Introduction

Information asymmetry generally exists in the upstream and downstream of the supply chain that adopts decentralized decision1, especially in the upstream of some electronic product supply chains. As the production process of the products is complex, the whole process including the production, research and development may be confidential, the production cost information is not transparent, which gives the upstream manufacturing enterprises the opportunity to misreport the cost.

The misreporting behaviors caused by information asymmetry are of great significance to the research of supply chain decision. Till now, most of the current researches on supply chain management are based on the assumption of supply chain information symmetry, that is, to consider the game or cooperation of various stakeholders in the supply chain without information advantage2,3,4,5. However, focusing on the real market, supply chain information is usually not completely transparent, and there is no shortage of supply chain members who misreport private information in order to gain profits6,7. The existing research on information misreporting in supply chains predominantly focuses on the content, perpetrators, and consequences of misreporting. In terms of the research on the content and subjects of misreporting, Zhao et al.8 focused on the influence mechanism of retailers’ misreporting leveraging their demand information advantages on supply chain decisions when manufacturers formulate direct sales channel strategies. Zheng et al.9 pointed out that in the community group-buying supply chain, due to information asymmetry, the supply chain entities may conceal the true preservation level of the products, thereby affecting the coordination of the supply chain. Du et al.10 employed the signal game model to explore the role of supply chain members’ concealment of effectiveness information on innovation input and return in the context of retailers’ overconfidence. Zhang et al.11 conducted an in-depth study on the impact of carbon emission information misreporting on supply chain coordination strategies against the backdrop of carbon quota trading policies. Ding et al.12 in the scenario of supply chain finance, revealed the motives of suppliers for concealing capital demands and proposed a credit contract design scheme. Zhou et al.13 and Liu et al.14 respectively focused on the problems of suppliers falsely reporting productivity information and retailers misreporting sales cost information. In the research field of the impacts of misreporting behavior, Zhao et al.15 verified through a non-cooperative game model that when bilateral cost information is asymmetrical, although misreporting behavior can increase the profits of liars, it will harm the interests of other members and eventually lead to supply chain imbalance. The research by Qin et al.16 and Liu et al.17 also indicates that the self-interest characteristic of misreporting decisions can have a negative impact on the overall efficiency of the supply chain, and members with information disadvantages are more likely to suffer losses due to misreporting behaviors. It is worth noting that Ding et al.18 found in their research that under specific conditions, reasonable misreporting decisions may generate benefits for the supply chain, but the realization of such positive impacts needs to meet strict constraints. Despite the remarkable achievements of existing research, the focus has been predominantly on the analysis of misreporting content, subjects, and impacts. The research on how to eliminate the misreporting motives of supply chain members is still relatively scarce, which provides an important direction for subsequent research.

The immutable and publicly searchable nature of information on blockchain plays an important role in curbing false information in the supply chain, bringing significant advantages to the management of the supply chain19. According to the degree of decentralization, blockchain can be classified into public chains, private chains and consortium chains. The electronic product supply chain involves multiple members such as suppliers and manufacturers, and requires all parties to upload information to achieve collaboration. At the same time, it is required that the internal information of the supply chain can be transparently shared among members, and the information must also be kept confidential externally. Consortium chains are jointly managed by multiple pre-authorized institutions, allowing each member of the supply chain to join as a node and upload information. The data is only visible to the members within the consortium and non-consortium members cannot access it. This can simultaneously achieve internal transparency and external confidentiality of information20. In contrast, the data of public chains is completely open and does not meet the confidentiality requirements, and private chains are controlled by a single institution and cannot meet the participation of multiple members. Therefore, consortium blockchain is the most suitable for the electronic product supply chain. At the policy level, the "Special Action Plan for Accelerating the Development of Digital and Intelligent Supply Chains" issued by the Chinese government in 2025 clearly states that leading enterprises in the supply chain should play a leading role, and by leveraging new technologies such as blockchain, the digitalization, intelligence, and visualization transformation of the supply chain should be promoted through "one chain, one strategy".

Against this backdrop, as blockchain technology continues to develop, the academic community’s attention to its in-depth application in supply chain cooperation is constantly increasing. Currently, most studies focus on the information traceability function of blockchain. For instance, Liu et al.21 proposed that the introduction of blockchain technology enables tracking of the source of medicines and thereby identify potential counterfeit medicines when discussing decisions in the pharmaceutical supply chain; Zhang et al.22, based on the blockchain agricultural product traceability system, proposed a "dual-chain" traceability system that integrates the alliance chain and the private chain, effectively solving the cost and data issues in the traceability process; Sun et al.23 targeted the demand for privacy data sharing and security protection in the blockchain traceability of fruits and vegetables, proposed a privacy data trusted sharing method based on content extraction signatures, and achieved privacy protection and information sharing in the supply chain. Other studies have explored from the perspective of blockchain enhancing cooperation efficiency. Jiang et al.24 conducted research on the supply chain of fresh products and found that the introduction of blockchain technology can accelerate the transaction process and shorten the circulation time, thereby reducing losses; Shi et al.25 constructed a supply chain model incorporating blockchain technology and studied the operational decisions of the platform supply chain under transaction supervision, improving the decision-making efficiency of the supply chain. Blockchain not only helps to improve the operational quality and efficiency of the supply chain and reduce losses, but also effectively curbs false reporting behaviors in the supply chain26. However, most scholars only focus on the realization of information transparency in the supply chain by blockchain27,28, and have not established a direct association between it and false reporting behaviors of information. As a frontier research, Chen et al.29 proposed that the introduction of blockchain technology can effectively curb the false reporting behavior of product freshness information by manufacturers, providing a theoretical basis for avoiding risks of false reporting in the supply chain.

Previous studies hold that supply chain collaborative decision can ensure the optimal final decision result, and most scholars refer to collaborative decision to conduct coordination research on various supply chains30,31. But the precondition of collaborative decision is the full transparency of supply chain information. Only under this condition, it is of practical significance to use collaborative decision as reference decision to coordinate supply chain. At present, relevant studies only consider that blockchain technology creates a game environment of information symmetry for decentralized decision, and directly assumes that there is no incentive for supply chain members to misreport under collaborative decision32. There is a lack of research on the introduction of blockchain technology to ensure information fairness when supply chain adopts collaborative decision-making.

Product after-sales is an indispensable part of the supply chain, meanwhile, it relates to the sustainable development of the supply chain. Product quality problems are the main cause of after-sales, and improving the quality control level of products in the production process can effectively reduce the after-sales rate of product. However, existing literature often focuses on the impact of R&D investment on product after-sales33, and few scholars have explored the relationship between quality control level and product after-sales rate. In addition, consumers will apply for after-sales service for products with quality defects. Most of the after-sales methods involved in current relevant studies are divided into two categories: Fwwirst, replacement service. For example, Lu et al.34 in the study of perishable high-tech products, considered that enterprise will decide whether to provide replacement service according to product performance threshold. The second is to provide maintenance service. Qiao et al.35 proposed a three-dimensional warranty policy for repairable products and pointed out that repairs could be profitable for the manufacturer and reduce conflicts with consumers. However, few studies have proposed the classification of after-sales services from the perspective of cost saving, let alone a detailed study of such classification.​

Based on previous studies, this paper focuses on decision-making issues in the closed-loop supply chain of electronic products. It takes into account manufacturers’ potential motives for misreporting behavior in the real market and explores paths to further achieve supply chain coordination in the context of blockchain technology application. The main innovations of this study are as follows: First, based on the residual quality value of defective products, after-sales handling methods (repair or replacement) are classified, and the positive impact of quality control level on product market demand and the negative impact on after-sales rate are integrated into the development of the Stackelberg game model. Second, when coordinating supply chains with misreporting behavior, the elimination effect of blockchain technology on such behavior is considered, and complete supply chain transparency is taken as a necessary condition for coordination, thereby highlighting the key role of blockchain technology in supply chain coordination.

The main issues explored in this paper are as follows: In supply chains with different power structures, will manufacturer adopt misreporting strategy? What is the impact of misreporting on various stakeholders in the supply chain? When should supply chain introduce blockchain technology to eliminate the incentive for misreporting? What is the impact of product quality control effectiveness and quality elasticity coefficient on the supply chain? Does after-sales classification have a positive impact on the supply chain?

Problem description and hypothesis

This paper studies an electronic product supply chain consisting of a single manufacturer and a single retailer. The structural information of the supply chain is shown in Fig. 1.

Fig. 1
figure 1

The supply chain of electronic product containing classified after-sales.

Full size image

The retail (\(R\)) decides the retail price (\(p\)), and the manufacturer (\(M\)) decides the wholesale price (\(b\)) and the quality control level (\(f\)) of the product. Refer to Gui et al.36, the cost of improving quality control level is \(\frac{1}{2}hf^{2}\), where \(h\) is the quality cost coefficient, \(h > 0\).

Suppose that the market demand is doubly affected by retail price and quality control level, and is expressed as \(Q = Q_{0} - mp + nf\), where \(Q_{0}\) is the potential market size, \(m\) is the price elasticity coefficient, \(n\) is the quality elasticity coefficient, \(m > 0\), \(n > 0\).

Since the quality control level determines the average quality of products, the after-sales rate of the product is negatively affected by the quality control level. Referring to the description of the product return rate function by Zhang et al.37, the after-sales rate of product is expressed as \(K = k_{0} - gf\), where \(k_{0}\) is the initial after-sales rate, \(g\) is the quality control effect, \(g > 0\).

When the consumers find that the product has quality problems during the warranty period, they will apply for after-sales service to the retailer, and the retailer will transfer the after-sales responsibility to the manufacturer, and the manufacturer will provide classified after-sales service (repair or replacement) according to the quality residual value of the problem product. Let the quality residual value of the problem product be \(q_{x}\), \(q_{x} \in [q_{0} ,q_{t} ]\), \(q_{t} > q_{0} > 0\), and assume that \(q_{x}\) follows uniform distribution. In the interval \([q_{0} ,q_{t} ]\), there exists a quality standard \(q_{b}\) as after-sales classification reference, when \(q_{t} \ge q_{x} \ge q_{b}\), the after-sales plan given by the manufacturer is maintenance, and the maintenance cost \(c_{x1}\) is related to the quality residual value of the product, and \(\frac{{\partial c_{x1} }}{{\partial q_{x} }} < 0\), \(\frac{{\partial^{2} c_{x1} }}{{\partial^{2} q_{x} }} < 0\); when \(q_{b} > q_{x} \ge q_{0}\), the after-sales plan given by the manufacturer is replacement. Because the research involves the recycling and remanufacturing of the product, the calculation of replacement cost should consider the remanufacturing value of the product. If the profit from the second sale of the product after remanufacturing is \(z\), then the replacement cost of the product is \(c_{x2} = c - z\), where \(c\) is the production cost of the product, \(c - z > 0\). In addition, considering the actual situation, the maximum maintenance cost of the product is not higher than the replacement cost. To sum up, the expected after-sales cost of a problem product is:

$$l = \int {\begin{array}{*{20}c} {q_{t} } \\ {q_{b} } \\ \end{array} c_{x1} \frac{1}{{q_{t} - q_{0} }}dq_{x} } + c_{x2} \frac{{q_{b} - q_{0} }}{{q_{t} - q_{0} }}$$
(1)

Therefore, it can be seen that the supply chain after-sales loss is \(lKQ\).

On the basis of the above supply chain information, this paper considers that when the supply chain does not introduce blockchain technology, the production cost information is asymmetric, and the manufacturer has the incentive to misreport about the cost. The actual production cost of the product is \(c\). When the misreporting occurs, the misreporting cost published by the manufacturer is \(ec\), where \(e\) is the misreporting ratio, and \(e > 0\). When the supply chain introduces blockchain technology (Wang et al.38), the unit introduction cost of blockchain technology is \(c_{0}\), the supply chain information is fully transparent, and there is no misreporting, that is, \(e = 1\).

In addition, due to the low quantity of replacement and the complex cost structure of replacement, the impact of the misreporting ratio on replacement cost is not considered. Without loss of generality, the costs of sales and transportation of product are normalized to 0, and it is assumed that manufacturer and retailer are rational decision makers.

The parameter symbols and their meanings involved in this research are shown in Table 1.

Table 1 The parameter symbols and meanings.
Full size table

In this study, Stackelberg game theory (leader–follower game theory) with sequential decision-making characteristics was employed to model the supply chain. This theory has significant advantages in depicting the dynamic interaction among supply chain members. The specific construction method of the model is as follows:

Firstly, based on the market positioning of supply chain members (manufacturer and retailer), the profit function models for all members are established. By verifying the concavity of the profit function within its domain, it is ensured that the twice-differentiable function satisfies the condition that its second derivative is negative, thereby mathematically proving the existence of a unique global optimal solution for the objective function. In the solution process, the backward induction method is adopted: first, the optimal decision of the follower is derived with the goal of maximizing its profit, and then this result is substituted into the leader’s profit function to solve for the leader’s optimal strategy.

Model building without blockchain technology

When there is no blockchain technology in the supply chain, the translucency of supply chain information provides manufacturer with the motivation to misreport. This section focuses on exploring manufacturer’s misreporting under different power structures. Therefore, two decision models are constructed, namely, manufacturer-led decentralized decision model (M1) and retailer-led decentralized decision model (R1) under information asymmetry. In the two models, the actual profit functions of retailer and manufacturer as well as the open profit function of manufacturer are respectively:

$$\prod_{M(M1/R1)} = (b_{(M1/R1)} - c)Q_{(M1/R1)} - lK_{(M1/R1)} Q_{(M1/R1)} - \frac{1}{2}hf_{(M1/R1)}^{2}$$
(2)
$$\prod_{R(M1/R1)} = (p_{(M1/R1)} - b_{(M1/R1)} )Q_{(M1/R1)}$$
(3)
$$\prod_{M^{\prime\prime}(M1/R1)} = (b_{(M1/R1)} - e_{(M1/R1)} c)Q_{(M1/R1)} - lK_{(M1/R1)} Q_{(M1/R1)} - \frac{1}{2}hf_{(M1/R1)}^{2}$$
(4)

Because of the preemptive nature of misreporting, the manufacturer’s misreporting decision always has priority, regardless of whether the dominant power is in the hands of the manufacturer or the retailer. The supply chain profit (\(\prod_{C}\)) is the sum of the real profit of the manufacturer and the real profit of the retailer.

The M1 model

In the M1 model, the manufacturer first determines the misreporting rate \(\left( {e_{(M1)} } \right)\), then determines the quality control level \(\left( {f_{{\left( {M1} \right)}} } \right)\) and wholesale price \(\left( {b_{{\left( {M1} \right)}} } \right)\), and then the retailer determines the retail price \(\left( {p_{(M1)} } \right)\).

After solving the supply chain equilibrium decision in this model can be obtained as follows:

$$\left\{ {\begin{array}{*{20}l} {f_{(M1)}^{*} = \frac{{\left( {n + g{\mkern 1mu} l{\mkern 1mu} m} \right){\mkern 1mu} \left( {c{\mkern 1mu} e{\mkern 1mu} m - Q_{0} + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)}}{{g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + n^{2} }}} \hfill \\ {b_{(M1)}^{*} = \frac{\begin{gathered} k_{0} {\mkern 1mu} l{\mkern 1mu} n^{2} - 2{\mkern 1mu} Q_{0} {\mkern 1mu} h + c{\mkern 1mu} e{\mkern 1mu} n^{2} - 2{\mkern 1mu} h{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m + Q_{0} {\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m \hfill \\ + Q_{0} {\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} n - 2{\mkern 1mu} c{\mkern 1mu} e{\mkern 1mu} h{\mkern 1mu} m + g{\mkern 1mu} k_{0} {\mkern 1mu} l^{2} {\mkern 1mu} m{\mkern 1mu} n + c{\mkern 1mu} e{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n \hfill \\ \end{gathered} }{{g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + n^{2} }}} \hfill \\ {p_{(M1)}^{*} = \frac{\begin{gathered} k_{0} {\mkern 1mu} l{\mkern 1mu} n^{2} - 3{\mkern 1mu} Q_{0} {\mkern 1mu} h + c{\mkern 1mu} e{\mkern 1mu} n^{2} - h{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m + Q_{0} {\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m \hfill \\ + Q_{0} {\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} n - c{\mkern 1mu} e{\mkern 1mu} h{\mkern 1mu} m + g{\mkern 1mu} k_{0} {\mkern 1mu} l^{2} {\mkern 1mu} m{\mkern 1mu} n + c{\mkern 1mu} e{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n \hfill \\ \end{gathered} }{{g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + n^{2} }}} \hfill \\ \end{array} } \right.$$
(5)

The real profits of manufacturer, retailer and supply chain in M1 model are as follows:

$$\left\{ {\begin{array}{*{20}l} {\prod_{M(M1)}^{*} = - \frac{{h{\mkern 1mu} \left( \begin{gathered} Q_{0}^{2} - 2{\mkern 1mu} Q_{0} {\mkern 1mu} c{\mkern 1mu} m - 2{\mkern 1mu} Q_{0} {\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m - c^{2} {\mkern 1mu} e^{2} {\mkern 1mu} m^{2} \hfill \\ + 2{\mkern 1mu} c^{2} {\mkern 1mu} e{\mkern 1mu} m^{2} + 2{\mkern 1mu} c{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m^{2} + k_{0}^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} \hfill \\ \end{gathered} \right)}}{{2{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}}} \hfill \\ {\prod_{R(M1)}^{*} = \frac{{h^{2} {\mkern 1mu} m{\mkern 1mu} \left( {c{\mkern 1mu} e{\mkern 1mu} m - Q_{0} + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)^{2} }}{{\left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)^{2} }}} \hfill \\ {\prod_{C(M1)}^{*} = \frac{{h{\mkern 1mu} \left( {c{\mkern 1mu} e{\mkern 1mu} m - Q_{0} + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right){\mkern 1mu} \left( \begin{gathered} Q_{0} {\mkern 1mu} n^{2} - 6{\mkern 1mu} Q_{0} {\mkern 1mu} h{\mkern 1mu} m + 8{\mkern 1mu} c{\mkern 1mu} h{\mkern 1mu} m^{2} - 2{\mkern 1mu} c{\mkern 1mu} m{\mkern 1mu} n^{2} \hfill \\ + Q_{0} {\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} - 2{\mkern 1mu} c{\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{3} - g^{2} {\mkern 1mu} k_{0} {\mkern 1mu} l^{3} {\mkern 1mu} m^{3} \hfill \\ - 2{\mkern 1mu} c{\mkern 1mu} e{\mkern 1mu} h{\mkern 1mu} m^{2} + c{\mkern 1mu} e{\mkern 1mu} m{\mkern 1mu} n^{2} + 6{\mkern 1mu} h{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m^{2} - k_{0} {\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n^{2} \hfill \\ - 2{\mkern 1mu} g{\mkern 1mu} k_{0} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} {\mkern 1mu} n + 2{\mkern 1mu} Q_{0} {\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n + c{\mkern 1mu} e{\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{3} \hfill \\ - 4{\mkern 1mu} c{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m^{2} {\mkern 1mu} n + 2{\mkern 1mu} c{\mkern 1mu} e{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m^{2} {\mkern 1mu} n \hfill \\ \end{gathered} \right)}}{{2{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)^{2} }}} \hfill \\ \end{array} } \right.$$
(6)

Solving process of M1 model:

It is easy to prove that \(\prod_{R(M1)}\) is a concave function with respect to \(p_{(M1)}\). Let \(\frac{{\partial \prod_{R(M1)} }}{{\partial p_{(M1)} }} = 0\), and solve \(P^{\prime}_{(M1)} = \frac{{Q_{0} + b{\mkern 1mu} m + f{\mkern 1mu} n}}{{2{\mkern 1mu} m}}\). By substituting \(P^{\prime}_{(M1)}\) into \(\prod^{\prime\prime}_{M(M1)}\), it is easy to find that the second-order Heisser matrix of \(\prod^{\prime\prime}_{M(M1)}\) with respect to \(f_{(M1)}\) and \(b_{(M1)}\) is \(H_{1} = \left( {\begin{array}{*{20}c} {g{\mkern 1mu} l{\mkern 1mu} n - h} & {\frac{n}{2} - \frac{{g{\mkern 1mu} l{\mkern 1mu} m}}{2}} \\ {\frac{n}{2} - \frac{{g{\mkern 1mu} l{\mkern 1mu} m}}{2}} & { - m} \\ \end{array} } \right)\), and \(g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + n^{2} < 0\) (denoted as condition 1) satisfies the negative definite of the Heisser matrix. This means that under condition 1, there is an equilibrium solution that maximizes \(\prod_{M(M1)}\). Let \(\frac{{\partial \prod_{M(M1)}^{^{\prime\prime}} }}{{\partial f_{(M1)} }} = 0\) and \(\frac{{\partial \prod_{M(M1)}^{^{\prime\prime}} }}{{\partial b_{(M1)} }} = 0\), we can get \(f_{(M1)}^{*}\) and \(b_{(M1)}^{*}\). Substituting \(f_{(M1)}^{*}\) and \(b_{(M1)}^{*}\) into \(p_{(M1)}\) can solve \(p_{(M1)}^{*}\), and finally it is easy to solve \(\prod_{M(M1)}^{*}\), \(\prod_{R(M1)}^{*}\) and \(\prod_{C(M1)}^{*}\).

Proposition 1

In the M1 model, the optimal misreporting ratio for manufacturer is 1.

Proof

By combining condition 1, we can get.

$$\frac{{\partial^{2} \prod_{M(M1)}^{*} }}{{\partial^{2} e_{(M1)} }} = \frac{{c^{2} {\mkern 1mu} h{\mkern 1mu} m^{2} }}{{g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + n^{2} }} < 0$$

That is, there is an optimal misreporting ratio \(e_{(M1)}^{*}\) that makes the manufacturer’s profit optimal. Let \(\frac{{\partial \prod_{M(M1)}^{*} }}{{\partial e_{(M1)} }} = 0\), we can get \(e_{(M1)}^{*} = 1\). Proposition 1 is proved.

Remark 1

Proposition 1 shows that when the manufacturer has the decision advantage, even in the presence of misreporting conditions, it will not choose to misreport because the dominant advantage has already optimized the manufacturer’s profit. At this point, there is no misreporting behavior in the supply chain, and retailer do not need to consider introducing blockchain technology to eliminate manufacturer’s misreporting incentive.

The R1 model

In the R1 model, the manufacturer first determines the misreporting ratio (\(e_{(R1)}\)), then the retailer determines the retail price (\(p_{(R1)}\)), and finally the manufacturer determines the quality control level (\(f_{(R1)}\)) and the wholesale price (\(b_{(R1)}\)).

The equilibrium decision in R1 model is:

$$\left\{ {\begin{array}{*{20}l} {f_{(R1)}^{*} = \frac{{\left( {n + g{\mkern 1mu} l{\mkern 1mu} m} \right){\mkern 1mu} \left( {c{\mkern 1mu} e{\mkern 1mu} m - Q_{0} + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)}}{{2{\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 4{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + 2{\mkern 1mu} n^{2} }}} \hfill \\ {b_{(R1)}^{*} = \frac{\begin{gathered} k_{0} {\mkern 1mu} g^{2} {\mkern 1mu} l^{3} {\mkern 1mu} m^{2} + c{\mkern 1mu} e{\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + Q_{0} {\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m + 3{\mkern 1mu} k_{0} {\mkern 1mu} g{\mkern 1mu} l^{2} {\mkern 1mu} m{\mkern 1mu} n + 3{\mkern 1mu} c{\mkern 1mu} e{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n \hfill \\ + Q_{0} {\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} n - 3{\mkern 1mu} h{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m + 2{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} n^{2} - 3{\mkern 1mu} c{\mkern 1mu} e{\mkern 1mu} h{\mkern 1mu} m + 2{\mkern 1mu} c{\mkern 1mu} e{\mkern 1mu} n^{2} - Q_{0} {\mkern 1mu} h \hfill \\ \end{gathered} }{{2{\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 4{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + 2{\mkern 1mu} n^{2} }}} \hfill \\ {p_{(R1)}^{*} = \frac{\begin{gathered} 2{\mkern 1mu} Q_{0} {\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + k_{0} {\mkern 1mu} g{\mkern 1mu} l^{2} {\mkern 1mu} m^{2} {\mkern 1mu} n + c{\mkern 1mu} e{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m^{2} {\mkern 1mu} n + 3{\mkern 1mu} Q_{0} {\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n \hfill \\ - h{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m^{2} + k_{0} {\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n^{2} - c{\mkern 1mu} e{\mkern 1mu} h{\mkern 1mu} m^{2} + c{\mkern 1mu} e{\mkern 1mu} m{\mkern 1mu} n^{2} - 3{\mkern 1mu} Q_{0} {\mkern 1mu} h{\mkern 1mu} m + Q_{0} {\mkern 1mu} n^{2} \hfill \\ \end{gathered} }{{2{\mkern 1mu} m{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}}} \hfill \\ \end{array} } \right.$$
(7)

In R1 model, the real profits of manufacturer, retailer and supply chains are as follows:

$$\left\{ {\begin{array}{*{20}l} {\prod_{M(R1)}^{*} = - \frac{{h{\mkern 1mu} \left( \begin{gathered} Q_{0}^{2} + 2{\mkern 1mu} Q_{0} {\mkern 1mu} c{\mkern 1mu} e{\mkern 1mu} m - 4{\mkern 1mu} Q_{0} {\mkern 1mu} c{\mkern 1mu} m - 2{\mkern 1mu} Q_{0} {\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m - 3{\mkern 1mu} c^{2} {\mkern 1mu} e^{2} {\mkern 1mu} m^{2} \hfill \\ + 4{\mkern 1mu} c^{2} {\mkern 1mu} e{\mkern 1mu} m^{2} - 2{\mkern 1mu} c{\mkern 1mu} e{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m^{2} + 4{\mkern 1mu} c{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m^{2} + k_{0}^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} \hfill \\ \end{gathered} \right)}}{{8{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}}} \hfill \\ {\prod_{R(R1)}^{*} = - \frac{{h{\mkern 1mu} \left( {c{\mkern 1mu} e{\mkern 1mu} m - Q_{0} + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)^{2} }}{{4{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}}} \hfill \\ {\prod_{C(R1)}^{*} = - \frac{{h{\mkern 1mu} \left( \begin{gathered} 3{\mkern 1mu} Q_{0}^{2} - 2{\mkern 1mu} Q_{0} {\mkern 1mu} c{\mkern 1mu} e{\mkern 1mu} m - 4{\mkern 1mu} Q_{0} {\mkern 1mu} c{\mkern 1mu} m - 6{\mkern 1mu} Q_{0} {\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m - c^{2} {\mkern 1mu} e^{2} {\mkern 1mu} m^{2} \hfill \\ + 4{\mkern 1mu} c^{2} {\mkern 1mu} e{\mkern 1mu} m^{2} + 2{\mkern 1mu} c{\mkern 1mu} e{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m^{2} + 4{\mkern 1mu} c{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m^{2} + 3{\mkern 1mu} k_{0}^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} \hfill \\ \end{gathered} \right)}}{{8{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}}} \hfill \\ \end{array} } \right.$$
(8)

Solving process of R1 model

Let \(p_{(R1)} = b_{(R1)} + x_{(R1)}\), it is easy to find that the second-order Heisser matrix of \(\prod_{M(R1)}\) with respect to \(b_{(R1)}\) and \(f_{(R1)}\) is \(H_{2} = \left( {\begin{array}{*{20}c} {2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} n - h} & {n - g{\mkern 1mu} l{\mkern 1mu} m} \\ {n - g{\mkern 1mu} l{\mkern 1mu} m} & { - 2{\mkern 1mu} m} \\ \end{array} } \right)\).

And \(g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} < 0\)( denoted as condition 2) satisfies the negative definite of the Heisser matrix. Let \(\frac{{\partial \prod_{M(R1)}^{^{\prime\prime}} }}{{\partial f_{(R1)} }} = 0\) and \(\frac{{\partial \prod_{M(R1)}^{^{\prime\prime}} }}{{\partial b_{(R1)} }} = 0\), we can get \(b_{(R1)}{\prime}\) and \(f_{(R1)}{\prime}\). Substituting \(b_{(R1)}{\prime}\) and \(f_{(R1)}{\prime}\) into \(\prod_{R(R1)}\), let \(\frac{{\partial \prod_{R(R1)} }}{{\partial x_{(R1)} }} = 0\), we can get \(x_{(R1)}^{*}\). Then substituting \(x_{(R1)}^{*}\) into \(b_{(R1)}{\prime}\) and \(f_{(R1)}{\prime}\), we can get \(f_{(R1)}^{*}\) and \(b_{(R1)}^{*}\), \(p_{(R1)}^{*} = b_{(R1)}^{*} + x_{(R1)}^{*}\). Finally it is easy to solve \(\prod_{M(R1)}^{*}\), \(\prod_{R(R1)}^{*}\) and \(\prod_{C(R1)}^{*}\).

Proposition 2

When the misreporting ratio is \(e_{(R1)}^{*}\) (\(e_{(R1)}^{*} = \frac{{Q_{0} + 2{\mkern 1mu} c{\mkern 1mu} m - k_{0} {\mkern 1mu} l{\mkern 1mu} m}}{{3{\mkern 1mu} c{\mkern 1mu} m}}\)), the manufacturer’s profit is the optimal; When the misreporting ratio is \(e_{(R1)}^{**}\) (\(e_{(R1)}^{**} = \frac{{2{\mkern 1mu} c{\mkern 1mu} m - Q_{0} + k_{0} {\mkern 1mu} l{\mkern 1mu} m}}{{c{\mkern 1mu} m}}\)), the supply chain profit is optimal, and \(e_{(R1)}^{*} > 1 > e_{(R1)}^{**}\). In addition, the manufacturer’s misreporting status and the profit changes of each member of the supply chain under different misreporting ratios are shown in Table 2.

Table 2 The impact of misreporting on the supply chain.
Full size table

Proof

From condition 2, it can be deduced that.

$$\frac{{\partial^{2} \prod_{M(R1)}^{*} }}{{\partial^{2} e_{(R1)} }} = \frac{{3{\mkern 1mu} c^{2} {\mkern 1mu} h{\mkern 1mu} m^{2} }}{{4{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}} < 0,$$

that is, there is a misreporting ratio that makes \(\prod_{M(R1)}^{*}\) optimal. Let \(\frac{{\partial \prod_{M(R1)}^{*} }}{{\partial e_{(R1)} }} = 0\), we can get \(e_{(R1)}^{*} = \frac{{Q_{0} + 2{\mkern 1mu} c{\mkern 1mu} m - k_{0} {\mkern 1mu} l{\mkern 1mu} m}}{{3{\mkern 1mu} c{\mkern 1mu} m}}\). Similarly, from \(\frac{{\partial^{2} \prod_{C(R1)}^{*} }}{{\partial^{2} e_{(R1)} }} = \frac{{c^{2} {\mkern 1mu} h{\mkern 1mu} m^{2} }}{{4{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}} < 0\), we know that there is a misreporting ratio that makes \(\prod_{C(R1)}^{*}\) optimal. Let \(\frac{{\partial \prod_{C(R1)}^{*} }}{{\partial e_{(R1)} }} = 0\), we can get \(e_{(R1)}^{**} = \frac{{2{\mkern 1mu} c{\mkern 1mu} m - Q_{0} + k_{0} {\mkern 1mu} l{\mkern 1mu} m}}{{c{\mkern 1mu} m}}\). Considering the practical significance of the decision (\(f_{(R1)}^{*} > 0\)), \(e_{(R1)} < \frac{{Q_{0} - k_{0} lm}}{cm}\) can be proved in combination with condition 2, and \(e_{(R1)}^{*} > 1 > e_{(R1)}^{**}\) can be deduced. Since both \(\prod_{M(R1)}^{*}\) and \(\prod_{C(R1)}^{*}\) are concave functions of \(e_{(R1)}\), proposition 2 is proved.

Remark 2

Proposition 2 shows that when the misreporting ratio increases, retailer and supply chain profits will decline accordingly; the manufacturer’s profit will increase first and then decrease (the maximum value is reached when \(e_{(R1)} = e_{(R1)}^{*}\)). When the manufacturer underreports the cost, the manufacturer’s profit decreases as the misreporting ratio decreases, while the supply chain’s profit increases and then decreases (the maximum value is reached when \(e_{(R1)} = e_{(R1)}^{**}\)). And when the underreporting ratio is higher than \(e_{(R1)}^{**}\), the retailer’s profit increases as the misreporting ratio decreases. The manufacturer is a rational self-interested party, and its purpose of misreporting is to realize the optimization of its own interest, so the manufacturer finally adopts the misreporting ratio of \(e_{(R1)}^{*}\). In this case, the manufacturer makes the most profit from misreporting, while the retailer and the supply chain will lose some profit.\(e_{(R1)}^{*}\) is the ideal misreporting ratio for manufacturer, and to further explore the influence of misreporting on the profits of each member of the supply chain, proposition 3 can be obtained by comparing the profits of manufacturer and retailer at \(e_{(R1)} = 1\) and \(e_{(R1)} = e_{(R1)}^{*}\) respectively.

Proposition 3

When \(e_{(R1)} = 1\), \(\prod_{R(R1)}^{*} > \prod_{M(R1)}^{*}\); when \(e_{(R1)} = e_{(R1)}^{*}\), \(\prod_{R(R1)}^{*} < \prod_{M(R1)}^{*}\).

Proof

If \(e_{(R1)} = 1\), then \(\prod_{R(R1)}^{*} - \prod_{M(R1)}^{*} = - \frac{{h{\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)^{2} }}{{8{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}}\), thus combining condition 1, we can get \(\prod_{R(R1)}^{*} > \prod_{M(R1)}^{*}\). If \(e_{(R1)} = e_{(R1)}^{*}\), then \(\prod_{R(R1)}^{*} - \prod_{M(R1)}^{*} = \frac{{h{\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)^{2} }}{{18{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}}\). Thus we can get \(\prod_{R(R1)}^{*} < \prod_{M(R1)}^{*}\). Proposition 3 is proved.

Remark 3

Proposition 3 shows that when the manufacturer does not misreport, the retailer, as the dominant player in the supply chain decision, has the decision-making advantage and is able to gain more profit in the game. And once the manufacturer tries to maximize its profit by misreporting, the retailer will lose its dominant player advantage and its profit will be lower than that of the manufacturer.

Model building with blockchain technology

Two models are constructed in this section, namely, the retailer-led decentralized decision model (R2) and the collaborative decision model (C1) after the introduction of blockchain technology, which mainly explore the changes of supply chain decision and profits of each member before and after the introduction of blockchain technology, and provide theoretical basis for the coordination of supply chain.

The R2 model

In order to avoid misreporting of the manufacturer, retailer will introduce blockchain technology to realize the transparency of all information in the supply chain when it has the dominant advantage. In this model, the cost of the introduction of blockchain technology is borne by the retailer, and the profit functions of the manufacturer and the retailer are respectively:

$$\prod_{M(R2)} = (b_{(R2)} - c)Q_{(R2)} - lK_{(R2)} Q_{(R2)} - \frac{1}{2}hf_{(R2)}^{2}$$
(9)
$$\prod_{R} = (p_{(R2)} - b_{(R2)} - c_{0} )Q_{(R2)}$$
(10)

In the R2 model, retailer gives priority to the decision of the retail price (\(p_{(R2)}\)), and manufacturer then decides the wholesale price (\(b_{(R2)}\)) and quality control level (\(f_{(R2)}\)). The equilibrium decision in this model is:

$$\left\{ {\begin{array}{*{20}l} {f_{(R2)}^{*} = \frac{{\left( {n + g{\mkern 1mu} l{\mkern 1mu} m} \right){\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + c_{0} {\mkern 1mu} m + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)}}{{2{\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 4{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + 2{\mkern 1mu} n^{2} }}} \hfill \\ {b_{(R2)}^{*} = \frac{\begin{gathered} 2{\mkern 1mu} c{\mkern 1mu} n^{2} - Q_{0} {\mkern 1mu} h + 2{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} n^{2} - 3{\mkern 1mu} c{\mkern 1mu} h{\mkern 1mu} m + c_{0} {\mkern 1mu} h{\mkern 1mu} m - 3{\mkern 1mu} h{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m \hfill \\ + c{\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} - c_{0} {\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + g^{2} {\mkern 1mu} k_{0} {\mkern 1mu} l^{3} {\mkern 1mu} m^{2} + Q_{0} {\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m \hfill \\ + Q_{0} {\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} n + 3{\mkern 1mu} c{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - c_{0} {\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n + 3{\mkern 1mu} g{\mkern 1mu} k_{0} {\mkern 1mu} l^{2} {\mkern 1mu} m{\mkern 1mu} n \hfill \\ \end{gathered} }{{2{\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 4{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + 2{\mkern 1mu} n^{2} }}} \hfill \\ {p_{(R2)}^{*} = \frac{\begin{gathered} Q_{0} {\mkern 1mu} n^{2} - 3{\mkern 1mu} Q_{0} {\mkern 1mu} h{\mkern 1mu} m - c{\mkern 1mu} h{\mkern 1mu} m^{2} - c_{0} {\mkern 1mu} h{\mkern 1mu} m^{2} + c{\mkern 1mu} m{\mkern 1mu} n^{2} \hfill \\ + c_{0} {\mkern 1mu} m{\mkern 1mu} n^{2} + 2{\mkern 1mu} Q_{0} {\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} - h{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m^{2} + k_{0} {\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n^{2} \hfill \\ + g{\mkern 1mu} k_{0} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} {\mkern 1mu} n + 3{\mkern 1mu} Q_{0} {\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n + c{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m^{2} {\mkern 1mu} n + c_{0} {\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m^{2} {\mkern 1mu} n \hfill \\ \end{gathered} }{{2{\mkern 1mu} m{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}}} \hfill \\ \end{array} } \right.$$
(11)

The profits of manufacturer, retailer and supply chain in R2 model are respectively:

$$\left\{ {\begin{array}{*{20}c} {\prod_{M(R2)}^{*} = - \frac{{h{\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + c_{0} {\mkern 1mu} m + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)^{2} }}{{8{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}}} \\ {\prod_{R(R2)}^{*} = - \frac{{h{\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + c_{0} {\mkern 1mu} m + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)^{2} }}{{4{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}}} \\ {\prod_{C(R2)}^{*} = - \frac{{3{\mkern 1mu} h{\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + c_{0} {\mkern 1mu} m + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)^{2} }}{{8{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}}} \\ \end{array} } \right.$$
(12)

If and only if, under condition 2, the above equilibrium decision exists. The solution of R2 model is similar to M1 model and R1 model, so it will not be repeated.

Proposition 4

When the blockchain technology unit introduces cost changes, the supply chain strategy and the profits of each member will also change, as shown in Table 3.

Proof

Let \(\prod_{R(R2)}^{*} \ge \prod_{R(R1)}^{*}\), we can get \(9\left( {cm - Q_{0} + c_{0} m + k_{0} lm} \right)^{2}\) \(\ge 4\left( {cm - Q_{0} + k_{0} lm} \right)^{2}\). According to the non-negativity of \(f_{(R2)}^{*}\), we can easily obtain \(c{\mkern 1mu} m - Q_{0} + c_{0} {\mkern 1mu} m + k_{0} {\mkern 1mu} l{\mkern 1mu} m < 0\). Then \(0 < c_{0} \le \frac{{Q_{0} - cm - k_{0} lm}}{3m}\).

Table 3 Impact of \(c_{0}\) on supply chain strategy and profits of each member.
Full size table

Let \(\prod_{C(R2)}^{*} \ge \prod_{C(R1)}^{*}\), we can get \(0 < c_{0} \le \frac{{(3\sqrt 3 - 2\sqrt 5 )(Q_{0} - cm - k_{0} lm)}}{3\sqrt 3 m}\).

According to \(\frac{{\prod_{M(R2)}^{*} }}{{\prod_{M(R1)}^{*} }} = \frac{{3{\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + c_{0} {\mkern 1mu} m + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)^{2} }}{{4{\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)^{2} }} < 1\), \(\prod_{M(R2)}^{*} < \prod_{M(R1)}^{*}\) can be proved.

According to \(\frac{{f_{(R2)}^{*} }}{{f_{(R1)}^{*} }} = \frac{{3{\mkern 1mu} c{\mkern 1mu} m - 3{\mkern 1mu} Q_{0} + 3{\mkern 1mu} c_{0} {\mkern 1mu} m + 3{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m}}{{2{\mkern 1mu} c{\mkern 1mu} m - 2{\mkern 1mu} Q_{0} + 2{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m}} > 1\), \(f_{(R2)}^{*} > f_{(R1)}^{*}\) can be proved. Proposition 4 is proved.

Remark 4

Proposition 4 shows that (1) when the introduction cost of blockchain technology satisfies condition \(0 < c_{0} < \frac{{Q_{0} - cm - k_{0} lm}}{3m}\), the retailer can profit by introducing blockchain technology. When \(c_{0} \ge \frac{{Q_{0} - cm - k_{0} lm}}{3m}\), the retailer gives up the introduction of blockchain technology due to the high input cost; (2) When \(0 < c_{0} \le \frac{{(3\sqrt 3 - 2\sqrt 5 )(Q_{0} - cm - k_{0} lm)}}{3\sqrt 3 m}\), the profit of the supply chain will be enhanced following the implementation of blockchain technology, otherwise, introducing blockchain technology will diminish the profit of the supply chain; (3) Manufacturer’s profits fell after implementing blockchain technology due to the absence of the misreporting condition and lacking dominant decision advantage; (4) The introduction of blockchain technology contributes to enhancing quality control within the supply chain.

The C2 model

Collaborative decision means that manufacturer and retailer use information they have known to make joint decisions, and the decision result can be used as a theoretical reference for supply chain coordination. However, the collaborative decision of supply chain members requires full transparency of supply chain information, and there is no possibility of misreporting information. Therefore, this study proposes that the construction of collaborative decision model depends on the introduction of blockchain technology, and the introduction cost is borne by the supply chain. In the C2 model, the total profit function of the supply chain is:

$$\prod_{C(C2)} = (p_{(C2)} - c - c_{0} )Q_{(C2)} - lK_{(C2)} Q_{(C2)} - \frac{1}{2}hf_{C2}^{2}$$
(13)

After solving, the equilibrium decision in C2 model is:

$$\left\{ {\begin{array}{*{20}l} {f_{(C2)}^{*} = \frac{{\left( {n + g{\mkern 1mu} l{\mkern 1mu} m} \right){\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + c_{0} {\mkern 1mu} m + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)}}{{g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} }}} \hfill \\ {p_{(C2)}^{*} = \frac{\begin{gathered} c{\mkern 1mu} n^{2} - Q_{0} {\mkern 1mu} h + c_{0} {\mkern 1mu} n^{2} + k_{0} {\mkern 1mu} l{\mkern 1mu} n^{2} - c{\mkern 1mu} h{\mkern 1mu} m \hfill \\ - c_{0} {\mkern 1mu} h{\mkern 1mu} m - h{\mkern 1mu} k_{0} {\mkern 1mu} l{\mkern 1mu} m + Q_{0} {\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m + Q_{0} {\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} n \hfill \\ + c{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n + c_{0} {\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n + g{\mkern 1mu} k_{0} {\mkern 1mu} l^{2} {\mkern 1mu} m{\mkern 1mu} n \hfill \\ \end{gathered} }{{g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} }}} \hfill \\ \end{array} } \right.$$
(14)

This decision is the optimal decision of the supply chain system, at this time, the total profit of the supply chain has reached the highest, which is:

$$\prod_{C(C2)}^{*} = - \frac{{h{\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + c_{0} {\mkern 1mu} m + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)^{2} }}{{2{\mkern 1mu} g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 4{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 4{\mkern 1mu} h{\mkern 1mu} m + 2{\mkern 1mu} n^{2} }}$$
(15)

The solution of C2 model is similar to M1 model and R1 model, so it will not be repeated.

Proposition 5

\(f_{(C2)}^{*} > f_{(R2)}^{*}\), \(p_{(C2)}^{*} < p_{(R2)}^{*}\), \(\prod_{(C2)}^{*} > \prod_{(R2)}^{*}\)

Proof

Combining condition 2, it is easy to prove.

$$f_{(C2)}^{*} - f_{(R2)}^{*} = \frac{{\left( {n + g{\mkern 1mu} l{\mkern 1mu} m} \right){\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + c_{0} {\mkern 1mu} m + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)}}{{2{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}} > 0$$
$$p_{(C2)}^{*} - p_{(R2)}^{*} = \frac{{\left( {n^{2} + g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - h{\mkern 1mu} m} \right){\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + c_{0} {\mkern 1mu} m + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)}}{{2{\mkern 1mu} m{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}} < 0$$

and \(\prod_{C(C2)}^{*} - \prod_{C(R2)}^{*} = - \frac{{h{\mkern 1mu} \left( {c{\mkern 1mu} m - Q_{0} + c_{0} {\mkern 1mu} m + k_{0} {\mkern 1mu} l{\mkern 1mu} m} \right)^{2} }}{{8{\mkern 1mu} \left( {g^{2} {\mkern 1mu} l^{2} {\mkern 1mu} m^{2} + 2{\mkern 1mu} g{\mkern 1mu} l{\mkern 1mu} m{\mkern 1mu} n - 2{\mkern 1mu} h{\mkern 1mu} m + n^{2} } \right)}} > 0\) Proposition 5 is proved.

Remark 5

Proposition 5 shows that the collaborative decision model leads to a reduction in product retail price, an increase in quality control level and supply chain profit. This implies that lower retail price and higher quality control level are advantageous decisions for the supply chain. Since the goal of collaborative decision is to optimize the profit of the supply chain, \(f_{(C2)}^{*}\) and \(p_{(C2)}^{*}\) can be used as reference decisions for supply chain coordination, and \(\prod_{C(C2)}^{*}\) represents the ultimate goal of supply chain profit optimization.

Contract coordination

According to proposition 5, achieving optimal supply chain profit is challenging even with full transparency of supply chain information due to the decentralized decision of manufacturer and retailer. Referring to the decision result of collaborative decision, this paper utilizes contract to coordinate the supply chain with decentralized decision under the environment of introducing blockchain technology to achieve the goal of optimal supply chain decision. To facilitate differentiation, the supply chain decision and profit in coordination are labeled with “S2”.

The coordination of contract is divided into three steps. Step 1: The supply chain introduces blockchain technology, and the cost of introduction is shared by all members. Step 2: Manufacturer and retailer make corresponding decisions based on the results of collaborative decision. Step 3: The members of the supply chain are required to achieve the goal so that each of them can benefit from the contract through various forms of benefit transfer.

The first step is to establish an environment of information transparency for coordinating the supply chain. The second step ensures the overall coordination effect of the contract on the supply chain. This is because when \(p_{(S2)} = p_{(C2)}^{*}\) and \(f_{(S2)} = f_{(C2)}^{*}\), the total profit of the supply chain in S2 model can reach its optimum level, denoted as \(\prod_{C(S2)} = \prod_{C(C2)}^{*}\). At this point, the manufacturer’s and retailer’s profits are respectively:

$$\prod_{M(S2)} = \left( {b_{(s2)} - c - lK_{c2} } \right)\left( {Q_{0} - mp_{(C2)}^{*} + nf_{(C2)}^{*} } \right) - \frac{1}{2}hf_{(c2)}^{*\,2}$$
(16)
$$\prod_{R(S2)} = (p_{(C2)}^{*} - b_{(S2)} - c_{0} )(Q_{0} - mp_{(C2)}^{*} + nf_{(C2)}^{*} )$$
(17)

The third step involves ensuring the effective implementation of the contract. It should be noted that optimizing the overall profitability of the supply chain does not necessarily guarantee benefits for every member involved in the contract. When the deciding is done according to the requirements of step 2, if one member’s profit decreases, it becomes challenging for all members to unanimously accept the contract. Consequently, those members who generate higher profit from the contract should be willing to share their gains with those who experience lower profits or even losses. There are various ways to distribute these profits; however, the ultimate objective remains that each supply chain member derives profitability from the contract.

In this study, \(b_{(S2)}\) is regarded as the benefit transfer coefficient, and the benefit transfer among the members of the supply chain is realized by adjusting \(b_{(S2)}\). \(b_{(S2)} > 0\) represents the retailer’s transfer of benefits to the manufacturer, \(b_{(S2)} < 0\) represents the transfer of benefits from the manufacturer to the retailer. Under the requirements of Step 3 of the contract, the profits of each member of the supply chain before and after supply chain coordination shall meet:

$$\left\{ {\begin{array}{*{20}c} {\prod_{M(S2)} \ge \prod_{M(R2)}^{*} } \\ {\prod_{R(S2)} \ge \prod_{R(R2)}^{*} } \\ \end{array} } \right.$$
(18)

Formula (18) can be used as a necessary condition for contract coordination, and the value range of \(b_{(S2)}\) can be solved as follows:

$$\frac{{\prod_{M(R2)}^{*} + \frac{1}{2}hf_{(C2)}^{*\,2} }}{{Q_{(C2)}^{*} }} + c + l\left( {K_{0} - gf_{{\left( {C2} \right)}}^{*} } \right) \le b_{{\left( {s2} \right)}} \le \frac{{ - \prod_{R(R2)}^{*} }}{{Q_{{\left( {C2} \right)}}^{*} }} + p_{{\left( {C2} \right)}}^{*} - c_{0}$$
(19)

In Eq. (19), \(Q_{(C2)}^{*} = Q_{0} - mp_{(C2)}^{*} + nf_{(C2)}^{*}\).

If \(b_{(S2)}\) takes a value within the above interval, all members of the supply chain can benefit from the contract. However, the size of \(b_{(S2)}\) is related to the income of manufacturer and retailer, so its specific value depends on the internal negotiations between manufacturer and retailer. This leads to proposition 6.

Proposition 6

When \(p_{(S2)} = p_{(C2)}^{*}\), \(f_{(S2)} = f_{(C2)}^{*}\), and the value of \(b_{(S2)}\) satisfies Eq. (19), the electronic product supply chain is coordinated and Pareto improvement is realized.

Example analysis

This section verifies the above research propositions and further explores the impact of key parameters on the supply chain. The assignment of the main parameters is as follows:

  1. (1)

    In the calculation example, considering the change of maintenance cost with quality residual value, it is reasonable to depict the maintenance cost function as a quadratic function about quality residual value, expressed as \(c_{x1} = \varphi q_{x}^{2} + \rho\),\(\varphi < 0\),\(\rho > 0\). The product quality residual value is divided into ten reference levels, namely \(q_{0} = 1\), \(q_{t} = 11\). Let \(q_{b} = 4\), which means that when the product quality residual value is within the range \([1,^{{}} 4]\), the supply chain provides a replacement service; while when the product quality residual value is within the range \((4,_{{}} 11]\), the supply chain provides a repair service.

  2. (2)

    The after-sales rate of electronic products is closely related to quality control and product attributes. For simple electronic products, if strict quality control measures are implemented, the after-sales rate can be as low as less than 1%; while for complex electronic products, if effective quality control measures are not implemented, the after-sales rate may exceed 10%. To conduct an intuitive analysis of the impact of quality control on the after-sales rate, in this example, let \(k_{0} = 0.1\), indicating that the initial after-sales rate of the electronic products is relatively high.

  3. (3)

    There are differences in the preferences of various consumer groups regarding the quality and price of electronic products. Specifically, the groups with stronger purchasing power tend to pay more attention to product quality, while the groups with relatively weaker purchasing power usually give higher priority to product prices. In this example, the initial assignment sets the preference of consumers for price slightly higher than for quality, that is, \(m > n\). Refer to Reference39, set \(m = 0.6\) and \(n = 0.5\).

Based on the studies of Zhang et al.37 and Ren et al.40, the values of the remaining parameters were determined according to the actual market situation of electronic products and the assumptions of the model. All parameter values are summarized in Table 4.

Table 4 Parameter assignment.
Full size table

The impact of \(e\) and \(c_{0}\) on the supply chain

In order to explore the impact of the misreporting ratio (\(c_{0}\)) on the profits of each member of the supply chain, Fig. 2 is drawn.

Fig. 2
figure 2

The impact of \(c_{0}\) on the profits of each member of the supply chain.

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As can be seen from Fig. 2, when the manufacturer underreports the production cost, with the decrease of the underreporting ratio, the profit of the supply chain and the profit of the retailer show an upward trend, while the profit of the manufacturer shows a downward trend. When the manufacturer overreports the production cost, with the increase of the overreporting ratio, the profit of supply chain and the profit of retailer show a downward trend, the manufacturer’s profit does not show a monotonous change trend (first increase and then decrease), and the profit reaches a peak when the misreporting ratio is about 2.8782. When there is asymmetric cost information in the supply chain, the manufacturer’s misreporting behavior generally aims at maximizing its own interests. Therefore, the manufacturer’s final decision on the misreporting ratio is unfavorable to the supply chain and the retailer, and the retailer should eliminate the manufacturer’s misreporting motivation by introducing blockchain technology and other ways.

Retailer will only consider introducing blockchain technology when the unit introduction cost (\(c_{0}\)) of blockchain technology meets certain conditions. Figure 3 shows that the impact of until introduction cost of blockchain technology on the profit of each member of the supply chain.

Fig. 3
figure 3

The impact of \(c_{0}\) on the profit of each member of the supply chain.

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As can be seen from Fig. 3, when the unit introduction cost of blockchain technology is high, although the introduction of blockchain technology can eliminate misreporting, retailer will suffer losses due to high input cost, and ultimately chooses not to introduce it. After numerical calculation, it can be obtained that: when \({\text{c}}_{0} { > 46}{\text{.9542}}\), retailer gives up the introduction of blockchain technology; When \({\text{c}}_{0} \le {46}{\text{.9542}}\), retailer chooses to introduce blockchain technology. When retailer chooses to introduce, both manufacturer profit and supply chain profit are negatively correlated with blockchain unit introduction cost. In addition, within the interval \((0,46.9542)\), there is a fixed value, when \({\text{c}}_{0}\) greater than this value, the introduction of blockchain technology is bad for supply chain profit; When \({\text{c}}_{0}\) it is less than this value, the introduction of blockchain technology is beneficial to supply chain profit. After numerical calculation, the fixed value is \({19}{\text{.6274}}\).

Analysis of contract coordination effect

To ensure that retailer takes the initiative to introduce blockchain technology in R2 model, let \(c_{0} = 10\). According to proposition 6, when the profit transfer coefficient \(b_{(S2)}\) fluctuates within the interval \(\left[ {42.17,58.53} \right]\), both the manufacturer and the retailer can profit from the contract. In order to verify this proposition, when analyzing the impact of contract coordination, the value interval of \(b_{(S2)}\) is set as \(\left[ {40,60} \right]\), and the relevant results are shown in Table 5.

Table 5 Numerical table of contract coordination effect under different \(b_{(S2)}\).
Full size table

According to Table 5, the contract can be successfully coordinated only when the value of \(b_{(S2)}\) is in the interval \(\left[ {42.17,58.53} \right]\). When \(b_{(S2)}\) is not in this range, the contract will be difficult to be accepted by all members of the supply chain due to the decline in the profit of the manufacturer or retailer, that is, the contract coordination is unsuccessful. \(b_{(S2)}\) refers to the profit transferring from the retailer to the manufacturer. When \(b_{(S2)}\) is larger, the retailer’s profit will be lower, the manufacturer’s profit will be higher, and the supply chain profit will not be affected. Compared with contract coordination before, the quality control level and supply chain profit after contract coordination have been significantly improved.

Sensitivity analysis of "\(g\)" and"\(n\)"

Let \(c_{0} = 10\). The effects of "\(g\)(The quality control effect) " and "\(n\)( The quality elasticity coefficient) " on supply chain profit and quality control level in S2/C2 model are shown in Fig. 4.

Fig. 4
figure 4

The impact of "\(g\)" and "\(n\)" on supply chain profit and quality control.

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According to the changing trend of the images in Fig. 4, it can be seen that "\(g\)" and "\(n\)" have a positive effect on the promotion of the quality control level and the profit of the supply chain. The specific reasons are mainly related to the dual impact of quality control level on market demand and after-sales rate: (1) Quality control level has a negative impact on the after-sales rate of products, and its impact depends on the quality control effect. With the improvement of quality control effect, the more obvious the effect of quality control level on the reduction of after-sales rate, the lower the loss caused by after-sales service in the supply chain. At this time, supply chain decision maker tend to improve the quality control level to avoid greater losses. (2) Quality control level has a positive impact on market demand, and its impact degree depends on the quality elasticity coefficient. The greater the quality elasticity coefficient, the higher the market demand will be brought to the supply chain by improving the quality control level, and the greater the profit the supply chain will be able to obtain. Therefore, supply chain decision maker will invest more costs to improve the quality control level due to the improvement of quality elasticity coefficient.

The Impact of "\(q_{b}\)" on the supply chain and its reasons

In order to explore the impact of \(q_{b}\) on the supply chain and its reasons, Fig. 5 and Fig. 6 are drawn.

Fig. 5
figure 5

Influence of \(q_{b}\) on quality control level and market demand.

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Fig. 6
figure 6

Influence of \(q_{b}\) on supply chain profit and after-sales loss.

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The larger \(q_{b}\) is, the higher the expected unit cost of after-sales will be, and decision maker will improve the quality control level and reduce the after-sales rate of the product, while the improvement of the quality control level can stimulate the market demand of the product. Therefore, in Fig. 5, both the quality control level and market demand are positively correlated with \(q_{b}\). As shown in Fig. 6, when \(q_{b}\) increases, the after-sales loss of the supply chain first increases and then decreases, mainly due to the impact of the continuous rise of quality control level on market demand and after-sales rate. The increase of market demand and expected unit cost led to the increase of after-sales loss, and with the continuous reduction of after-sales rate, after-sales loss eventually shows a downward trend. Supply chain profit is continuously shrinking. The larger \(q_{b}\) is, the higher the execution degree of classification after-sales in the supply chain is. The above conclusions indicate that classification after-sales can help the supply chain save after-sales costs and reduce profit losses.

Conclusions and suggestions

In the closed-loop supply chain of electronic products, asymmetric cost information creates conditions for manufacturers to misreport, but supply chain information can be made completely transparent with the help of blockchain technology. This paper uses Stackelberg game theory to build multiple supply chain decision models under different dominant structures and information transparency. Firstly, it explores the timing and impact of manufacturers’ misreporting in an environment of information asymmetry. Secondly, it analyzes the impact of blockchain introduction costs on supply chain decisions, and then considers the coordination of the supply chain under blockchain technology. Finally, the coordination effect of the contract and the positive influence of after-sales classification are verified in the example analysis, and a sensitivity experiment is carried out.

The findings are as follows: (1) The manufacturer chooses to misreport only when the retailer makes the decision. As a rational decision-maker, the manufacturer will eventually overreport costs, which will not only cause the retailer to lose its dominant advantage but also damage the interests of the supply chain. (2) Only when the unit introduction cost of blockchain technology is within a certain range will the retailer introduce blockchain technology. After introduction, the quality control level of the supply chain will be improved, while the manufacturer’s profits will fall due to the lack of a misreporting advantage. When the cost is less than a certain value, the introduction of blockchain technology is beneficial to the supply chain; otherwise, the supply chain will suffer losses. (3) In a blockchain environment, collaborative decision-making by supply chain members can achieve optimal supply chain profits, while the supply chain’s quality control level can be increased to the highest and the after-sales rate reduced to the lowest. (4) Both the quality control effect and the quality elasticity coefficient have a positive effect on promoting the quality control level and supply chain profits, which is attributed to the dual influence of the quality control level on market demand and the after-sales rate. (5) After-sales classification has a positive impact on the supply chain. As the quality standards referenced by after-sales classification improve, the supply chain’s quality control level and market demand continue to rise, supply chain profits continue to decline, and supply chain after-sales losses first increase and then decrease. In addition, this paper uses a benefit transfer contract to balance the interests of supply chain members and achieve perfect coordination of the electronic product supply chain. It also verifies that the coordination effect of the benefit transfer contract is not affected when it fluctuates within a certain range.

Based on the above conclusions, this paper puts forward the following suggestions: Retailers should only consider introducing blockchain technology to eliminate manufacturers’ motivation for misreporting when they have a dominant advantage. "Cooperation through blockchain platforms" and "sharing the cost of blockchain introduction" can be taken as basic requirements for selecting manufacturers. When blockchain technology is introduced into the supply chain, manufacturers and retailers should choose collaborative decision-making that is most beneficial to the supply chain, and both parties can balance each other’s interests through benefit transfers. Both the quality elasticity coefficient and the quality control effect have a positive impact on supply chain profits. Therefore, managers can, on the one hand, improve consumers’ preference for quality control through advertising and quality comparisons, and on the other hand, improve quality control efficiency to reduce product after-sales rates. Managers should promote the classification of after-sales electronic products and comply with the after-sales concept that "repair should have the highest priority" under reasonable standards.

This research aims to guide blockchain technology to realize the sustainable development of the electronic product supply chain, and the relevant conclusions and suggestions provide a theoretical reference for achieving this goal. However, there are still some limitations in the study. The paper only considers cost information asymmetry, but in the actual market, information asymmetry exists in both upstream and downstream supply chains. Future research will deeply explore supply chain decision-making in situations of multilateral information opacity.