision of the retailer who acts as the follower in the game. In response to the manufacturer's decisions of e d , w d , and q d , the retailer determines his optimal advertising effort t d and retail price p d . We phrase the retailer's issue as follows: From the first-order and second-order conditions of Eq. (5), we find that r d p d , t d is jointly concave in (p d , w d ), and the unique optimal decision pair p * d , t * d in reaction to e d , w d , and q d can be given as Next, consider the problem of the manufacturer who acts as the leader in the game. Under the marginal production cost c, the manufacturer has the following profit functions: Substitute Eqs. (5) and (6) into Eq. (7), and applying the first-order and second-order conditions of Eq. (7) can obtain the manufacturer's game equilibrium strategies. Combining Eqs. (5) and (6), we conclude the following Theorem 2.
Theorem 2. Under the price-only contract, the Stackelberg equilibrium of the supply chain can be given as follows: Substituting the game equilibrium results into Eq. (4) and (7), receive the production and the total profit of the manufacturer, the retailer, and the entire supply chain under the price-only contract: It is time to employ Corollary 2 to investigate the effects of specific system parameters on the optimal decisions of the manufacturer and retailer under a price-only contract.
Corollary 2. The optimal decisions under a price-only contract have the following properties: (1) The proof of Theorem 2 and Corollary 2 can be found in Appendix 2.
Corollary 2 shows that even when manufacturers and retailers make independent decisions based on their profit maximization, the impact of the optimal decision of the Having completed the game analysis under the price contract, let us next investigate the marketing cost-sharing model.

Game equilibrium under a two-part tariff contract (tt)
The two-part tariff system is a typical price discrimination strategy used by monopolistic players. On the one hand, it enables to convert all consumer surplus into producer surplus. However, on the other hand, it can eliminate the surplus loss caused by monopoly and achieve the Pareto optimal result (Basak and Wang 2016). This subsection assumes that the manufacturer uses the two-part tariff system, i.e., a price discrimination strategy, for the retailer. The price charged by the manufacturer to the retailer consists of two parts: the wholesale price w tt and a fixed fee T. The decision-making order under a two-part tariff contract is described in Fig. 3.
Therefore, the retailer's objective function converts into the following form: Meanwhile, the manufacturer's objective function can be expressed by the following equation: Since the manufacturer is the leader in the Stackelberg game, it can take full advantage of its first-mover advantage m tt w tt , T, e tt , q tt = w tt − c 1 − p tt + k 1 e tt + k 2 q tt + t tt − e 2 tt − q 2 tt + T s.t. p * tt − w tt 1 − p * tt + k 1 e tt + k 2 q tt + t * tt − t * 2 tt − T ≥ r * d to maximize its profits; i.e., it can increase its fixed fee charges until the retailer is just ready to accept the contract. Therefore, the following equation holds: Thereby, the manufacturer's objective function converts into Applying the first-order and second-order conditions of Eqs. (9), (10), and (11) in the framework of the Stackelberg game, we obtain the unique optimal strategy for the manufacturer and the retailer stated in Theorem 3.
Theorem 3. Under a two-part tariff contract model, the Stackelberg game between the manufacturer and the retailer reaches the following equilibrium results: The proof of Theorem 3 can be found in Appendix 3.
Substituting the game equilibrium results given in Theorem 3 into Eqs. (9) and (11), get the production and the total profit of the manufacturer, the retailer, and the entire supply chain under the two-part tariff contract: m tt w tt , e tt , q tt = p * tt − c 1 − p * tt + k 1 e tt + k 2 q tt + t * tt − e 2 tt − q 2 tt − t * 2 tt Fig. 3 Decision-making order under a two-part tariff contract Next, we investigate the decisions of the manufacturer and the retailer in a marketing cost-sharing scenario.

Game equilibrium under marketing cost-sharing (cs)
Under the price-only contract and the two-part tariff contract, either the manufacturer or the retailer chooses strategies to maximize its profits, ignoring the cooperation in the supply chain. This subsection investigates a limited form of collaboration between the manufacturer and the retailer in the supply chain, namely, the sharing of marketing costs.
Under the mode of marketing cost-sharing, the manufacturer, i.e., the leader of the Stackelberg game, takes the lead in determining the percentage of cost-sharing for advertising efforts. Then, the retailer, i.e., the followers of the Stackelberg game, determines the amount of advertising effort and the product's price under the given cost-sharing ratio. As one can see, in this model, the marketing costs affect the profitability of both parties. Thus, depart from the priceonly contract and the two-part tariff contract, the marketing cost-sharing model requires the cooperation of both parties. However, this cooperation is only on one aspect of marketing cost-sharing, and it is a limited cooperation model for manufacturers and retailers. The following Fig. 4 shows the decision-making order under marketing cost-sharing. * Assume that the proportion of marketing costs that the manufacturer is willing to share is η. Then, the proportion of marketing costs borne by the retailer is (1η), and it has the following objective function: Meanwhile, the manufacturer's objective function can be given by Eq. (13)  Substituting the game equilibrium results into Eqs. (12) and (13), we obtain the production and the total profit of the manufacturer, the retailer, and the entire supply chain under the marketing cost-sharing: (12) r cs p cs , t cs = p cs − w cs 1 − p cs + k 1 e cs + k 2 q cs + t cs − (1 − ) t 2 cs (13) m cs w cs , e cs , q cs , cs = w cs − c 1 − p cs + k 1 e cs + k 2 q cs + t cs − e 2 cs − q 2 cs − t 2 cs q * cs = 4 k 2 (c−1) , t * cs = 6 (c−1) ; r * cs = Results discussion We have investigated the optimal strategies of the manufacturer and retailer under four scenarios: full channel coordination, a price-only contract, a two-part tariff contract, and a marketing cost-sharing contract. This section will provide a comparative analysis of the strategies under these scenarios.

Participants' strategies and profits
Analyzing the game behavior of manufacturers and retailers in the four cases, we propose the following Proposition 1. Proposition 1. The greenness of the product, the conformance quality of the product, the marketing effort, the retail price, and the market demand in the four cases meet the following relationships: We put the proof of Proposition 1 in Appendix 5.
In the four cases mentioned above, the entire channel coordination eliminates competition between the manufacturer and the retailer. The profit consortium they formed can use this advantage to improve product quality and greenness, enhance product marketing, and minimize price to promote demand and producer surplus. Therefore, the highest greenness and product quality, the most outstanding marketing effort, the lowest product price, and the most significant product demand can reach in this case. However, we have shown that full cooperation is impossible to achieve. Therefore, a two-part tariff contract may be an excellent alternative to full channel coordination. As shown in Theorem 1 and Theorem 3, the results under this scheme are identical to the full cooperation, except for the difference in the manufacturer's and retailer's split of total profits. The reason is that under the two-part tariff contract, the manufacturer takes full advantage of its first-mover advantage and replaces the centralized decision-maker in the fully cooperative consortium. The retailer reduces to the role under the arrangement by the manufacturer where it has to accept the manufacturer's proposed solution for decision-making. Therefore, the manufacturers who have achieved the status of central decision-makers make a strategic choice from the overall optimality point of view. So that the overall result, in this case, is the same as in the case of full cooperation. On the other hand, in terms of profit distribution, the manufacturer makes full use of its first-mover advantage to maximize its profit, thus leaving the retailer with a profit only equal to its profit under the price-only contract.
A marketing cost-sharing approach is a limited form of cooperation between the manufacturer and the retailer in the supply chain; the manufacturer in this form actively bears part of the retailer's marketing effort to promote product sales, which will lead to an increase in the product sales effort. According to Corollary 1 and Corollary 2, marketing efforts will improve product quality and greenness, lower prices, and lift demand. Therefore, in this model, marketing effort, conformance quality, greenness, and demand are the second highest, while product price is the second lowest.
The manufacturer and the retailer compete to maximize their profits under a price-only contract, with the manufacturer responsible for improving product quality and greenness and the retailer responsible for marketing the product. Although marketing efforts also affect the manufacturer's profits, the manufacturer does not invest in it. Likewise, product greenness and quality improvements benefit the retailer while not spending money on them. Therefore, the marketing effort, product greenness, conformance quality, and demand are minimal in this case.
Next, let us use Proposition 2 to investigate the impact of marketing cost-sharing on the retailers' marketing inputs.
Proposition 2. Instead of causing the retailer to invest less in marketing, the manufacturer's sharing of marketing costs will cause it to invest more in marketing, i.e., The proof of Proposition 2 is put in Appendix 6.
One may assume that if the manufacturer shares in the marketing costs, the retailer will take the opportunity to reduce its marketing investment. Proposition 2, however, gives an opposite conclusion. It is because to the extent that an increase in marketing inputs increases consumer demand. Therefore, the retailer drives the manufacturer's investment in marketing to increase demand for the product by increasing its inputs, thus benefiting both the manufacturer and the retailer.
Profitability is a central consideration for manufacturers and retailers when choosing a strategy. Below, we use Proposition 3 to compare the profit situation in four scenarios. Proposition 3. Among the price-only contract, the two-part tariff contract, and the marketing cost-sharing contract, the profits of the manufacturer and the retailer satisfy the following relationships: Please see the proof of Proposition 3 in Appendix 7.
Proposition 3 shows that the manufacturer makes the highest profits under a two-part tariff contract. It is because that the manufacture, through the two-part tariff contract, on the one hand, maximizes the profit of the entire supply chain (equal to the profit at full cooperation) and, on the other hand, minimizes the profit of the retailer (equal to the profit at price-only contract) so that the manufacturer maximizes its profit. The marketing cost-sharing results in the manufacture obtaining the second highest profit because the manufacturer and the retailer cooperate to market the product, promoting the product's sale. Under a price-only contract, the manufacturer's profit is the lowest. It is the same as the prisoner's dilemma in the classic game case: each game participant chooses its optimal strategy while ignoring each other's cooperation and ends up with the lowest payment. This case illustrates the importance of cooperation between the participants in the game. Now we investigate the profits of the retailer. While the manufacturer obtains the highest profits under the two-part tariff system, the retailer obtains the same minimum profits as in the price-only contract in this case. Because the manufacturer takes full advantage of its first-mover advantage under the two-part tariff system, the retailer as the postactor in the game can only accept the manufacturer's contract. Therefore, the manufacturer will not give the retailer a higher profit margin than under a price-only contract. Nevertheless, if they implement marketing cost-sharing, the profit level of the retailer is expected to increase under this limited form of cooperation.

Consumer surplus, environmental impact, and social welfare
Next, we analyze the consumer surplus under different game approaches. Consumer surplus is the difference between the maximum price consumers willing to pay and the price they pay. It reflects the degree of improvement in the consumer's welfare situation obtained by consuming the good. The following formula calculates it: where CS denotes the consumer surplus and ⌢ p is the maximum price consumers are willing to pay, at this time D * = 0.
Substituting the results for the four cases of full channel coordination, price-only contracts, marketing cost-sharing, and the two-part fee system into Eq. (14), one can get Examining the consumer surplus in the four cases yields the following Proposition 4.

Proposition 4.
Consumer surplus is the highest under full manufacturer-retailer cooperation and a two-part fee system. A marketing cost-sharing contract follows it. When implementing the price-only contract, consumers achieve the lowest surplus, i.e., CS * Please see the proof of Proposition 4 in Appendix 8.
Under full manufacturer-retailer cooperation and a twopart fee system, as shown in Proposition 1, its price is the lowest, and demand is the highest, so consumer surplus is also the highest. On the other hand, the demand in the priceonly contract case is the lowest, which leads to the lowest consumer surplus.
Next, we examine the beneficial effects of the increased greenness or reduced pollution emissions. Referring to Krass et al. (2013) and Hong and Guo (2019), we assume that the environmental benefits can be measured in monetary terms and the coefficient of conversion of environmental benefits into money is ε. Furthermore, since the product's greenness is minimal under a price-only contract, the amount of currency that can be converted in this case is assumed to be 0, i.e., EI d = 0. Taking the environmental benefits in this case as a benchmark, the environmental benefits in each of the other three cases can be expressed as Substituting the corresponding results obtained in the third section into them, we get Investigating the environmental benefits under the several strategies, we obtain the following Proposition 5.
Proposition 5. These are the following relationships about the environmental benefits under the four strategies: Please see the proof of Proposition 5 in Appendix 9. Now, let us consider social welfare in four cases. In this paper, social welfare can be composed of three components: total supply chain profit, consumer surplus, and environmental benefits and is given by the following equation: Substituting the corresponding results obtained into Eq. (15), obtain social welfare in the four cases as Based on the above expression for social welfare, we give the following proposition: Proposition 6. The social welfare following relationships exist between the four cases: Please see the proof of Proposition 6 in Appendix 9.

Numerical examples
Up to this point, we have obtained the main conclusions through calculations and direct comparative analysis. Next, allow us to further demonstrate the conclusions with some numerical examples. For this purpose, we refer to relevant studies by Hong and Guo (2019) to determine the range of values for each parameter and make initial assignments for each parameter. Then, carry out an initial numerical simulation. Finally, adjust the initial assignments of the parameters according to the simulation results until the simulation results of all variables are economically meaningful, and they are c = 0.05, k 1 = 1.2, k 2 = 1.5, α = 2.6, β = 2.2, and ϕ = 1.1.
Apply MATLAB software to simulate the main variables and obtain the following simulation analysis graphs. Figures 5,6 and 7 show the same order of the optimal results under the different strategies derived in the subsection Consumer surplus, environmental impact, and social welfare. Moreover, from it, one can derive the following new implications.
In terms of product quality and greenness, supply chain profitability, and social welfare, marketing cost-sharing, two-part charging system, and complete cooperation have advantages over the price-only contract. Moreover, the latter two have apparent advantages. Looking at individual graphs, Fig. 5 shows that increasing green and conformance quality preferences improves product greenness and conformance quality under the four strategies. Furthermore, from the slope of the curve, the marginal effect of product greenness preference on greenness improvement is greater than the marginal effect on quality improvement; the marginal effect of conformance quality preference on quality improvement is greater than the marginal effect on greenness improvement. Figure 6 depicts the effect of the three difficulty factors on the greenness and conformance quality of the product. In general, the difficulty coefficients of product greenness and conformance quality improvement and the difficulty coefficients of marketing effort increase on both product greenness and quality improvement with unfavorable marketing. In particular, the difference in the marginal effects of the same difficulty coefficients on greenness and quality improvement is not significant.
One can find from Fig. 7 that overall profits and social welfare are significantly higher in the two cases of price discrimination and full cooperation than in the other two cases, and they are the lowest in the case of price-only contracts. However, in profit-maximizing manufacturers and retailers, manufacturers prefer price discrimination contracts, while retailers prefer the marketing cost-sharing case.
So far, we have obtained several significant conclusions through direct comparative analysis and data example analysis of the game results between the manufacturer and retailer in the supply chain. For example, increased environmental awareness among consumers leads to a greener, cleaner environment, higher profit levels, and improved social welfare for manufacturers and retailers. This finding is consistent with some previous research, such as Hong et al. (2021) and Wu et al. (2021). Based on this discovery, in addition to environmental policies, strengthening consumers' awareness of environmental protection through environmental publicity is also an essential means of environmental governance, which has important guiding significance for the government's formulation of environmental governance strategies. In addition, we find that operation coordination of a green supply chain has a significant impact on supply chain performance. For example, manufacturers' sharing of marketing costs can increase each other's profits, improve product greenness, and even improve social welfare. This finding is analogous to previous studies such as Wu et al. (2021).
In particular, our study has two significant findings different from previous studies. One is that compared with the cost-sharing model, a two-part charging system makes the total profit of the supply chain higher. Furthermore, we have proved that, compared with cost-sharing, the limited cooperation mode of supply chain members, the two-charge system is a kind of similar to the operation mode of full cooperation. Under the two-charge system, the supply chain decision-making left by the cost-sharing from two becomes one, so the manufacturer who plays a dominant role can, according to their profit maximization goal, design its strategy. In this way, the overall profit of the supply chain has reached the profit level of complete cooperation. The second important conclusion, different from previous studies, is a complementary relationship between carbon emission reduction investment and conformance quality improvement investment. This discovery is well exemplified in China's automobile industry. On the one hand, Chinese auto-companies are continuously investing in quality improvement, resulting in continuous improvement of automobile quality. For example, the "2020 New Passenger Car Quality Report" 1 shows that although Sweden, Japan, and France still occupy the top three positions in the country's overall PPH rankings, the quality improvement of Chinese cars is most evident compared with those of many other countries, followed by Italian cars. On the other hand, automobile manufacturers are constantly investing in carbon emission reduction at both the production and consumption ends. The mass production of new energy vehicles is an example of carbon emission reduction at the consumption end. At present, the scale and quality of new energy vehicles in China have been at the forefront of the world. In conclusion, our study has the following theoretical and practical implications. In terms of theoretical significance, we have extended the theoretical study of green supply chain use decisions by including an essential consideration for supply chain firms and product conformance quality improvement, into the decisionmaking of green supply chain firms, providing a research paradigm for subsequent studies. In addition, we present several findings that differ from the existing literature in terms of practical implications. This paper has several significant new findings compared with previous studies. These findings have essential reference significance for the government's environmental management and economic development strategy and provide decision-making guidance for the management and operation coordination of supply chain enterprises.

Conclusion
This study investigates the decision issue of the green product supply chain considering conformance quality of the product improvement and stakeholders' environmental responsibility. Conformance quality preferences and environmental awareness of consumers are important market drivers for achieving a sustainable supply chain. The manufacturer determines the product design strategy in the business process, represented by the conformance quality and greenness. The retailers, in turn, determine the product marketing efforts to drive demand for their products.
We analyzed four competitive and cooperative decisions between the manufacturer and retailer.
Interesting management findings emerge from the comparison and discussion of the results for the four types of contracts: (1) In all four cases, increased environmental awareness and conformance quality preferences promote improved conformance quality and greenness. Therefore, increasing consumers' environmental awareness is a necessary tool for ecological improvement.
(2) Although full channel coordination can lead to the highest product quality, product greenness, and total profit and social welfare, full cooperation between the manufacturer and retailer with different interests in the supply chain is difficult to achieve. (3) The manufacturer-led two-part tariff contract results in outcomes consistent with full cooperation. Therefore, from the perspective of social managers, two-part tariff Fig. 6 Changes in greenness and conformance quality with greenness and conformance quality improvement difficulty and marketing difficulty contracts are an excellent alternative to full channel coordination. (4) Although two tariff contracts can lead to a socially optimal outcome, they may not ensure economic benefits for all partners. For example, the manufacturer can achieve the maximum profit under this contract, while the retailer receives a profit equal to the profit at the price-only contract, which is lower than the retailer's profit at the marketing cost-sharing.
When making decisions, these findings can provide valuable references for regulators and manufacturers and retailers in a supply chain.
This study has several limitations left to extend in future studies. In the model, we only consider the manufacturer's sharing of the retailer's marketing costs. Nevertheless, in reality, the buyer may also share the supplier's technology investment cost. For example, to improve the competitive advantage of the supply chain, Apple shares the cost of innovative technologies and technological development with its suppliers. In addition, from the government's perspective, designing optimal environmental policies to incentivize supply chains to reduce environmental externalities for sustainable development is another critical issue for future research.
Meanwhile, we have obtained e * tt = e * c . In conclusion, e * d < e * cs < e * tt = e * c . Similarly, we obtain the remaining inequalities by subtracting the denominator, subtracting the numerator, or subtracting both the numerator and the denominator of the expression of the optimal result. Finishing the proof.

Proof of Proposition 3
Proof m * d < m * cs < m * tt 1) Rectifying m * tt − m * cs , we get Fo r e a s e o f p r e s e n t a t i o n , w h e r e we l et k 2 1 + k 2 2 = x > 0 . Same below. Looking at Eq. (17), we find that all parts are greater than zero except for the numerator part in the curly braces. Therefore, we analyze the numerator in the curly braces below.