Blockchain technology embedded in the power battery for echelon recycling selection under the mechanism of traceability

This paper examines the use of blockchain technology in power battery echelon recycling. The technology helps to improve battery capacity identification and market transaction trust. The study focuses on power battery manufacturers and recycling participants. Two recycling modes are constructed using the Stackelberg game method, and the optimal decision-making of the participating subjects in the two modes of power battery echelon recycling under the embedding of blockchain technology is compared. The influence of each parameter on the optimal decision-making is analyzed. The research findings indicate that the degree of blockchain technology integration rises as the preference coefficient for traceability information increases. When recycling competition is intense and the sensitivity of recycling prices is low, the optimal recycling model for the number of spent power batteries (SPBs) to be recycled is the model in which echelon utilizers do not participate in recycling if the level of cost optimization coefficient embedded in blockchain technology is high, otherwise, it is the model in which echelon utilizers participate in recycling. The profit of power battery manufacturers and echelon utilizers decreases with the increase of the intensity of power battery recycling competition, the cost optimization coefficient of echelon utilizers and the cost optimization coefficient of manufacturers.

intensities and echelon utilization rates, considering consumers' traceability preferences.The impacts of these factors on the number of SPBs recycled, as well as the profits of manufacturers and echelon utilizers, are further analyzed to provide theoretical support for the implementation of the extended producer responsibility system by manufacturers of power batteries and new energy vehicles, as well as for joint recycling cooperation between manufacturers and echelon utilizers of power batteries.This study provides theoretical support for the implementation of the extended producer responsibility system by manufacturers of power batteries and new energy vehicles and for the cooperation with echelon users in the recycling of power batteries.

Problem description
After power battery manufacturers embed blockchain technology, it has two main benefits.Firstly, it makes it possible to clearly identify the remaining capacity of SPBs and their recyclability, which reduces the processing cost of power batteries' Echelon utilization and improves market demand.Secondly, the embedding of blockchain technology in power battery recycling systems provides strong regulatory support for establishing traceability mechanisms and ensuring timely, true, and accurate uploading of traceability information.Embedding blockchain technology in the power battery recycling system to establish a real-time traceability mechanism for trustworthy transactions requires the cooperation of participating subjects and significant investment in resources and technological research by power battery manufacturers, which enables data openness, transparency, and decentralization.Through this traceability mechanism, each participant in the recycling process can record and store information on the production, sales, and recycling of each level and subject of the closed-loop supply chain using the blockchain consensus and trust mechanisms.This information can be used for traceability management of the closed-loop supply chain for the recycling of power batteries for echelon utilization.However, power battery manufacturers must consider market demand resulting from the embedding of blockchain technology under the traceability mechanism, the reduced cost of echelon utilization processing, and the cost effect of technology investment, so as to realize the optimization of decision-making at the level of embedding blockchain technology.Based on this, there are two typical modes of embedding blockchain technology into a closed-loop supply chain consisting of a power battery manufacturer, a retailer, an echelon utilizer, and a thirdparty recycler under the traceability mechanism.(1) Model I involves joint recycling by retailers and third-party recyclers.For example, Ningde Times relies on 4S stores and Guangdong Bangpu Recycling Technology Co. to recycle retired power batteries 35 .(2) Model II involves joint recycling efforts between retailers, third-party recyclers, and echelon utilizers.For instance, Shanghai Tesla Ltd. relies on 4S stores to recycle SPBs and has also signed a recycling agreement with Shanghai Huadong Wrecking Co. and Shanghai Greenmax Co.The closedloop supply chain structure is illustrated in Fig. 1.
The paper addresses the following problem: 1. What are the optimal pricing decisions and optimal profits of each subject in the supply chain under the two recycling models?2. How do key parameters such as the level of blockchain technology embedded, consumers' preference for traceability information, and the intensity of competition among the recycling participants of SPBs affect the decision-making results? 3. What are the results of the comparative analysis of the optimal recycling quantity of SPBs for each recycling participant in the supply chain under the two recycling models?
Figure 1.Blockchain technology embedded in power battery echelon recycling mode under traceability mechanism.
4. What is the sensitivity of the optimal decision-making results under different conditions for each subject in the supply chain under the two recycling models?
In the forward supply chain, manufacturers produce new energy power batteries using newly purchased raw materials or recycled materials extracted from power batteries that cannot be used in the echelon, while blockchain technology is embedded in the power batteries, which are then sold to consumers through retailers.Blockchain technology can record all sales and recycling information of power batteries in a closed-loop supply chain.The information can be traced in the block according to the timestamp to ensure transparency and information sharing.Smart contract technology can enhance transaction speed for participating entities in power battery recycling, saving time and cost.In the reverse supply chain, retailers and third-party recyclers recycle SPBs.These recycling participants then resell the recycled SPBs to echelon utilizers.The echelon utilizer identifies SPBs based on the information in the block and divides them into two categories: batteries that can be used for echelon purposes and those that cannot, based on their remaining capacity.It processes the batteries that can be used for echelon purposes, sells them as products for echelon use in the echelon use market, and is responsible for collecting the batteries that cannot be used for echelon purposes from the echelon use market.Finally, the echelon user will sell the non-echelon usable power battery back to the manufacturer for raw material extraction.It is important to note that in the entire closed-loop supply chain of new energy vehicles, retailers (4S stores) and third-party recyclers are closer to consumers and have advantages in recycling.Therefore, such recycling channels as retailer recycling and third-party recycler recycling are essential 6 .

Basic assumptions
Assumption 1 Manufacturers sell and recycle the same type of power battery.The leaders and echelon utilizers are the manufacturers, while third-party recyclers and retailers are the followers.Batteries not used by echelon refer to the portion of spent power batteries that have not undergone echelon utilization, as well as the recycled materials such as lithium, nickel, and slam extracted from these batteries.The quality of power batteries produced using recycled materials is equivalent to those produced using raw materials 6 .
Assumption 2 Blockchain technology relies on smart contracts, consensus mechanisms, timestamps, and other technologies to achieve data transparency and sharing in the recycling process of spent power batteries.This enhances consumer trust while satisfying their traceability preferences, resulting in new market demand 3 .The demand for power batteries is related to consumers' preference for traceability information under blockchain embedding.The demand function for power batteries is represented by D = a − bp + kt 23 , where a denotes the potential market demand when the retail price is zero and blockchain technology is not embedded, b denotes the coefficient of sensitivity of consumers to the retail price of power batteries, p denotes the retail price, k denotes the preference of consumers for traceability information under blockchain embedding, and t denotes the level of blockchain technology embedding.

Assumption 3
The EU's New Battery Regulation, issued in July 2023, requires battery manufacturers to extend their producer responsibility to include organizing the classification, recovery, regeneration, and recycling of spent power batteries, as well as echelon use activities.The manufacturer fully bears the input cost of blockchain technology embedded in power batteries, which is a quadratic function of the level of blockchain technology embedded.The input cost of blockchain technology embedded in power battery is fully borne by the manufacturer and is a quadratic function of the level of blockchain technology embedded, i.e., C= 1 2 µt 2 17 , µ denotes the investment cost coefficient of blockchain technology embedded, and t denotes the level of blockchain technology embedded.Once the power battery manufacturer is integrated into the blockchain, the cost of production for both the manufacturer and the echelon utilizer will decrease.This is due to the increase in consumer trust and the reduction of market transaction costs.The cost optimization coefficients will be represented by ϕ and ρ(0 < ϕ < 1, 0 < ρ < 1) , respec- tively.Smaller values of ϕ and ρ indicate greater cost optimization ability, while larger values indicate the opposite 28 .

Assumption 4
The recycling quantity of spent power batteries is Q i j = q + mp j − np l , m > n > 0 , i ∈ {I, II} , j, l ∈ {r, c, t}, j = l , where mode I and mode II denote two different modes, respectively.Retailers, echelon utiliz- ers, and third-party recyclers are denoted by r,c,t , respectively.q denotes the recycling quantity when the recycling price and the price of the competitive channel are zero.m denotes the sensitivity coefficient of the recycling price, p j denotes the recycling price, while n denotes the price sensitivity coefficient of the competitive channel, and p l denotes the competitive channel's recycling price.The total quantity of spent power batteries that have been recycled is represented by 32,36 .Among the spent power batteries that have been recycled, a portion of them (denoted as β ) can be utilized for echelon use.These batteries are processed into echelon use products, with the remaining capacity ranging between 20 and 80%, and are sold to consumers for echelon use.The batteries that can not be utilized for echelon use are all resold to the manufacturers to be directly dismantled and recycled (the remaining capacity of the batteries that can not be utilized for echelon use is less than 20% and also contains batteries that are recycled from consumers for echelon use).Non-recyclable batteries are sold to manufacturers for direct dismantling and recycling if they have less than 20% residual capacity.This includes batteries recycled from consumers who use them in a gradient.The recycled materials extracted from these batteries can be used to produce new batteries at a lower cost than using new materials, resulting in c n − c r ρ > 0 .Meanwhile, during the process of recycling materials into new power batteries, there is inevitably some loss.As a result, there is a residual rate of α(0 < α < 1).

Model establishment and solution
Model I : joint recycling by the retailer and the third-party recycler This model involves the power battery manufacturer determining parameters w , p m , and t , and the echelon utilizer responding by determining the transfer price of the power battery, p b .The retailer (4S store) and the third-party recycler respond to the decisions made by the manufacturer and the echelon utilizer by determining parameters p , p r , and p t .Based on the aforementioned parameter design and basic assumptions, the respective profits of the third-party recycler, the retailer, the manufacturer, and the echelon utilizer can be derived using the following functions: In formulas (1)-( 4), the manufacturer profit function is defined as the sum of the net wholesale battery profit and the cost savings from producing batteries from renewable materials, minus the blockchain technology embedding cost.The retailer's profit function is the net profit from the sale of batteries, plus the net proceeds from recycling of SPBs.The third-party recycler's profit function is the net proceeds from recycling of SPBs.The profit function of the echelon utilizers is comprised of two components: the net profit derived from processing (1) The profit function of j in model i , where i = I, II represents joint recycling by retailers and third-party recyclers, and joint recycling by retailers, third-party recyclers, and echelon utilizers, respectively The recycling quantity function for j in Model i , where i = I, II , j = r, c, t , has the same meaning as previously defined Vol:.( 1234567890) Proposition 1 In model I , when µ > k 2 4b , the optimal decisions of the manufacturer, retailer, echelon utilizer, and third-party recycler are as follows: where it can be seen by the expression of F that if the residual rate α of the power battery for echelon utilization into the dismantling and utilization stage and the rate β of the recycled SPBs that can be echelon utilized in the recycled SPBs are larger, F is larger.If the optimization coefficient ρ of the processing cost of blockchain technology embedded in the echelon utilization of the power battery and the optimization coefficient ϕ of the cost of the production of the power battery by using recycled material are smaller, F will be larger.
Proof See Online Appendix A.
Model II : joint recycling by the retailer, the echelon utilizer and the third-party recycler In this model, the power battery manufacturer first determines w , p m and t , and the echelon utilizer responds to the manufacturer by determining the transfer price of the power battery p b and the recycling price p c .The retailer and the third-party recycler respond to the decisions of the manufacturer and the echelon utilizer by determining p , p r and p t .Based on the aforementioned parameter design and scenario assumptions, the profit functions of the third-party recycler, the retailer, the manufacturer, and the echelon utilizer are obtained as follows: In formulas ( 12)-( 15), the manufacturer profit function is defined as the sum of the net profit from wholesale batteries and the cost savings from producing batteries from renewable materials, minus the cost of embedding the blockchain technology.The retailer profit function is defined as the net profit derived from battery sales and the net gain from recycled SPBs.The third-party recycler profit function is the net revenue generated from recycled SPBs.The profit function of the echelon utilizers comprises two elements: the net profit derived from processing the SPBs recovered directly from consumers into echelon utilizable batteries and selling them, and the net profit from recycling the non-echelon utilizable batteries to the manufacturers, as compared to Model I. Please find specific revisions on pages 8 and 9 of the revised manuscript.

Proposition 2
In model II , when m > 2n and µ > k 2 4b are satisfied, the optimal decisions of the manufacturer, the retailer, the echelon utilizer, and the third-party recycler are: Vol.:(0123456789)The proof is similar to model I and will not be repeated here.

Analysis and comparison of equalization results
Propositions 1 and 2 provide the optimal decision results for manufacturers, retailers, echelon utilizers, and third-party recyclers under model I and mode II , respectively.By analyzing the optimal decisions and benefits of the two recycling models, the following inferences can be made.

Corollary 1
The relationship between the manufacturer's optimal wholesale price, the level of blockchain technology embedding, the retailer's optimal retail price, and the consumer's optimal quantity demanded under the two recycling models is shown below: Corollary 1 demonstrates that the optimal wholesale price, level of blockchain technology embedding, optimal retail price, and optimal quantity demanded by consumers for manufacturers are the same under the two different recycling modes, i.e., the forward supply chain sales decision is not related to the choice of the reverse supply chain recycling mode, and power battery sales and recycling are two relatively independent businesses, and power battery manufacturers are not affected by the recycling mode when making sales decisions.

Corollary 2 In the both recycling modes, the relationship between the variation of manufacturer's profit with the increase of the residual rate α of power battery entering the disassembly and utilization stage, the investment cost coefficient µ embedded in the blockchain technology, the cost optimization coefficient ρ of using recycled materials to produce power batteries, and the consumer's preference k of traceability information exists as follows: ∂π
Corollary 2 demonstrates that the profit of the manufacturer increases as the residual rate α of the power bat- tery entering the dismantling and utilization stage increases in both models.the larger α indicates that the manu- facturer obtains more recycled materials, and since the cost of using recycled materials to produce new power batteries is lower than that of using raw materials 34 , the more recycled materials that enter the dismantling and utilization stage, the more profit the manufacturer obtains.The profit of manufacturers decreases as the investment cost coefficient µ embedded in blockchain technology increases in both models.This is because a higher value of µ results in a higher investment cost embedded in the blockchain technology, leading to lower profits for the manufacturer.The manufacturer's profit decreases in both modes as the cost optimization coefficient ρ for using recycled materials to produce power batteries increases after blockchain embedding.The manufacturer must evaluate and test recovered non-echelon utilization power batteries to screen out recycled materials for use in producing power batteries.This is necessary because non-echelon utilization power batteries contain waste materials.Therefore, embedding blockchain technology can reduce the cost of using recycled materials to produce power batteries for manufacturers to a certain extent.The cost optimization ability embedded in blockchain technology is expressed by 1 − ρ .The larger ρ is, the higher the cost of using recycled materials ρc r to produce power batteries is, and therefore the lower the profit of the manufacturer c n − ρc r is.Manufactur- ers' profits in both modes increase with the enhancement of consumers' preference for traceability information k , which stems from the fact that the embedding of blockchain technology under the traceability mechanism can make the gradient of the remaining capacity degradation of SPBs clearly labeled, reduce the information asymmetry in the closed-loop supply chain of the gradient recycling, satisfy the consumers' preference for traceability information, enhance the consumers' sense of trust in the transaction, and expand the market breadth for the demand for the gradient utilization, which in turn enhances the manufacturers' market share and increases the manufacturers' profits.

Corollary 3
The transfer prices of manufacturers and echelon utilizers for the two recycling models are related as follows: (1) Proof See Online Appendix D.
Corollary 3 demonstrates that: (1) the transfer prices of manufacturers and echelon utilizers in Mode I are higher than in Mode II due to the diversity of scenarios used by echelon utilizers and the low saturation of battery capacity in Mode II .This results in higher recycling prices than those of retailers and third-party recyclers in Mode I .As a result, consumers are more likely to choose the recycling channels of echelon utilizers, and retailers and third-party recyclers will increase the recycling price to gain access to the recycling market.This will lead to an improvement in the market supply of SPBs in Mode II , which will be higher than in Mode I .In this case, as the market supply increases, the recycling price starts to fall.Consequently, the transfer price will also decrease, leading to an increase in the profit of each recycling participant.
(2) when the recycling channel has a high competitive intensity and the sensitivity of consumers' recycling is low, if the cost optimization coefficient embedded in the block technology is smaller, i.e., the cost optimization ability is larger, the recycling price of Mode I is lower than the recycling price of Mode II If the cost optimization factor is large, meaning that the cost optimization capacity is small, the recovery price Model I is higher than that of Model II .This is due to the enhanced cost optimization capacity of blockchain technology, which results in higher recycling prices for echelon utilizers compared to that of retailers and third-party recyclers in Mode II .Although the competition sensitivity factor of the recycling channel is larger, due to the smaller recycling price sensitivity factor, the increase of recycling prices by retailers and third-party recyclers will not have a significant impact on the quantity of recycling.Consequently, compared with Mode I , the recycling prices of retailers and third-party recyclers in Mode II are higher.However, the weaker cost optimization ability does not confer an advantage on echelon utilizers in recycling prices in Mode II .Furthermore, due to the smaller recycling price sensitivity coefficients, retailers and third-party recyclers choose to lower their recycling prices in order to offset the loss of revenues resulting from the reduction in recycling quantities as a consequence of the entry of echelon utilizers into the recycling market.
(3) When the competition in the recycling channel is low and consumers are more sensitive to recycling, the recycling price of Model I is lower than that of Model II if the cost optimization coefficient is smaller.Conversely, if the cost optimization coefficient is larger, the recycling price of Model I is higher than that of Model II .This is because the stronger cost-optimization capability makes the echelon utilizer's recycling price significantly higher than that of the retailer and third-party recycler in Mode II , and although the competitive sensitivity coefficient of the recycling channel is smaller, the amount of recycling changes significantly when the retailer and third-party recycler increase their recycling price due to the larger recycling price sensitivity coefficient, so the retailer and third-party recycler will increase their recycling price in Mode II and thus higher than in Model I .When the cost optimization ability is weak, the recycling price of the echelon utilizer in Model II is not significantly different from that of the retailer and the third-party recycler, and although the recycling price sensitivity coefficient is larger, the retailer and the third-party recycler will choose to lower the recycling price to reduce the profit loss.

Corollary 4
The optimal recycling quantities for third-party recyclers and retailers under the two recycling models have a relationship as follows: (1) Corollary 4 demonstrates that (1)the recycling quantities of retailers and third-party recyclers in Model I and Model II of the closed-loop supply chain for the echelon recycling of power batteries embedded in the blockchain under the traceability mechanism are equal when they reach optimal profit.Additionally, the optimal recycling quantities in Model I are higher than those in Model II due to the smaller competition intensity of the recycling channel in Model I .(2) When the residual rate α of the SPBs into the stage of dismantling and utilization is large, the difference between the optimal recycling quantities of retailers and third-party recyclers in Mode I and Mode II increases with the increase of the spent power battery's echelon utilization rate β , and conversely, www.nature.com/scientificreports/ the difference between the optimal recycling quantities decreases with the increase of β .This is because when α is larger, the manufacturer can get more recycled materials to produce power batteries.This is more profit- able than using raw materials to produce power batteries, which prompts the manufacturer to produce more power batteries.As a result, the recycling quantity increases.The increase in recycling quantity is greater for Mode I , which has a lower competitive intensity of recycling subjects, than for Mode II .This leads to a greater difference between the recycling quantity of retailers and third-party recyclers in Mode I and Mode II .On the contrary, when α is small, manufacturers will produce fewer power batteries, and the number of SPBs recycled will decrease, and the decrease in the number of recycled batteries in Mode I , where the intensity of competition among recycling entities is lower, is greater than that in Mode II .This results in a decrease in the difference in the number of recycled batteries recycled by retailers and third-party recyclers between Mode I and Mode II .(3) As ϕ and ρ increase, the difference in recycling quantity between retailers and third-party recyclers decreases in both Mode I and Mode II .Increases in ϕ indicate a weakened ability for cost optimization, resulting in higher costs for laddering utilizers.This prompts a decrease in transfer prices, leading to reduced recycling prices for retailers and third-party recyclers.As a result, the quantity of recycling decreases.Increases in ρ indicate higher manufacturing costs for power batteries, leading to a decrease in the number of batteries produced and recycled.
The decrease in the number of recycled batteries is larger in Mode I than in Mode II.
Proof See Online Appendix F.
Corollary 5 demonstrates that: (1) When the recycling channel's competitive intensity is low and the recycling price sensitivity is high, the total recycled quantity of retired power batteries of Model I is always smaller than that of Model II .This is because, although the sensitivity coefficient of competition in recycling channels is smaller, the sensitivity coefficient of recycling prices is larger, and each recycling participant is more sensitive to price changes, while the participation of echelon utilizers in recycling in Mode II can offer higher recycling prices, which attracts more SPBs to the recycling market.(2) When the competition among recycling channels is high and the price sensitivity of recycling is low, and at the same time the level of cost optimization coefficient embedded in the blockchain technology is low, the total quantity of retired power batteries recycled for Model I is smaller than that for Model II .Conversely, when the competition among recycling channels is higher and the price sensitivity of recycling is lower, and at the same time the level of cost optimization coefficient embedded in the blockchain technology is higher, the total quantity of retired batteries recycled for Model I is greater than that for Model II .This is due to the fact that when the cost optimization factor of blockchain technology is at a low level, both echelon utilizers and manufacturers in the two modes tend to set lower transfer prices and recycling prices, and although the sensitivity coefficient of competition in recycling channels is larger, the lower sensitivity coefficient of recycling price makes the recycling quantity of SPBs in Mode II higher than that in Mode I .How- ever, if the cost optimization factor of blockchain technology is increased to a higher level, the echelon utilizers and manufacturers in both modes will increase the transfer price and recycling price accordingly, and this change will make the recycling quantity of SPBs in Mode II lower than that in Mode I .The manufacturer must adjust the cost optimization coefficient based on the competitive intensity of the recycling channel, price sensitivity of recycling, and recycling mode.For instance, if the competition among recycling participants in the recycling channel is intense and consumers are moderately sensitive to the recycling price, the manufacturer should decrease the level of cost optimization coefficient for recycling mode II and increase it for recycling mode I.

Corollary 6 The profit relationship between the third-party recycler and the retailer under the two recycling models is as follows:
(1) π Corollary 6 demonstrates that: (1) Given a recycling market size, both retailers and third-party recyclers in Model I are more profitable than in Model II .This is due to the higher optimal quantity of recycling in Model I compared to Model B, as well as the lower intensity of competition in the recycling channel in Model I .(2) The optimal profit difference between retailers and third-party recyclers in Model I and Model II increases with β when α is larger; otherwise, it decreases with β .This is because manufacturers can obtain more recycled materials when the residual rate of power batteries entering the dismantling and utilization stage is higher.This is more profitable than using raw materials to produce power batteries, which enhances the manufacturer's incentive to produce and recycle.As a result, the optimal profit increases successively.Mode I , which has a lower intensity of recycling competition, experiences a larger profit increase than Mode II .On the contrary, if the residual rate of power batteries during the dismantling and utilization stage is low, the manufacturer's production of power batteries using recycled materials decreases.This leads to a decrease in marginal revenue, recycling incentives, and the number of recycling, resulting in a decrease in the manufacturer's optimal profit.The decrease in profit is larger in Model I than in Model II .(3) The difference in optimal profits between retailers and third-party recyclers in Mode I and Model II decreases as ϕ and ρ increase.This is because an increase in the optimization coefficient of the processing cost of the power battery's echelon use, ϕ , weakens the ability to optimize the cost and increases the cost of echelon users.This drives the transfer price down, resulting in a decrease in optimal profits for both retailers and third-party recyclers.An increase in the optimization factor ρ for the processing cost of power batteries using recycled materials results in an increase in the manufacturer's production cost of power batteries.This, in turn, leads to an increase in the selling and recycling prices of power batteries.As a result, the optimal profit of retailers and third-party recyclers decreases.In Mode I , the decrease in profit is greater than that in Mode II.
Proof See Online Appendix H.
Corollary 7 demonstrates that: (1) the profit of Model I is greater than that of Model II when the competitive intensity of the recycling channel is high, recycling price sensitivity is low, and the level of cost optimization factor embedded in the blockchain technology is low.Conversely, when the competitive intensity of the recycling channel is high, recycling price sensitivity is low, and the level of cost optimization factor embedded in the blockchain technology is high, the profit of Model I is less than that of Model II .This is due to the fact that when the cost optimization factor of blockchain technology is at a higher level, the cost of the echelon utilizer can be effectively reduced, which leads it to set a higher transfer price or recycling price, which effectively increases the amount of SPBs recycled, and despite the higher competitive sensitivity factor of the recycling channel, the profit of the echelon utilizer in Mode II is lower than that in Mode I due to the lower sensitive factor of the recycling price; On the contrary, when the cost optimization factor of the blockchain technology is low, the cost of the echelon utilizer will increase, thus setting a lower transfer price or recycling price, resulting in a lower recycling quantity of SPBs, and when the competitive sensitivity coefficient of the recycling channel is high, even if the sensitivity coefficient of the recycling price is low, the profit of the echelon utilizer in the more competitive Mode II is greater than that of Mode I .(2) When the recycling channel's competitive intensity is lower and the price sensitivity of recycling is higher, the echelon utilizer profit of Model I is always less than that of Model II .This is because although the competitive sensitivity coefficient of the recycling channel is smaller, the price sensitivity coefficient is larger, and each recycling participant is more sensitive to price changes, while the participation of echelon utilizers in recycling in Mode II is able to provide higher recycling prices and transfer prices, which attracts more SPBs to enter the recycling market, and thus the profits of echelon utilizers in Mode II are higher than those in Mode I.
Proof See Online Appendix I.
Corollary 8 demonstrates that: (1) When the recycling channel's competitive intensity is high, the recycling price's sensitivity is low, and the blockchain technology's cost optimization coefficient is low, the profit of Model I is greater than that of Model II .Conversely, if the recycling channel's competitive intensity is high, the recy- cling price's sensitivity is low, and the blockchain technology's cost optimization coefficient is high, the profit of Model I is smaller than that of Model II .This is because when the cost optimization coefficient of blockchain technology is at a high level, the manufacturer's cost can be effectively reduced, leading to the setting of a higher transfer price, and the amount of SPBs recycling will increase.Despite the high competitive sensitivity coefficient of recycling channels, the manufacturer's profit in Mode II is smaller than that in mode I due to the low sensitive coefficient of recycling price.With a low cost optimization factor of blockchain technology, the manufacturer's cost will be increased, which will cause it to set a lower transfer price, then the number of SPBs recycling will be reduced, and despite the high competitive sensitivity coefficient of the recycling channel, a sufficiently low sensitivity coefficient of the recycling price will lead to a larger manufacturer profit in Mode II than in Mode I .(2) When the competition intensity in the recycling channel is lower and the sensitivity to recycling prices is higher, the manufacturer's profit in Mode I is always smaller than that in Mode II , regardless of the level of the cost optimization coefficient embedded in the blockchain technology.This is due to the fact that, according to Corollary 1, the manufacturer in Mode I sells power batteries at a wholesale price and in quantities equal to that in Mode II .Therefore, the production cost of power batteries determines the profit size of the two models.Based on Corollary 3, the manufacturer's price for recycling materials is higher in Model I than in Model II .Therefore, the manufacturer's marginal revenue from using recycled materials to produce power batteries in Model I is lower than in Model II .Additionally, Corollary 5 states that the quantity of recycled materials in Model I is lower than in Model II , resulting in lower profits for the manufacturer in Model I compared to Model II.
Corollary 7 and Corollary 8 demonstrate that the manufacturer and echelon utilizer can both achieve maximum profit under the same conditions.This means that when the manufacturer earns the maximum profit, the www.nature.com/scientificreports/echelon utilizer will also earn the maximum profit, resulting in a mutually beneficial outcome.This provides theoretical support for cooperation between the manufacturer and the echelon utilizer.

Results and analysis
To analyze the impact of different parameters on optimal decision-making for manufacturers and echelon utilizers of blockchain-embedded power battery echelon recycling, this paper combines assumptions and draws on parameter settings from the literature 7 and 33. the optimal recycling quantity of SPBs and the optimal profits of manufacturers and secondary utilizers in different recycling modes are taken into account to be affected by the level of cost optimization coefficients embedded in blockchain technology, the level of consumer recycling prices, the degree of recycling price sensitivity, and the intensity of competition in recycling channels.Each inference's accuracy is confirmed through MATLAB numerical simulation.The parameters are assigned as follows:t = 0.25 ,

Optimal total recovery quantity analysis
The recycling quantities of both recycling models increase as the sensitivity coefficient of recycling price m increases and decrease as the sensitivity coefficient of recycling channel competition n increases.Additionally, in Model II , the recycling quantities are more significantly affected by n .When m is larger and n is smaller, the recycling quantities in Model I are consistently lower than those in Model II .Additionally, when the level of the cost optimization coefficient embedded in the blockchain technology is lower, indicating a higher cost optimization ability (F > F 4 ) , and when m is smaller and n is larger (2n < m < m 2 ) , the recycling quantity of power batteries in Mode I is higher than that in Mode II , as shown in Fig. 2. The simulation results above align with the findings of Corollary 5. Compared to Mode I , Mode II shows a greater change in the number of SPBs recycled due to increased competition among recycling channels and the participation of more recycling subjects.Figure 3 shows that the quantity of recycled materials increases with α in both recycling models.By increas- ing the transfer price, the manufacturer can obtain more recycled materials, which lowers the marginal cost of producing new batteries compared to using raw materials.This, in turn, allows for an increase in the recycled quantity of SPBs.The recycling quantity decreases as the SPBs' echelon utilization rate β increases, when the  www.nature.com/scientificreports/residual rate α of power batteries entering the dismantling and utilization stage is small.A smaller size of non- echelon utilization batteries results in higher costs for the manufacturer to dismantle and process them, extract recycled materials, and produce new power batteries.This lower profit margin reduces the manufacturer's incentive to recycle non-echelon utilization power batteries.Corollaries 7 and 8 demonstrate that in this scenario, the recycling profit and motivation of the echelon utilizer will decrease.Additionally, an increase in β will reduce the profit of both parties, leading the manufacturer and the echelon utilizer to opt for a lower transfer price, resulting in a reduction in recycling quantity.When α is larger, the quantity of recycling increases with the increase of β .This indicates that the manufacturer's cost of disassembling and treating the non-echelon utilization batteries, extracting the recycled materials, and producing new power batteries is lower than the profit.As a result, the manufacturer's profit and incentive to recycle the non-echelon utilization power batteries increase.It is evident from corollaries 7 and 8 that the recycling profit and incentive of the echelon utilizer increase in this scenario.
Additionally, an increase in β leads to higher profits for both parties.Both the manufacturer and echelon utilizer opt to raise the transfer price to boost the recycling quantity.Figure 4 shows that as the color of the phase changes from the lower left to the upper right of the bubble map, and the area decreases, the cost optimization ability decreases.This is due to the increase in the cost optimization coefficient ϕ of the echelon utilizer and the cost optimization coefficient ρ of the manufacturer embedded in the blockchain technology under the traceability mechanism.The recycling quantity of the power battery under the two recycling modes is on a downward trend.The increase in the cost optimization coefficient ϕ for the echelon utilizer results in a rise in marginal cost and a decrease in transfer and recycling prices.This leads to a decrease in the recycling price for both the retailer and third-party recycler, ultimately reducing losses by decreasing the recycling quantity.An increase in ρ results in an increase in the marginal cost, causing the manufacturer to reduce losses by lowering the transfer price.This, in turn, leads to a rise in the marginal cost of the echelon utilizer and a decrease in the recycling price for retailers and third-party recyclers, ultimately resulting in a decrease in the recycling quantity.Furthermore, the change in recycling quantity with respect to ρ is more significant than the change with respect to ϕ , when a certain amount of ϕ is held constant and ρ remains unchanged.This is due to the manufacturer's dominant position in the recycling process and their role as the final link in the echelon recycling of SPBs.The recycling cost set by the manufacturer determines the price of the entire closed-loop supply chain.If the dismantling and utilization of a product cannot be significantly improved to optimize costs, and there is an upper limit on the marginal gain, then the amount of recycling will be determined by the marginal gain.In this scenario, even if blockchain technology is embedded in the cost of recycling for echelon recyclers, it may not result in a significant change in the amount of recycling.

Comparison of optimal profitability and sensitivity analysis for manufacturers and echelon utilizers
As shown in Fig. 5, the manufacturer's profit increases with an increase in m and decreases with an increase in n in both recycling modes.The echelon utilizer also changes synchronously with the manufacturer's profit, but the change amplitude is more significant in mode II than in mode I .The simulation results demonstrate that the manufacturer is responsible solely for disassembling and extracting recycled materials from SPBs that cannot be used in a echelon manner to produce new power batteries, and the larger the amount of recycled SPBs, the higher the profit of echelon utilizers, and the more the manufacturer saves the material cost, and the profit is synchronously increased, which is consistent with the theoretical results in the literature 6,37 .The recycling price increases as the sensitivity coefficient of recycling channel competition grows, leading to greater competition in the spent power battery recycling market and decreased profits for manufacturers and echelon utilizers, while the intensity of competition among recycling participants is greater in Model II with more recycling channels, and the magnitude of the change in manufacturers' and echelon utilizers' profits in response to recycling channel competition is more significant.In Fig. 5, the intersection of the two planes indicates that when the competitive intensity of the recycling channel is low and the recycling price sensitivity is high (m > m 2 ) , Manufacturers and ladder utilizers in Model I are less profitable than those in Model II .In addition, when the cost optimization ability is high (F > F 5 ) and the competitive intensity of the recycling channel is high while the recycling price sensitivity is low (2n < m < m 2 ) , Manufacturers and ladder utilizers in Model I are more profitable than those in Model II .This finding is consist- ent with Corollaries 7 and 8.The magnitude of changes in manufacturer and echelon utilizer profits with the intensity of recycling competition in Model II is more pronounced compared to Model I .The reason for this is that the rise in recycling participants in Model II intensifies competition in the channel, thereby making the impact of competition on the profits of manufacturers and echelon utilizers more pronounced.
Figures 6 and 7 demonstrate that increasing both β and α results in an upward trend in profits for manu- facturers and echelon utilizers in the two recycling modes.This may be attributed to the embedding of blockchain technology in the process of echelon recycling and utilization of power batteries in the standardization of the spent battery market.The information on remaining capacity is now more transparent, which has led to increased transaction activity among market participants.This has also enhanced trust, and the profits obtained by manufacturers as a terminal link and key link echelon utilizer have grown synchronously with both β and α .However, when α is small, the profits of manufacturers and echelon utilizers decrease as β increases.According to Assumption 4, recycled materials extracted from non-echelon-utilized batteries can satisfy the production of new batteries at a lower cost than producing power batteries using new materials 6,37 .However, the residual rate of recycled materials at the dismantling and utilization stage is low, and manufacturers can only support a limited amount of recycled materials for new battery production, resulting in the limited reduction of marginal production cost.Moreover, the current technical level of recovery of recycled materials by manufacturers needs to be further improved, and some of the recyclable materials have entered the final form and have not been used in the production of new batteries so that the production cost of manufacturers cannot be significantly reduced by using recycled materials.When α is larger, the profits of manufacturers and echelon utilizers increase with the increase of β .This indicates that the echelon utilizers have achieved a higher level of value transformation of SPBs before entering the dismantling and utilization stage.After entering the dismantling and utilization stage,  the manufacturers have a higher level of technology to extract recyclable materials for the production of new power batteries.This leads to a reduction in the marginal cost of production, achieving the ideal state of the closed-loop supply chain of SPBs for echelon utilization under the mechanism of traceability.
As shown in Figs. 8 and 9, the color of the lower left to upper right phase of the bubble diagram darkens gradually, and the area decreases, indicating that the profits of both the manufacturer and the echelon utilizer decrease in both recycling modes as the cost optimization coefficient ϕ of the echelon utilizer and the cost optimization coefficient ρ of the manufacturer increase with the embedding of blockchain technology under the traceability mechanism.From Sect.6.1, it is evident that the recycling quantity of SPBs decreases as ϕ and ρ increase.This results in a reduction of the proportion of recycled materials used in the production of new batteries by the manufacturer.As a consequence, the marginal production cost increases, and the profit decreases.The optimal profit conditions of the echelon utilizer and the manufacturer remain the same, as shown in corollary 7 and corollary 8.The profit of the echelon utilizer decreases accordingly.In addition, the profit of manufacturers and echelon utilizers is more significant when ρ changes while ϕ remains constant, compared to when ϕ changes while ρ remains constant.This is due to the dominant position of the manufacturer in the recycling process and their involvement in the final stage of echelon recycling of SPBs.The price of the entire closed-loop supply chain is determined by its recycling cost.If the cost optimization ability of dismantling and utilization is not significantly improved, there will be an upper boundary of marginal revenue.This is a key factor in determining the recycling quantity and profit.Even if the blockchain is embedded in the recycling cost of echelon utilizers with a large range of changes, it cannot bring about a significant change in profit.

Blockchain technology embedding and consumer traceability information preference analysis
According to Proposition 1, the optimal level of blockchain technology embedding is equal under both recycling modes, expressed as t * t * = t I * = t II * .Figures 10 and 11 show that the level of blockchain technology embedding and the manufacturer's profit increase with the increase of the coefficient of consumer preference for traceability information k and decrease with the increase of the coefficient of investment cost of blockchain technology µ .This simulation result demonstrates that as an emerging market, consumers have a strong demand for clear and traceable identification of the remaining capacity of power batteries that can be utilized in an echelon   financial losses for both the manufacturer and the echelon recycler.To address this issue, manufacturers should focus on improving the level of dismantling and utilization, as well as implementing blockchain technology to enhance the efficiency of the dismantling and recycling processes.(3) The cost-effectiveness of blockchain technology is a crucial factor in deciding to embed the technology in the echelon recycling utilization of power batteries.The cost-effectiveness includes the size of the investment cost of the blockchain and the degree of utility value added by the consumer's traceability preference, and an increase in the investment cost coefficient of the blockchain technology will lead to a decrease in the level of embedding of the blockchain technology and a decrease in the manufacturer's profit under the two recycling modes, The recycling of power batteries may be hindered if the investment cost coefficient of the blockchain is too low.This could result in the manufacturer's utility value added from the consumer's traceability preference being lower than the cost effect of the embedding of the blockchain technology.In this case, the government should strengthen the manufacturer's implementation of the extended producer responsibility system and provide subsidies.Additionally, the government should unite digital service platforms, financial service institutions, and the main enterprises of the power battery manufacturing chain to actively promote the coalition of SPBs capacity for digital labeling and standard construction.This will reduce the manufacturer's investment in the cost of the blockchain.Moreover, to promote the embedding of its entire chain of the blockchain, and the effective transmission of the blockchain credit, which will create a higher value, and effectively improve the rights and interests of consumers, expand the overall size of the market for echelon recycling of the overall scale and completeness of the recycling market, to increase the profitability of the supply chain system.
Currently, the market for recycling power batteries is still in its growth stage.Other recycling methods include direct manufacturer participation in recycling and joint recycling among manufacturers.This paper focuses on the recycling of SPBs and explores two typical recycling modes: one in which SPB users participate in recycling and one in which they do not.The degree of marking the capacity of SPBs and consumer trust in the market are key factors that influence the recycling of SPBs.Thus, this study analyzes the impact of blockchain technology on the traceability mechanism, specifically on the power battery recycling volume and the profit of the recycling participant in the two modes mentioned above.The government's behavior in the supply chain decision-making of the recycling participant is not taken into account.Additionally, the demand for power batteries is modeled as a stochastic function, and this paper simplifies it linearly without affecting the main inference.Future research will explore the impact of blockchain technology on the carbon quota mechanism and its effect on the power battery recycling volume and the profit of the recycling participant. https://doi.org/10.1038/s41598-024-65748-0 14:15069 | https://doi.org/10.1038/s41598-024-65748-0

Figure 2 .
Figure 2. The effect of m and n on the number of recycles.

Figure 3 .
Figure 3.The influence of α and β recycling quantity Q I * and Q II * .

Figure 4 .
Figure 4.The influence of α and β recycling quantity Q I * and Q II * .

Figure 5 .
Figure 5.The impact of m and n on the profits of manufacturers and echelon users.

Figure 6 .
Figure 6.The impact of α and β on the profits of manufacturers π I * m and π II * m .

Figure 7 .Figure 8 .Figure 9 .
Figure 7.The impact of α and β on the profits of echelon users π I * c and π II * c .

Figure 10 .
Figure 10.The influence of µ and k on the optimal blockchain technology embedding level.

Figure 11 .
Figure 11.The impact of µ and k on the profits of manufacturers π I * m and π II * m .

Parameters of the model Table
1 displays the relevant parameters of the model:

Table 1 .
Related parameters and their description.
SPBs recovered from retailers and third-party recyclers into recycled power batteries and selling them, and the net profit derived from recycling non-echelon recyclable power batteries to manufacturers.