Multi-Oligopoly Sequential Pricing Mechanisms and Their Game Analysis in Raw Material Supply Chains

Round 1

Reviewer 1 Report

Section one, introduction, is too big. Part of section 1 should be passed to section 2.

The article has a small bibliography in number of citations; and old. Authors should increase the number of references, preferably with articles from 2022 and 2021.

All formulas must be numbered and quoted in the text.

Author Response

We greatly appreciate your time and very professional and helpful comments. These comments are valuable and very helpful for revising and improving our paper. We have carefully studied the comments and made revisions in the hope of the final approval. The revised part is marked in red in our revised paper. The main revisions in the paper and our response to the reviewers’ comments are as follows.

 

Point 1: Section one, introduction, is too big. Part of section 1 should be passed to section 2.

Response 1: Thank you for your valuable questions and professional suggestions. Following your valuable suggestions, we have rewritten the introduction. Which is shown as below.

As the social economy has been extensively reformed and opened up alongside its rapid development, the competition among firms is becoming increasingly intense. In a multi-oligopolistic supply chain market, there is market competition among suppliers, who not only have to calculate their own costs and profits, but also must consider multiple games with competitors and downstream firms. Some raw material supply markets are multi-oligopolistic supply chain markets, in which there are usually multiple suppliers, with one supplier in the leading position and others in following positions. The dominant supplier not only has the largest market share, but also has a dominant role in raw material pricing, while the following suppliers have no dominant capacity in the process of raw material pricing, despite having some pricing power, and they often have to adopt the "follow the market" strategy. However, uncertainty in suppliers' product supply is a common phenomenon in supply chain management, and to a certain extent, it can cause losses to firms [1]. Therefore, to reduce the risk of raw material supply chain breakage, downstream manufacturers often avoid adopting the raw material procurement strategy of "putting eggs in one basket” but sign long-term minimum supply purchase agreements with leading suppliers and also purchase raw materials through various channels. At this point, in the face of demand uncertainty, it is worth determining what pricing mechanism should be adopted by multi-oligopolistic suppliers in order to consolidate their market position and enhance their competitiveness.

Over a long period of time, academics have conducted a great deal of research regarding the pricing problem in supply chains, and many scholars have adopted different game approaches for use in different supply chain structures. Ji et al. [2] developed a dynamic game model regarding "upstream", wholesale price and retail price to study "upstream" decisions and product pricing in a retail supply chain, considering the differences in the brand image of two suppliers. Razmi et al. [4] developed a dynamic mixed integer linear programming (DMILP) model to optimize a seasonal raw material supply chain network by considering a multi-level supply chain with multiple products and multiple time periods. Das et al. [5] used centralized and decentralized models to study interconnected, three-stage forward and reverse supply chains with green conscious markets providing green products. Taleizadeh et al. [6] studied a problem related to decentralized, three-level supply chain total cost optimization using the Stackelberg–Nash model. Zarouri et al. [7] used the Stackelberg model to study a problem related to dynamic pricing in a perishable supply chain with one manufacturer, one retailer and two production and distribution periods. Guo et al. [8] used the Stackelberg game to study a problem related to the pricing game regarding two service providers with homogeneous consumers. Keskin and Taskin [9] constructed a two-stage pricing decision model for a two-oligopolistic game in the presence of asymmetric market shares based on consumer preferences. Jiang and Yang [10] constructed a dynamic game model to study the pricing mechanism and quality decisions of vendors in a community learning context. Gong and Yang [11] used a sequential pricing game model to study the pricing mechanisms of suppliers in a raw material supply chain. Ma and Xie [12] studied the pricing process of boundedly rational retailers for bundled products with limited information access and found that sequential games can be used to obtain a more stable system than simultaneous games. A sequential game is a form of game in which participants choose their strategies in a temporal sequence, and the choice of the first actor affects the choices available to the second actor. Unlike the traditional Bertrand model, it is a more typical dynamic game and provides an analytical tool to represent dynamic games of related firms. It is also different from the general delayed finite rationality model, in which the strategies of firms in the current period are influenced by the strategies of other firms in the previous period. For example, in the raw material supply market mentioned in our paper, Gong and Yang pointed out that the pricing mechanism of this type of market is a sequential game, in which the dominant supplier holds the "boss" position and has dominant power in each period, and its pricing can adopt a "delayed" strategy to make quotations at the end of the period, while the supplier in the following position provides quotations at the beginning of the period. This allows for better characterization of the dynamic evolution of the firm's game.

Supply chains are complex systems which consist of multiple member firms. In the study of supply and demand relationships, the existing literature focuses on the relationship between two suppliers and one retailer [13]-[22] and multi-level supply chain relationships [4][6] [23][24] [25]. Shen et al. [26] studied a supply chain consisting of used product contributors, used consignment platforms and new product suppliers, and they analyzed the platforms under the consignment contracts pricing strategy and the product selection strategy under a consignment contract. Huang and Li [27] investigated how a closed-loop supply chain consisting of a recycler and two competing manufacturers can simultaneously optimize the membership strategy and alleviate problems regarding profit allocation. Sadjadi et al. [28] developed a game model for a two-level supply chain consisting of a manufacturer and two retailers to study the effects of pricing structure and cooperative advertising decisions on supply chain coordination performance. Dey et al. [25] used the Stackelberg model to determine the best decision for a closed-loop supply chain consisting of a manufacturer, two suppliers and two competing retailers. Rajabi et al. [29] studied joint pricing and inventory in a competitive supply chain consisting of a dominant manufacturer and two follower retailers facing nonlinear, price-dependent demand operating under Gounod model decisions. Hubert et al. [30] analyzed the role of blockchain adoption decisions and differentiated the pricing strategies of genuine manufacturers in combating counterfeit and counterfeit products based on a single-tier manufacturer framework. In this paper, we modeled the game between multi-oligopolistic suppliers and downstream producers and focused on the purchase of raw materials. In this regard, the goal of our paper was most similar to that of the study by Gong and Yang in [11]. However, Gong and Yang only considered the sequential pricing game model of two upstream producers, which assumes that the maximum demand and price sensitivity coefficients of downstream firms to two upstream producers are the same and does not fully reflect the characteristics of dominant firms; the model only considers the influence of two upstream firms' own factors on prices, and other influencing factors such as downstream firms are set as ideal. This approach has some significance in the study of pricing mechanisms, but its results are not in line with the actual market scenario. In fact, upstream firms have certain bargaining power in the process of pricing, and the sales price of downstream firms affects the market demand for the product, which in turn affects the price and profit of upstream producers. Therefore, the purchase volume of downstream firms and the size of the dominant and following coefficients have an impact on the profitability and pricing of firms, and the pricing mechanism studied by Gong and Yang lacks certain degrees of scientificity and rationality, as such actual influencing factors are not considered.

Based on these problems and ideas, in this paper, we further investigated the problem of the multi-oligopoly pricing mechanism in a raw material supply chain based on the research of Gong and Yang. We constructed a constrained sequential pricing game model by taking relevant parameters such as product demand function, marginal production cost, dominant coefficient, following coefficient and minimum purchase volume as constraints and transforming the model into a nonlinear bilevel programming model to facilitate model solving. In addition to the Nash equilibrium point, the boundary solution is also a stable equilibrium point and enables a following firm to obtain a higher sales price than the Nash equilibrium price. In this paper, we explored this concept. Finally, we carried out numerical simulations using MATLAB software, which reveal that the constrained sequential pricing game model with is more effective than the unconstrained sequential pricing game model in solving multi-oligopoly pricing mechanism problems.

Compared with the existing literature, the marginal contributions of this paper are mainly reflected in the following aspects: (1) From the perspective of demand uncertainty, the influence of downstream firms on upstream producers' pricing was incorporated into the game time series, constraints that are more in line with the market reality were added, and a class of sequential pricing game models that are more similar to the real market were constructed, making the pricing mechanism under study more scientific. (2) A nonlinear bilevel programming model was established to solve the constrained sequential pricing game model, and analytical solution formulas were derived for six special cases. (3) The validity of the constrained sequential pricing game model proposed in this paper was verified through numerical simulation experiments, and we found that the agreed minimum purchase volume and the dominant and following coefficients affect the stability of the market.

 

Point2: The article has a small bibliography in number of citations; and old. Authors should increase the number of references, preferably with articles from 2022 and 2021.

Response 2: Thank you for your valuable questions and professional suggestions. Following your valuable suggestions, we have revised the bibliography, and cited many articles from 2022 and 2021. Which are shown as below:

 

References:

1. Gurnani H, Gerchak Y. Coordination in decentralized assembly systems with uncertain component yields [J]. European Journal of Operational Research, 2007, (176):1559-1576.
2. Ji Q, Zhang F, Fang G, Hu X. Game model of blockchain adoption and product pricing in retail supply chain[J]. Chinese Journal of Management Science, 2022, DOI: 16381/j.cnki.issn1003-207x.2022.0315
3. Wang C, Li Y, Wang Z. Supply chain network optimization with consideration of raw material and final product substitutions driven by price and carbon emissions[J]. Kybernetes: The International Journal of Systems & Cybernetics, 2018, 47(8):1585-1603.
4. Razmi J, Kazerooni M P, Sangari M S. Designing an integrated multi-echelon, multi-product and multi-period supply chain network with seasonal raw materials[J]. Economic Computation & Economic Cybernetics Studies & Research, 2016, 50(1).
5. Das M, Jana D K, Alam S. Game theoretic analysis of a three-stage interconnected forward and reverse supply chain[J]. Environment, Development and Sustainability, 2022, 24(6): 7976-8007.
6. Taleizadeh A A, Noori-Daryan M. Pricing, manufacturing and inventory policies for raw material in a three-level supply chain[J]. International Journal of Systems Science, 2016, 47(4): 919-931.
7. Zarouri F, Khamseh A A, Pasandideh S H R. Dynamic pricing in a two-echelon stochastic supply chain for perishable products[J]. RAIRO-Operations Research, 2022, 56(4): 2425-2442.
8. Guo P, Hassin R. On the advantage of leadership in service pricing competition[J]. Operations Research Letters, 2013, 41(4): 397-402.
9. Keskin T, Taskin N. Strategic Pricing of Horizontally Differentiated Services with Switching Costs: APricing Model for Cloud Computing[J]. International Journal of Electronic Commerce, 2015, 19(3): 34-53.
10. Jiang B, Yang B. Quality and pricing decisions in a market with consumer information sharing[J]. Management Science, 2019, 65(1):272 -285.
11. Gong Q, Yang J. Dynamic of sequential pricing game with bounded rationality[J]. Chinese Journal of Management Science, 2020, 4(4): 186-194.
12. Ma J, Xie L. The stability analysis of the dynamic pricing strategy for bundling goods: a comparison between simultaneous and sequential pricing mechanism[J]. Nonlinear Dynamics, 2019, 95(2): 1147-1164.
13. Chen J, Chen J. Supply Chain Profit Game and Equilibrium Pricing[J]. Chinese Journal of Management Science, 2022, 30(9): 128-139.
14. Xu M, Li X. Unified pricing and service effort strategy in a dual-channel supply chain with bidirectional free-riding[J]. Journal of Shandong University (Natural Science), 2022, 57(9): 55-70.
15. Niu B, Mu Z, Cao B, et al. Should multinational firms implement blockchain to provide quality verification?[J]. Transportation Research Part E: Logistics and Transportation Review, 2021, DOI: 10.1016/j.tre.2020.102121.
16. Niu B, Shen Z, Xie F. The value of blockchain and agricultural supply chain parties' participation confronting random bacteria pollution[J]. Journal of Cleaner Production, 2021, DOI: 10.1016/j.jclepro.2021.128579.
17. Niu B, Dong J, Liu Y. Incentive alignment for blockchain adoption in medicine supply chains[J]. Transportation Research Part E: Logistics and Transportation Review, 2021, DOI: 10.1016/j.tre.2021.102276.
18. Li X, Liu R, Zhang Q. Research on cost information sharing and coordination contract of a supply chain with two suppliers and a single retailer[J]. Industrial Engineering and Management, 2021, 26(4): 1-10.
19. Li W, Chen J. Pricing and quality competition in a brand-differentiated supply chain[J]. International Journal of Production Economics, 2018, 202: 97-108.
20. Wen H, Xu M, Tao J. Sales model selection and pricing strategy for green degree concerned fresh agricultural products supply Chain[J]. Journal of Wuhan University (Science Edition), 2020, 66(5): 495-504.
21. Zhan B, Zhang H, Wang X. Procurement and pricing decision in dual-sourcing supply chain with buyers’s investment [J]. Chinese Journal of Management Science, 2021, 29(4): 104-114.
22. Lan T. The impact of different supply chain power structure for optimal pricing and brand differentiation strategy [J]. Soft Science, 2018, 32(2): 139-144.
23. Eghbali‐Zarch M, Taleizadeh A A, Tavakkoli‐Moghaddam R. Pricing decisions in a multiechelon supply chain under a bundling strategy[J]. International Transactions in Operational Research, 2019, 26(6): 2096-2128.
24. Giri B C, Bardhan S, Maiti T. Coordinating a three-layer supply chain with uncertain demand and random yield[J]. International Journal of Production Research, 2016, 54(8): 2499-2518.
25. Dey S K, Giri B C. Analyzing a closed-loop sustainable supply chain with duopolistic retailers under different game structures[J]. CIRP Journal of Manufacturing Science and Technology, 2021, 33: 222-233.
26. Shen B, Xu X, Yuan Q. Selling secondhand products through an online platform with blockchain[J]. Transportation Research Part E: Logistics and Transportation Review, 2020, DOI: 10.1016/j.tre.2020.102066.
27. Huang C, Li D. Research on closed-loop supply chain pricing and profit distribution based on noncooperative-cooperative biform game and deposit return to recyclers[J]. Chinese Journal of Management Science, 2022, DOI：16381/j.cnki.issn1003-207x.2021.2244.
28. Sadjadi S J, Alirezaee A. Impact of pricing structure on supply chain coordination with cooperative advertising[J]. RAIRO-Operations Research, 2020, 54(6): 1613-1629.
29. Rajabi N, Mozafari M, Naimi-Sadigh A. Bi-level pricing and inventory strategies for perishable products in a competitive supply chain[J]. RAIRO-Operations Research, 2021, 55(4): 2395-2412.
30. Hubert P, Jayashankar M S, Hou P. Blockchain adoption for combating deceptive counterfeits[J]. Production and Operations Management, 2021, DOI:10.1111/poms.13348.

 

Point 3: All formulas must be numbered and quoted in the text.

Response 3: Many thanks for the valuable questions and professional suggestions. Following your valuable suggestions, we have numbered all the formulas and quoted them in the text. Please see the revised manuscript.

Author Response File: Author Response.docx

Reviewer 2 Report

This paper constructs a sequential price competition model with constraints by incorporating the parameters related to the product demand function, marginal production cost, dominant coefficient, following coefficient, and agreed on minimum purchase quantity into constraints, and converted it into a non-linear two-layer programming model for solving. Using MATLAB software to conduct numerical simulation and find that the sequential price competition model with constraints is more effective than the sequential price competition model without constraints in solving the problem of the multi-oligopoly pricing mechanism

 

The research questions are interesting, and the contribution fills several important gaps in the literature. However, authors need to do some additional work to make their manuscripts ready for publication. 

 

Comments to the Author

 

#1: The language of the paper is not friendly enough. It is recommended to proofread the manuscript carefully and preferably get it edited by a professional language editor. Upload a language proofing certificate if necessary.

 

#2: The introduction should be strengthened. The authors need to include the research methods and findings in the introduction. The authors may need to briefly describe the idea model construction and the advantages and necessity of this model in the introduction.

Then answer several questions: Why is the topic important (or why do you study it)? What are the research questions? What has been studied? What has this paper done? What are your contributions?

 

#3: Lack of literature summary. More literature, especially the latest ones, should be reviewed in more detail as many papers are missing. References should be refined and updated.

 

 

#4: The authors need to summarize the significance of this study (theoretical and practical implications) in the conclusion.

Author Response

This paper constructs a sequential price competition model with constraints by incorporating the parameters related to the product demand function, marginal production cost, dominant coefficient, following coefficient, and agreed on minimum purchase quantity into constraints, and converted it into a non-linear two-layer programming model for solving. Using MATLAB software to conduct numerical simulation and find that the sequential price competition model with constraints is more effective than the sequential price competition model without constraints in solving the problem of the multi-oligopoly pricing mechanism.

The research questions are interesting, and the contribution fills several important gaps in the literature. However, authors need to do some additional work to make their manuscripts ready for publication.

Response: Thanks a lot for your encouragement. We greatly appreciate your time and very professional and helpful comments. These comments are valuable and very helpful for revising and improving our paper. We have carefully studied the comments and made revisions in the hope of the final approval. The revised part is marked in red in our revised paper. The main revisions in the paper and our response to the reviewers’ comments are as follows:

 

Point 1: The language of the paper is not friendly enough. It is recommended to proofread the manuscript carefully and preferably get it edited by a professional language editor. Upload a language proofing certificate if necessary.

Response 1: Thank you for your valuable questions and professional suggestions. Following your valuable suggestions, we have requested English editing services through MDPI's Author Services system and revised the manuscript accordingly as requested.

 

Point 2: The introduction should be strengthened. The authors need to include the research methods and findings in the introduction. The authors may need to briefly describe the idea model construction and the advantages and necessity of this model in the introduction. Then answer several questions: Why is the topic important (or why do you study it)? What are the research questions? What has been studied? What has this paper done? What are your contributions?

Response 2: Thank you for your valuable questions and professional suggestions. Following your valuable suggestions, we have rewritten the introduction. Which is shown as below.

As the social economy has been extensively reformed and opened up alongside its rapid development, the competition among firms is becoming increasingly intense. In a multi-oligopolistic supply chain market, there is market competition among suppliers, who not only have to calculate their own costs and profits, but also must consider multiple games with competitors and downstream firms. Some raw material supply markets are multi-oligopolistic supply chain markets, in which there are usually multiple suppliers, with one supplier in the leading position and others in following positions. The dominant supplier not only has the largest market share, but also has a dominant role in raw material pricing, while the following suppliers have no dominant capacity in the process of raw material pricing, despite having some pricing power, and they often have to adopt the "follow the market" strategy. However, uncertainty in suppliers' product supply is a common phenomenon in supply chain management, and to a certain extent, it can cause losses to firms [1]. Therefore, to reduce the risk of raw material supply chain breakage, downstream manufacturers often avoid adopting the raw material procurement strategy of "putting eggs in one basket” but sign long-term minimum supply purchase agreements with leading suppliers and also purchase raw materials through various channels. At this point, in the face of demand uncertainty, it is worth determining what pricing mechanism should be adopted by multi-oligopolistic suppliers in order to consolidate their market position and enhance their competitiveness.

Over a long period of time, academics have conducted a great deal of research regarding the pricing problem in supply chains, and many scholars have adopted different game approaches for use in different supply chain structures. Ji et al. [2] developed a dynamic game model regarding "upstream", wholesale price and retail price to study "upstream" decisions and product pricing in a retail supply chain, considering the differences in the brand image of two suppliers. Razmi et al. [4] developed a dynamic mixed integer linear programming (DMILP) model to optimize a seasonal raw material supply chain network by considering a multi-level supply chain with multiple products and multiple time periods. Das et al. [5] used centralized and decentralized models to study interconnected, three-stage forward and reverse supply chains with green conscious markets providing green products. Taleizadeh et al. [6] studied a problem related to decentralized, three-level supply chain total cost optimization using the Stackelberg–Nash model. Zarouri et al. [7] used the Stackelberg model to study a problem related to dynamic pricing in a perishable supply chain with one manufacturer, one retailer and two production and distribution periods. Guo et al. [8] used the Stackelberg game to study a problem related to the pricing game regarding two service providers with homogeneous consumers. Keskin and Taskin [9] constructed a two-stage pricing decision model for a two-oligopolistic game in the presence of asymmetric market shares based on consumer preferences. Jiang and Yang [10] constructed a dynamic game model to study the pricing mechanism and quality decisions of vendors in a community learning context. Gong and Yang [11] used a sequential pricing game model to study the pricing mechanisms of suppliers in a raw material supply chain. Ma and Xie [12] studied the pricing process of boundedly rational retailers for bundled products with limited information access and found that sequential games can be used to obtain a more stable system than simultaneous games. A sequential game is a form of game in which participants choose their strategies in a temporal sequence, and the choice of the first actor affects the choices available to the second actor. Unlike the traditional Bertrand model, it is a more typical dynamic game and provides an analytical tool to represent dynamic games of related firms. It is also different from the general delayed finite rationality model, in which the strategies of firms in the current period are influenced by the strategies of other firms in the previous period. For example, in the raw material supply market mentioned in our paper, Gong and Yang pointed out that the pricing mechanism of this type of market is a sequential game, in which the dominant supplier holds the "boss" position and has dominant power in each period, and its pricing can adopt a "delayed" strategy to make quotations at the end of the period, while the supplier in the following position provides quotations at the beginning of the period. This allows for better characterization of the dynamic evolution of the firm's game.

Supply chains are complex systems which consist of multiple member firms. In the study of supply and demand relationships, the existing literature focuses on the relationship between two suppliers and one retailer [13]-[22] and multi-level supply chain relationships [4][6] [23][24] [25]. Shen et al. [26] studied a supply chain consisting of used product contributors, used consignment platforms and new product suppliers, and they analyzed the platforms under the consignment contracts pricing strategy and the product selection strategy under a consignment contract. Huang and Li [27] investigated how a closed-loop supply chain consisting of a recycler and two competing manufacturers can simultaneously optimize the membership strategy and alleviate problems regarding profit allocation. Sadjadi et al. [28] developed a game model for a two-level supply chain consisting of a manufacturer and two retailers to study the effects of pricing structure and cooperative advertising decisions on supply chain coordination performance. Dey et al. [25] used the Stackelberg model to determine the best decision for a closed-loop supply chain consisting of a manufacturer, two suppliers and two competing retailers. Rajabi et al. [29] studied joint pricing and inventory in a competitive supply chain consisting of a dominant manufacturer and two follower retailers facing nonlinear, price-dependent demand operating under Gounod model decisions. Hubert et al. [30] analyzed the role of blockchain adoption decisions and differentiated the pricing strategies of genuine manufacturers in combating counterfeit and counterfeit products based on a single-tier manufacturer framework. In this paper, we modeled the game between multi-oligopolistic suppliers and downstream producers and focused on the purchase of raw materials. In this regard, the goal of our paper was most similar to that of the study by Gong and Yang in [11]. However, Gong and Yang only considered the sequential pricing game model of two upstream producers, which assumes that the maximum demand and price sensitivity coefficients of downstream firms to two upstream producers are the same and does not fully reflect the characteristics of dominant firms; the model only considers the influence of two upstream firms' own factors on prices, and other influencing factors such as downstream firms are set as ideal. This approach has some significance in the study of pricing mechanisms, but its results are not in line with the actual market scenario. In fact, upstream firms have certain bargaining power in the process of pricing, and the sales price of downstream firms affects the market demand for the product, which in turn affects the price and profit of upstream producers. Therefore, the purchase volume of downstream firms and the size of the dominant and following coefficients have an impact on the profitability and pricing of firms, and the pricing mechanism studied by Gong and Yang lacks certain degrees of scientificity and rationality, as such actual influencing factors are not considered.

Based on these problems and ideas, in this paper, we further investigated the problem of the multi-oligopoly pricing mechanism in a raw material supply chain based on the research of Gong and Yang. We constructed a constrained sequential pricing game model by taking relevant parameters such as product demand function, marginal production cost, dominant coefficient, following coefficient and minimum purchase volume as constraints and transforming the model into a nonlinear bilevel programming model to facilitate model solving. In addition to the Nash equilibrium point, the boundary solution is also a stable equilibrium point and enables a following firm to obtain a higher sales price than the Nash equilibrium price. In this paper, we explored this concept. Finally, we carried out numerical simulations using MATLAB software, which reveal that the constrained sequential pricing game model with is more effective than the unconstrained sequential pricing game model in solving multi-oligopoly pricing mechanism problems.

Compared with the existing literature, the marginal contributions of this paper are mainly reflected in the following aspects: (1) From the perspective of demand uncertainty, the influence of downstream firms on upstream producers' pricing was incorporated into the game time series, constraints that are more in line with the market reality were added, and a class of sequential pricing game models that are more similar to the real market were constructed, making the pricing mechanism under study more scientific. (2) A nonlinear bilevel programming model was established to solve the constrained sequential pricing game model, and analytical solution formulas were derived for six special cases. (3) The validity of the constrained sequential pricing game model proposed in this paper was verified through numerical simulation experiments, and we found that the agreed minimum purchase volume and the dominant and following coefficients affect the stability of the market.

 

Point 3: Lack of literature summary. More literature, especially the latest ones, should be reviewed in more detail as many papers are missing. References should be refined and updated.

Response 3: Many thanks for your valuable questions and professional suggestions. Following your valuable suggestions, we have added a literature summary in the introduction, revised the bibliography, and cited many latest articles from 2022 and 2021. Which are shown as below:

 

References:

1. Gurnani H, Gerchak Y. Coordination in decentralized assembly systems with uncertain component yields [J]. European Journal of Operational Research, 2007, (176):1559-1576.
2. Ji Q, Zhang F, Fang G, Hu X. Game model of blockchain adoption and product pricing in retail supply chain[J]. Chinese Journal of Management Science, 2022, DOI: 16381/j.cnki.issn1003-207x.2022.0315
3. Wang C, Li Y, Wang Z. Supply chain network optimization with consideration of raw material and final product substitutions driven by price and carbon emissions[J]. Kybernetes: The International Journal of Systems & Cybernetics, 2018, 47(8):1585-1603.
4. Razmi J, Kazerooni M P, Sangari M S. Designing an integrated multi-echelon, multi-product and multi-period supply chain network with seasonal raw materials[J]. Economic Computation & Economic Cybernetics Studies & Research, 2016, 50(1).
5. Das M, Jana D K, Alam S. Game theoretic analysis of a three-stage interconnected forward and reverse supply chain[J]. Environment, Development and Sustainability, 2022, 24(6): 7976-8007.
6. Taleizadeh A A, Noori-Daryan M. Pricing, manufacturing and inventory policies for raw material in a three-level supply chain[J]. International Journal of Systems Science, 2016, 47(4): 919-931.
7. Zarouri F, Khamseh A A, Pasandideh S H R. Dynamic pricing in a two-echelon stochastic supply chain for perishable products[J]. RAIRO-Operations Research, 2022, 56(4): 2425-2442.
8. Guo P, Hassin R. On the advantage of leadership in service pricing competition[J]. Operations Research Letters, 2013, 41(4): 397-402.
9. Keskin T, Taskin N. Strategic Pricing of Horizontally Differentiated Services with Switching Costs: APricing Model for Cloud Computing[J]. International Journal of Electronic Commerce, 2015, 19(3): 34-53.
10. Jiang B, Yang B. Quality and pricing decisions in a market with consumer information sharing[J]. Management Science, 2019, 65(1):272 -285.
11. Gong Q, Yang J. Dynamic of sequential pricing game with bounded rationality[J]. Chinese Journal of Management Science, 2020, 4(4): 186-194.
12. Ma J, Xie L. The stability analysis of the dynamic pricing strategy for bundling goods: a comparison between simultaneous and sequential pricing mechanism[J]. Nonlinear Dynamics, 2019, 95(2): 1147-1164.
13. Chen J, Chen J. Supply Chain Profit Game and Equilibrium Pricing[J]. Chinese Journal of Management Science, 2022, 30(9): 128-139.
14. Xu M, Li X. Unified pricing and service effort strategy in a dual-channel supply chain with bidirectional free-riding[J]. Journal of Shandong University (Natural Science), 2022, 57(9): 55-70.
15. Niu B, Mu Z, Cao B, et al. Should multinational firms implement blockchain to provide quality verification?[J]. Transportation Research Part E: Logistics and Transportation Review, 2021, DOI: 10.1016/j.tre.2020.102121.
16. Niu B, Shen Z, Xie F. The value of blockchain and agricultural supply chain parties' participation confronting random bacteria pollution[J]. Journal of Cleaner Production, 2021, DOI: 10.1016/j.jclepro.2021.128579.
17. Niu B, Dong J, Liu Y. Incentive alignment for blockchain adoption in medicine supply chains[J]. Transportation Research Part E: Logistics and Transportation Review, 2021, DOI: 10.1016/j.tre.2021.102276.
18. Li X, Liu R, Zhang Q. Research on cost information sharing and coordination contract of a supply chain with two suppliers and a single retailer[J]. Industrial Engineering and Management, 2021, 26(4): 1-10.
19. Li W, Chen J. Pricing and quality competition in a brand-differentiated supply chain[J]. International Journal of Production Economics, 2018, 202: 97-108.
20. Wen H, Xu M, Tao J. Sales model selection and pricing strategy for green degree concerned fresh agricultural products supply Chain[J]. Journal of Wuhan University (Science Edition), 2020, 66(5): 495-504.
21. Zhan B, Zhang H, Wang X. Procurement and pricing decision in dual-sourcing supply chain with buyers’s investment [J]. Chinese Journal of Management Science, 2021, 29(4): 104-114.
22. Lan T. The impact of different supply chain power structure for optimal pricing and brand differentiation strategy [J]. Soft Science, 2018, 32(2): 139-144.
23. Eghbali‐Zarch M, Taleizadeh A A, Tavakkoli‐Moghaddam R. Pricing decisions in a multiechelon supply chain under a bundling strategy[J]. International Transactions in Operational Research, 2019, 26(6): 2096-2128.
24. Giri B C, Bardhan S, Maiti T. Coordinating a three-layer supply chain with uncertain demand and random yield[J]. International Journal of Production Research, 2016, 54(8): 2499-2518.
25. Dey S K, Giri B C. Analyzing a closed-loop sustainable supply chain with duopolistic retailers under different game structures[J]. CIRP Journal of Manufacturing Science and Technology, 2021, 33: 222-233.
26. Shen B, Xu X, Yuan Q. Selling secondhand products through an online platform with blockchain[J]. Transportation Research Part E: Logistics and Transportation Review, 2020, DOI: 10.1016/j.tre.2020.102066.
27. Huang C, Li D. Research on closed-loop supply chain pricing and profit distribution based on noncooperative-cooperative biform game and deposit return to recyclers[J]. Chinese Journal of Management Science, 2022, DOI：16381/j.cnki.issn1003-207x.2021.2244.
28. Sadjadi S J, Alirezaee A. Impact of pricing structure on supply chain coordination with cooperative advertising[J]. RAIRO-Operations Research, 2020, 54(6): 1613-1629.
29. Rajabi N, Mozafari M, Naimi-Sadigh A. Bi-level pricing and inventory strategies for perishable products in a competitive supply chain[J]. RAIRO-Operations Research, 2021, 55(4): 2395-2412.
30. Hubert P, Jayashankar M S, Hou P. Blockchain adoption for combating deceptive counterfeits[J]. Production and Operations Management, 2021, DOI:10.1111/poms.13348.

Point 4: The authors need to summarize the significance of this study (theoretical and practical implications) in the conclusion.

Response 4: Thank you for your valuable questions and professional suggestions. Following your valuable suggestions, we have summarized the significance of this study (theoretical and practical implications) in the conclusion. Which are shown as below:

Based on the raw material supply chain market, in this paper, we investigated the sequential pricing game of multi-oligopolistic firms under constraints. By analyzing the mutual constraints between oligopolistic firms and downstream producers in the raw material supply chain and setting constraints such as parameters related to the product demand function, dominant coefficient, following coefficient and agreed minimum purchase volume, a constrained sequential pricing game model was constructed. A numerical simulation of the game model was also conducted using MATLAB software, which showed that changes in each parameter had impacts on the equilibrium quoted prices and profits of both firm 1 and firm 2. The closer the dominant coefficient is to the following coefficient, the more chaotic the market is, i.e., the longer it takes for firms to reach equilibrium, and vice versa, for the more stable the market is. The agreed minimum purchase volume between the dominant and downstream firms also affects the quoted prices and profits of the oligopolistic firms, and a larger agreed minimum purchase volume will lead to a decrease in the profits of the oligopolistic firms, which is not conducive to their sustainable development. Therefore, regulators and industry organizations should try to reasonably regulate the gap between the dominant and following coefficients, control a reasonable range of agreed minimum procurement volumes and determine a reasonable pricing mechanism to maintain a stable market situation and guide the market in an orderly manner.

Compared with the existing unconstrained sequential pricing mechanism, the proposed constrained sequential pricing game model considers constraints such as the parameters related to the product demand function, marginal production cost, dominant coefficient, following coefficient and agreed minimum purchase volume. The subsequently constructed nonlinear bilevel programming solving model is an extension and effective supplement to the model analysis, thus making the model more similar to the real market. Some of the conclusions obtained from this study also have connotations and implications in management and market economics. Some of the results can be used as references for decision making in production strategy reconstruction and the strategic cooperation of supply chain firms and can also provide theoretical support and methodological references for governments or market managers for the management of raw material supply chain markets.

Future research could explore the following aspects: (1) this model only considers the case of two firms, and when multiple dominant or following firms are involved, the model will become more complex, and further research is worthwhile; (2) this paper did not consider the impact of the dynamic demand of downstream firms on the pricing of upstream firms, and further research can be conducted regarding the impact of the product demand of downstream firms on the pricing of upstream firms.

Author Response File: Author Response.docx

Reviewer 3 Report

I enjoyed reading your paper.

Author Response

We are very grateful to your full approval and praise of the paper, which enabled us to gain motivation and confidence in academic study. And we have further embellished and enriched the paper. 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

improve the equations citations

Author Response

Reviewer 1: improve the equations citations

Response: We greatly appreciate your time and very professional and helpful comments. These comments are valuable and very helpful for revising and improving our paper. We have carefully studied the comments and improved the equations citations in the revised paper in the hope of the final approval. In addition, we also revised the paper according to the comments of the academic editor. The revised part is marked in red in our revised paper and hope that our revisions live up to your expectation.

Author Response File: Author Response.docx