Investment Decision of Blockchain-based Traceability Service Input in a Competitive Agri-food Supply Chain

Applications of the blockchain-based traceability service (hereafter, BBTS) will not only help members of high-quality agri-food supply chain (hereafter, FPSC) improve consumers' perception on product quality and safety, but also increase their extra expenditure. Competitive AFSC as an important component of AFSC, its investment and coordination laws after using the BBTS obtain more attentions. To explore these laws, we constructed two competitive AFSCs, and each of them includes a supplier and a retailer. Considering the new changes of consumers' perception on product quality and safety after using the BBTS, the demand function was modied. Then, considering the BBTS costs and the new changes of consumers perceived on quality and safety, we built the income functions of chain members under the proposed three situations, i.e., 1) neither of the two supply chains invests in the BBTS, and 2) one supply chain invests in the BBTS, and 3) both supply chains invest in the BBTS. The research nds that: 1) if both of the two supply chains invest in the BBTS, supply chain members will gain a bigger threshold value sum of the BBTS costs, moreover, supply chain members will gain more benets compared with them no investment BBTS. Thus, governments need to guide more enterprises to adopt BBTS. 2) The competitor’s perceived quality is negative with the threshold value sum of the BBTS costs. When the competitor’s perceived quality is high, investors should reduce investment costs. 3) If investors or decision makers about BBTS want to get a big the threshold value sum of the BBTS costs, they should reduce the cost optimization coecient and avoid erce price competition as much as possible. Results can offer a theoretical guidance of adopting BBTS for FPSC.


Introduction
With the dramatic development of China's economy and the improvement of people's living standards, consumers' demands for agricultural products are developing in a greener and safer direction. However, a number of produce scandals have occurred in the past decades. Such as, the horse meat was found in several ground beef products in Europe in 2013, and 100000 tons expired meat was con scated by Chinese authorities in 2015. In 2018, 44% of Canadian seafood products were mislabeled (Köhler and adverse, these data may be modi ed. So, the credibility of the traditional traceability service is not high. As a distributed data structure, blockchain technology can share data on peer-to-peer network (Pearson, May et al. 2019, Sunny, Undralla et al. 2020). In the blockchain environment, the data were converted into digital code and stored in a shared database with higher transparency and limited risk of deletion and modi cation. So the blockchain cannot be usurped (Esmaeilian, Sarkis et al. 2020). Blockchain technology has received extensive attention in the agricultural product traceability area (Niknejad, Ismail et al. 2021).
In fact, some supply chain enterprises have adopted blockchain technology. For example, Wal-Mart put the blockchain-based traceability service (hereafter, BBTS) into the mango supply chain, and it took only 2.2 seconds to track the mango (Yiannas 2021). JD, Procter & Gamble, Amazon and other companies also used blockchain. According to the measurement of consumption data from JD Zhizhen chain, we found that applications of the BBTS could effectively improve the repurchase rate and sales volume.
Therefore, more and more supply chain enterprises want to use the BBTS, but this will also increase their extra expenditure. Thus, investment rules of the BBTS obtain more attention from supply chain members, particularly, the competitive AFSC become an important component of AFSC, its investment laws of using the BBTS are very important. Therefore, the study will discuss the two competitive AFSCs' investment strategies of the BBTS.
Although, some literatures have discussed the investment problems about the traceability system, they are in the traditional environment, in the blockchain environment, considering the BBTS cost as a variable, studying the BBTS investment decision rules are few in a competitive AFSC. For instance, product traceability could increase the value of products, and enhanced consumers' con dence in agricultural products, and had a higher willingness to pay for such products (Charlebois and Haratifar 2015, Riccioli, Moruzzo et al. 2020, Zhang, Mankad et al. 2020). At the same time, the research showed that the main cost of the investment blockchain technology for the supply chain is the variable cost, and the xed cost of the investment has little in uence on the supply chain (De Giovanni 2020). The research of Chen, Tian et al. (2018) showed that consumers were sensitive to price, and agricultural products' sales price was low. If the price of agricultural products increases signi cantly because of the increase of the BBTS costs, it will decline the agricultural products' sales volume, which is not conducive to the pro ts of the supply chain. The existing researches mainly focuses on the technology and signi cance of blockchain, but there is little research on how the supply chain should invest blockchain, especially in the current competitive business environment. The research on blockchain investment in competitive AFSC is even less.
Aims of our study are to research the investment decision strategies of the BBTS in a competitive highquality AFSC. Based on the above considerations, we rstly constructed two competitive AFSCs, which including a supplier and a retailer respectively to study the investment decision of chain members about the BBTS. Based on the new changes of consumers' perception to product quality and safety after using the BBTS, the demand function model was modi ed. Then, considering the BBTS costs and the new changes of consumers perceived on quality and safety, we built the income functions of chain members under the proposed three situations.
There were three innovations in this paper: (1) a competitive demand function model was established based on consumers' price sensitivity and consumers' perception to product quality and safety. (2) We consider two competing supply chains, each supply chain has two investment options, thus there are four situations. Due to the symmetry of two supply chains, we only need to study three situations, when the two supply chains do not invest blockchain technology was N situation, only one supply chain invests blockchain technology was I situation, and both the two supply chains invest blockchain technology was M situation. (3) Chain members pro t models were established under the proposed three kinds of investment situations considering the BBTS costs.
The signi cances of this study are as follows: (1) considering the new changes of consumers' perception to product quality and safety under the new background, we modi ed the demand function of agricultural products, and it will enrich the research perspective of demand function in AFSCs. (2) Considering the BBTS costs, we constructed chain members' bene ts functions under the three competitive supply chain models (N, I, M). This will expand the theory research on investment decision-making of competitive AFSC under the new background. Meanwhile, the results will provide theoretical support for competitive AFSC to invest the BBTS.
The article structure is shown in Figure 1.

Literature Review
The research of this study mainly involved the following three aspects: rst, the application of blockchain technology in AFSC; second, the application of traceability service in AFSC; third, AFSC decision-making.

Application of Blockchain Technology in AFSCs
Because of its traceability, digitalization and security, many scholars studied how the supply chain uses blockchain technology. ( Through the above analyses, more and more scholars were interested in this eld. The research also showed that the research of blockchain in the eld of agricultural products was mainly divided into traceability system, blockchain technology and blockchain bene ts. To sum up, it can be found that there were few studies on the effect of blockchain on the decision-making of high-quality AFSC, and the research of this paper can make up for the de ciency in this aspect.

Application of traceability service in AFSCs
In recent years, with the promotion of national policy and consumers, traceability service has gradually become an important part of AFSC management (Bosona and Gebresenbet 2013). Badia-Melis, Mishra et al. (2015) summarized the technological development of traditional traceability service, such as RFID, NFC, isotope analysis and DNA barcode, but did not show the development of blockchain technology in this study. Yang, Li et al. (2021) used blockchain technology to design the supply chain traceability system of fresh agricultural products, which improved the transparency and credibility of supply chain information and made up for the shortcomings of traditional traceability service in transparency and credibility. Sun and Wang (2019) studied the purchasing decisions of supply chain buyers considering traceability and found that buyers were more likely to purchase suppliers with high traceability. Collart and Canales (2021) believed that future research should focus on traceable economic sustainability data and the economic feasibility of blockchain technology based on a case study of high-quality AFSC.
Casino, Kanakaris et al. (2020) designed a traceability system of agricultural products based on blockchain, and evaluated the feasibility of the model through a speci c study of a real dairy enterprise.
Through the above researches, we can nd that the current traceability researches are mainly focused on the signi cance of traceability service and the technical level of traceability system. There are few studies on the economic pro ts and the decision-making impact of the traceability service for the competitive supply chain.

Investment decision of competitive AFSCs
This research is also participant with the investment decision of competitive AFSC. Dai, Nu et al. (2021) studied the coordination and pricing of competitive supply chain. They divided the competition of supply chain into three models: upstream competition, downstream competition and a mixed supply chain model with both upstream and downstream competition, and designed a mixed competition mode to study the effect of traceability and product recall in the supply chain. Based on this mode, Dai believed that traceability investment is always bene cial to manufacturers, and the impact on retailers depends on the cost of traceability. Niu, Mu et al. (2021) designed a co-opetitive supply chain model composed of an multinational rm located in high tax region and an e-tailer, the e-tailer purchased and resold the multinational rm's products. Choi, Feng et al. (2020)designed a game mode of duopoly competition, and studied the effect of product information disclosure based on blockchain technology on the supply chain of rental service platforms. This study indicated that risk attitude is an important factor to accurately describe the impacts brought by the blockchain technology. In the eld of AFSC, Wang and Chen (2016) studied the decision-making problem of portfolio contracts in fresh supply chain and designed a model concluding suppliers and retailers. They found that option prices have diverse impressions for supply chain members' income. Wang and Zhao (2018) also studied the investment decision about the cold chain invested in the fresh supply chain. Results suggested that cooperative cold chain investment and collaborative pricing are the dominant strategies of the supply chain. Wu, Fan et al. (2021) studied the coordinated pricing of investment blockchain technology in fresh supply chain, and designed a three-level supply chain model concluding suppliers, third-party logistics and retailers. Their research found that the investment of blockchain technology is related to consumer acceptance, cost sharing ratio and deterioration rate of the fresh product. Considering freshness and greenness, Liu, Long et al. (2020) designed an AFSC composed of a manufacturer and a retailer, and studied integrating blockchain with big data. The research indicated that when the investment cost changed in a certain range, it is bene cial to supply chains' pro ts. The above researches do not involve the competitive decision-making of dualchannel AFSC. In view of this, this study designed a dual-channel supply chain, each of which concluding a supplier and a retailer, which enriched the research of competitive supply chain decision-making.
Based on the aforementioned analyses, the existing researches have the following shortcomings: (1) the current research is mainly focused on blockchain technology, and there are few studies on the decisionmaking impact of blockchain in high-quality AFSC. (2) At present, the traceability research is primarily focused on the meaning of traceability service and the technical level of traceability system, but there are few studies on the economic pro ts of traceability service and how the competitive supply chain making decisions about traceability service. (3) The above researches do not involve the competitive decisionmaking of dual-channel AFSC. In order to solve the de ciency of the above researches, considering the new changes of consumer price sensitivity and consumer perception of product quality and safety, this paper discussed the investment decision-making of the BBTS in competitive AFSC under different investment situations.

Model description
In order to study the effect of BBTS investment strategy on FPSCs' pro ts, we constructed a Stackelberg game model constructed two competitive AFSCs, and each of them includes a supplier and a retailer, as shown in Figures 2. Investing in BBTS can improve consumers' quality perception of fresh agricultural products. The demand of each supply chain is linear with its own retail price, product perceived quality and the retail price and perceived quality of competitors' products. In general, supply chain has two choices in decision-making, i.e. investment and non-investment. We consider two competing supply chains, each supply chain has two investment options, thus there are four situations as follow: 1) both supply chains do not invest in BBTS; 2) supply chain 1 invests in BBTS, supply chain 2 does not invest in BBTS; 3) supply chain 1 does not invest in BBTS, supply chain 2 invests in BBTS; 4) both supply chains invest in BBTS. Due to the symmetry of two supply chains, we only need to study three situations:(1) neither of the two AFSCs invests the BBTS, namely, N situation; (2) only one AFSC invests the BBTS, namely, I situation; (3) both AFSCs invest the BBTS, namely, M situation.
The relevant parameters involved in the construction of the model and their descriptions are shown in Table 1. Two kinds of substitutable agricultural products, i={1,2}.
Revenues of the retailer in the situation.     The perceived quality safety factor of the kind of agricultural products in the situation.
The quality and safety level of agricultural products, this paper assumes that the quality and safety level of two kinds of agricultural products are equal.

a i
The potential demand for the kind of agricultural products in the market β The sensitivity coe cient of market demand to the price of substitutes, the greater the β, the higher the sensitivity, and the stronger the competitiveness of the supply chain. κ The sensitivity coe cient of market demand to the quality of substitutes, the greater the κ , the higher the sensitivity, and the stronger the competitiveness of the supply chain.
c r The retailer's cost of sales, this paper presumed that sales' cost of the two products is the same.
c m The supplier's cost of sales, this paper presumed that sales' cost of the two products is the same.

Hypothesis
(1) The quality of the two alternative agricultural products are satisfy the national quality and safety of agricultural products or agricultural industry standards. Therefore, it is assumed that the quality of the two agricultural products is the same. The supply chain invested in the blockchain technology can improve customers quality perception. Consumers prefer to buy fresh agricultural products with complete information because they think such products' quality are higher (Patelli and Mandrioli 2020).
(2) In the face of two kinds of alternative products, it is assumed that consumers decide whether to buy the product mainly according to the retail price and the degree of quality and safety of the product. There is no difference in the quality and safety level of the same product under the three investment situations.
In addition, consumers' perceived quality and safety of products is expected to be improved, through the investment of the BBTS, for example, λ N i cript > .The members of the supply chain make decisions with the goal of maximizing their own incomes.
(3) BBTS can increase the credibility among supply chain members. By eliminating intermediaries, we can improve audit e ciency and reduce communication and nancial costs (Gurtu and Johny 2019). We assumed the optimization coe cient of cost is θ.
(4) The supplier has su cient production capacity to ensure that the products are not out of stock. The members of the supply chain are risk-neutral and completely rational. (5) Suppose the market demand is de nite, and it is equal to the retails' order amount. Therefore, the market demand of product 1 is D x 1 = a 1 − p x 1 + βp x 2 + λ x 1 q 1 − κq 2 . The market demand of product 2 is D x 2 = a 2 − p x 2 + βp x 1 + λ x 2 q 2 − κq 1 , a 1 > 0, a 2 > 0. Suppose 1 > β ⩾ 0, demand is more sensitive to its own price. {\lambda ^x} \geqslant 0, \kappa \geqslant 0, the greater the β and k, the stronger the competition between the two products. Suppose {\lambda ^x} \geqslant \kappa, the demand is more sensitive to its own quality level than to the substitute quality level. (6)In order to facilitate the research, it is presumed that the production costs of the suppliers in the two supply chains is zero. In order to enhance the competitiveness of the whole supply chain and obtain more revenue, both suppliers and retailers have the inherent motivation to invest the BBTS. It is assumed that suppliers and retailers bear their own the BBTS costs, and indirectly share the BBTS costs of each other by adjusting wholesale prices and ordering quantities.

Revenue model of supply chain members in the N situation
In the N situation, suppliers and retailers in both supply chains do not invest the BBTS. The wholesale price w_{i}^{N} will sell by the supplier of product to its exclusive retailer. The demand of the retailer is D_{i}^{N}, and the retail price of the product is p_{i}^{N}. Then the expected returns of supply chain members \pi _{{ri}}^{N} and \pi _{{mi}}^{N} are as follows: The retailer determines the retail price and the product's order demand according to the supplier's wholesale price. Therefore, using backward induction to solve the retail price, we can get the retail price p_{i}^{N} of agricultural products .Then, putting the p_{i}^{N} into (1) to get the supplier's equilibrium wholesale price w_{i}^{{N*}}. According to the equilibrium wholesale price w_{i}^{{N*}}, we can get the equilibrium retail price p_{i}^{{N*}}. Putting the equilibrium retail price p_{i}^{{N*}} into the demand function D_{i}^{N} to get the equilibrium order quantity D_{i}^{{N*}}. Base on the equilibrium wholesale price w_{i}^{{N*}}, the equilibrium retail price p_{i}^{{N*}} and the equilibrium order quantity D_{i}^{{N*}}, we can derive the equilibrium incomes of the supplier and the retailer in Lemma 1.

Proof
Base on function (4) and (5) According to Proposition 1, we nd that price competition coe cient will increase the pro ts of FPSC member when the two supply chains does not invest in BBTS. In addition, quality competition will reduce the pro ts of FPSC members.

Lemma 2
When supply chain 1 invests in the BBTS and supply chain 2 does not invest in the BBTS, the demand of supplier and retailer are given by, respectively. Base on the equilibrium pro ts of FPSC members, we can get Proposition 2.

Proposition 2
With the raise of \lambda _{1}^{I}, the pro ts of supplier, retailer and the whole FPSC will increase.

Proof
Base on the function (22), (23), (24) and (25) According to Proposition 2, we nd that improving consumers' perceived quality will increase the pro ts of supplier, retailer and the whole FPSC members.

Revenue model of supply chain members in the M situation
In the M situation, retailers and suppliers in both supply chains invest the BBTS. The wholesale price sold by the supplier of product to its exclusive retailer is w_{i}^{M}. The demand of the retailer is D_{i}^{M}, and the retail price of the product is p_{i}^{M}. Then the expected returns of supply chain members \pi _{{ri}}^{M} and \pi _{{mi}}^{M} are as follows: The retailer identi ed the retail price and order demand of the product according to the supplier's wholesale price. Therefore, using backward induction to solve the retail price, and we can get the retail price p_{i}^{M} of agricultural products .Then, putting the p_{i}^{M} into (24) to get the supplier's equilibrium wholesale price w_{i}^{{M*}}. Based on the equilibrium wholesale price w_{i}^{{M*}}, we can get the equilibrium retail price p_{i}^{{M*}} and then put the equilibrium retail price p_{i}^{{M*}} into the demand function D_{i}^{M} to get the equilibrium order quantity D_{i}^{{M*}}. Base on the equilibrium wholesale price w_{i}^{{M*}}, the equilibrium retail price p_{i}^{{M*}} and the equilibrium order quantity D_{i}^{{M*}}, we can derive the equilibrium incomes of the supplier and the retailer in the Lemma 3.

Analysis Of Equilibrium Investment Strategy Of Bbts
Base on the above hypothesis and analysis, we can easy to nd that each pro t of two FPSC in N situation is same. In order to further study the equilibrium investment strategy of BBTS, we analysis the change of pro ts after investment the BBTS by comparing the pro ts of supplier and retailer before and after investing in BBTS (i.e. situation, N, I and M). According to Proposition 4, we can obtain the threshold value of investment cost. The two competitive FPSCs will invest in the BBTS when the investment cost less than the threshold value. In addition, we obtain that the threshold value sum of the BBTS costs {c_{om}}+{c_{or}} has a negative correlation with the cost optimization coe cient \theta and the sensitivity coe cient of price competition \beta of sales industry based on the BBTS. This demonstrates that if investors or decision makers about BBTS want to get a big the threshold value sum of the BBTS costs {c_{om}}+{c_{or}}, they should reduce the cost optimization coe cient \theta and price competition coe cient \beta as much as possible.
Base on Proposition 4, we can nd that the perceived quality coe cient after investing in BBTS \lambda _{1}^{I} have a positive correlation with the threshold value sum of the BBTS costs {c_{om}}+{c_{or}},but the perceived quality coe cient without BBTS \lambda _{2}^{I} has a negative correlation with the threshold value sum of the BBTS costs {c_{om}}+{c_{or}}. Namely, when the perceived quality coe cient \lambda _{1}^{I} is high, FPSC have a wider range of acceptable investment costs {c_{om}}+{c_{or}}. If the competitor's perceived quality is high, the investment cost should not be large.

Numerical Simulation
In order to further study the changes of supply chain revenue under the three situations, we assume a set of parameter values based on the previous literature in terms of marketing and operations management (Liu, Long et al. 2020).
Base on the above analysis, we make {a_1}={a_2}=10, {q_1}={q_2}=2, \kappa =0.6. The perceived quality safety factor of the supply chain before investing in BBTS \lambda _{i}^{N}=0.7. And the perceived quality safety factor of the supply chain have been improved \lambda _{i}^{M}=0.8 after investing in BBTS. In addition, assume that the optimization coe cient of the sales cost of agricultural products \theta =0.75. 1. Figure 4 indicates, with price competition coe cient \beta raise, retail price, wholesale price and demand will increase in three situations (i.e. N, I and M). This is because the price competition will expand market demand. Then the retailer will raise the retail price and the supplier also will raise wholesale price following the retailer.
2. Figure 5 indicates, with {\lambda ^M} raise, retail price, wholesale price and demand will increase in three situations (i.e. N, I and M). It can be explained as follow. With {\lambda ^M} increases, fresh agricultural products' quality is more reliable. And Consumers prefer products with reliable quality. In addition, supply chain 1 in I situation and two supply chains in M situation increase faster. That indicates, it is bene ts to increase price and expand demand by investing in BBTS.

Figure 6
Then, we will use numerical examples to discuss the investment strategy of BBTS. In general, we set price competition coe cient \beta is 0.5. Using above parameter value, the Figure 7a shown the change of pro ts after investing in BBTS with different investment cost {c_{om}}+{c_{or}}. We can see that if FPSC want to invest in BBTS, the investment cost should be less than 0.3833 when the price competition coe cient \beta is 0.5. In addition, the Figure 7b shown the threshold value sum of BBTS costs {c_{om}}+ {c_{or}} following the change of price competition coe cient \beta. We can nd that condition H 2 contains conditionH 1 as Proposition 4, and the minimum threshold value sum of BBTS costs is 0. 35 Figure 8 shown the change of FPSCs' pro ts with price competition coe cient \beta. We can nd that the supply chain's income grows with the increase of the price competition intensity of agricultural products. In addition, no matter what is the value of \beta, the pro ts of FPSC will increase when they invest in BBTS (i.e. \pi _{{sc}}^{M}>\pi _{{sc1}}^{I}>\pi _{{sc2}}^{I}>\pi _{{sc}}^{N}). The reason perhaps that with the price competition coe cient \beta increase, the retail price and the demand will also increase, as observed in Figure 4.  Figure 10 are different with \beta raise. When price competition coe cient \beta around 0.5, investing in BBTS will reduce the pro ts. And when \beta around 0.8, it is same as Figure 9. It is can be explained that{c_{om}}=0. 29 The BBTS plays a crucial role in the modern FPSC system. Compared with the traditional traceability service which has some defects in the security of information storage, the BBTS can ensure the security of information storage. More and more enterprises are trying to invest the BBTS. Wal-Mart's mango traceability system based on blockchain technology and JD Zhizhen chain based on blockchain technology have proved that blockchain technology can improve product traceability. Considering the investment cost of the BBTS, how should suppliers and retailers of agricultural products make decisions in the face of industry competition?
In order to study the decision-making of investment the BBTS in competitive AFSCs, this paper designed two supply chains, each of which concluding a supplier and a retailer. Considering the new changes of consumers perceived quality and safety, the demand function of agricultural products was modi ed. Due to the symmetry of two supply chains, the revenue model under three situations (N, I, M) was considered respectively. The study found that: (1) The quality competition intensity \kappa will reduce retail price , wholesale price and demand . But if decision makers can improve customers' perceived quality by using BBTS, it can help decision makes increase their bene ts and the demand. This tells us that the decision makers of BBTS should try their best to absorb the value of BBTS in product quality traceability, and then improve the customers' perceived quality after using BBTS (i.e., \lambda _{i}^{M} and \lambda _{1}^{I} ), and nally, this will help decision makes increase their bene ts.
(2) The perceived quality coe cient \lambda _{1}^{I} after investing in BBTS has a positive correlation with the threshold value sum of the BBTS costs {c_{om}}+{c_{or}}, but the perceived quality coe cient of not invest in BBTS \lambda _{2}^{I} have a negative correlation with the threshold value sum of the BBTS costs {c_{om}}+{c_{or}}. This demonstrate that when the decision maker wants to investment BBTS, not only improve their perceived quality \lambda _{1}^{I}, but also should pay attention to the perceived quality of competitor without BBTS \lambda _{2}^{I}. When the competitor's perceived quality \lambda _{2}^{I} is high, investors should reduce their investment costs {c_{om}}+{c_{or}}.
(3) When the cost of investment satis es certain conditions, investing in BBTS will increase the pro ts of FPSC. In addition, the threshold value sum of the BBTS costs {c_{om}}+{c_{or}} has a negative correlation with the cost optimization coe cient \theta and price competition coe cient \beta of sales industry based on the BBTS. This demonstrates that if investors or decision makers about BBTS want to get a big the threshold value sum of the BBTS costs {c_{om}}+{c_{or}}, they should reduce the cost optimization coe cient \theta and avoid erce price competition as much as possible.
(4) When the threshold value sum of the BBTS costs {c_{om}}+{c_{or}} is in a certain range, the supply chain invested in the BBTS will obtain more bene ts than the competitive supply chain without investing in the BBTS. In addition, if both of the two supply chains invested in the BBTS, supply chain members will gain a bigger threshold value sum of the BBTS costs {c_{om}}+{c_{or}}, moreover, supply chain members will gain more bene ts compared with them no investment BBTS. Thus, governments need to guide more enterprises to adopt blockchain-based traceability platforms.
In this research, we nd some Management suggestion. FPSC should know that whether adopt BBTS is mainly related to investment cost and the perceived quality from customers. In addition, FPSC should adopt price competition instead of quality competition.

Research signi cance
There are some academic values in this study.

Future researches
This paper studied a simpli ed model of two competitive AFSCs, each of them was composed of a supplier and a retailer. AFSC is a complex system. In the future research, third-party logistics and multichannel supply chain should be added to the model. In addition, the impression of uncertain demand on the income of the supply chain should be taken into account. Therefore, the next study will establish a multi-node model and consider uncertain requirements to study this problem.    . This is because the price competition will expand market demand. Then the retailer will raise the retail price and the supplier also will raise wholesale price following the retailer.  . It can be explained as follow. With λ M increases, fresh agricultural products' quality is more reliable. And Consumers prefer products with reliable quality. In addition, supply chain 1 in I situation and two supply chains in M situation increase faster. That indicates, it is bene ts to increase price and expand demand by investing in BBTS.

Figure 6
Figure 6 indicates, with quality competition coe cient α raise, retail price, wholesale price and demand will reduce in three situations (i.e. N, I and M). The reason is that erce quality competition will increase cost, reduce the market demand. Then the FPSC member will reduce its retail price and wholesale price.

Figure 7
Page 29/30 Figure 7a shown the change of pro ts after investing in BBTS with different investment cost . We can see that if FPSC want to invest in BBTS, the investment cost c om + c or should be less than 0.3833 when the price competition coe cient β is 0.5. In addition, the Figure 7b shown the threshold value sum of BBTS costs c om + c or following the change of price competition coe cient β. We can nd that condition H 2 contains conditionH 1 as Proposition 4, and the minimum threshold value sum of BBTS costs is 0.35.

Figure 8
Please see the Manuscript PDF le for the complete gure caption. Figure 9