Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper studies the supplier channel encroachment strategy considering the fairness concerns of retailers in the context of low carbon, combining the game model analysis of four scenarios of information symmetry/asymmetry, and has certain innovation. However, the following problems still exist.

The literature review section of the paper points out that the existing research is insufficient in systematically studying the integration of green investment levels and information structure differences under the “dual carbon” goals, but it does not clearly expound the core correlation mechanism between the low-carbon background and channel encroachment, as well as fairness concerns. Then, does the low-carbon transformation have a unique impact on the power structure of supply chain channels? How does this influence interact with concerns about fairness and channel encroachment? Are there any relevant theoretical or empirical studies in the existing literature that can support this association?

The model assumption mentions that “only retailers have fairness concerns, while suppliers do not consider fairness at all.” The rationality of this setting needs further explanation. In the real low-carbon supply chain, suppliers, as the dominant channel players, may also pay attention to the fairness of profit distribution when formulating wholesale prices and direct sales strategies due to considerations of long-term cooperation stability.

In the scenario of information asymmetry, the paper assumes that retailers have a grasp of the real market demand, while suppliers only know its probability distribution, but does not consider the information transmission strategy of retailers. In the actual supply chain, retailers may convey demand information through signals such as order volume and pricing, and fairness concerns may affect the authenticity of their signal transmission. Then, does the magnitude of the fairness concern coefficient θ affect the information transmission strategy of retailers? What specific impacts does this strategic information behavior have on suppliers' channel encroachment decisions and the level of green investment?

In the parameter assignment, the setting of v_h=12 and v_l=4 is based on the principle that “rural e-commerce accounts for 27.6%”, but the data source year and regional representativeness are not specified. For instance, does this proportion apply to high-priced low-carbon products?

The conclusion mentioned that "the green premium is mainly captured by suppliers and retailers' profits are compressed", but did not delve deeply into the channel power mechanism behind it. In a low-carbon supply chain, retailers may enhance the low-carbon premium of their products through green marketing, consumer education and other behaviors. If the green marketing investment of retailers is incorporated into the model, will the distribution structure of the green premium change? Will retailers' concerns about fairness vary in intensity due to their contributions to green value creation?

Author Response

We sincerely thank you for the detailed, in-depth, and insightful comments on our manuscript. We are truly grateful for the time and effort devoted to reading our work so carefully and for providing such constructive feedback. These valuable suggestions not only helped us identify and correct shortcomings in the original version but also offered important guidance for further advancing our research.

In the revision process, we carefully examined each comment and made corresponding modifications with great care. Substantive improvements have been implemented in the literature review, model assumptions, information structure analysis, parameter assignments, and conclusion sections. Through these revisions, we sought to enhance the logical clarity, the rigor of theoretical explanations, and the practical relevance of the paper.

For transparency, all changes have been revised point by point and highlighted in red in the manuscript to facilitate verification.

Comments1:

The literature review section of the paper points out that the existing research is insufficient in systematically studying the integration of green investment levels and information structure differences under the "dual carbon" goals, but it does not clearly expound the core correlation mechanism between the low-carbon background and channel encroachment, as well as fairness concerns. Then, does the low-carbon transformation have a unique impact on the power structure of supply chain channels? How does this influence interact with concerns about fairness and channel encroachment? Are there any relevant theoretical or empirical studies in the existing literature that can support this association?

 

Response1:

We sincerely thank you for raising this important point. We fully agree that the literature review should more explicitly clarify the correlation mechanism between low-carbon transformation, channel encroachment, and fairness concerns, and provide stronger theoretical and empirical support.

During the revision: we first clarified the logical framework: the low-carbon transformation drives suppliers to increase green investment, which enhances their channel power and may intensify the risk of channel encroachment; at the same time, retailers, when facing the spillover of green costs, are more likely to develop fairness concerns, making them more sensitive to the channel power structure. Based on this logic, we revised the literature review sequentially—starting with the impact of low-carbon policies and green investment on channel power, moving to the intertwining of fairness concerns with green cost transmission, then to the compounded effects of information asymmetry and green investment, and finally highlighting the research gap in the overall evaluation.

Specifically, in Section 2.1, we added studies discussing how low-carbon transformation reshapes channel power structures; in Section 2.2, we further emphasized how green cost transfer triggers retailer fairness concerns; in Section 2.3, we reinforced the complex effects when green investment interacts with information asymmetry on game outcomes and channel encroachment; and in Section 2.4, we introduced relevant theoretical and empirical studies (e.g., Li et al., 2021; Chen & Xiao, 2015; Wu et al., 2020), while concluding that although existing studies offer insights, they have not systematically integrated the chain of "low-carbon transformation—information structure differences—fairness concerns—channel encroachment," thus highlighting the contribution of our work.

All these revisions are located in Sections 2.1–2.4 of the literature review, and the changes have been highlighted in the revised manuscript.

 

Comments2:

The model assumption mentions that "only retailers have fairness concerns, while suppliers do not consider fairness at all." The rationality of this setting needs further explanation. In the real low-carbon supply chain, suppliers, as the dominant channel players, may also pay attention to the fairness of profit distribution when formulating wholesale prices and direct sales strategies due to considerations of long-term cooperation stability.

 

Response2:

We sincerely thank you for raising this crucial point, and we fully agree that the rationality of the assumption that "only retailers have fairness concerns" requires further explanation. Indeed, in real low-carbon supply chains, suppliers as dominant channel players may also care about fairness in profit distribution for the sake of long-term cooperation stability.

During the revision: our approach was to first acknowledge the realism that suppliers may also possess fairness concerns. However, for the sake of research focus and model tractability, we chose to model only retailers' disadvantageous inequity aversion. This choice is motivated by the fact that retailers often face higher operational costs and greater demand uncertainty, while their profits are doubly squeezed by channel encroachment and green cost transfer. Consequently, retailers are more likely to display sensitivity to disadvantageous fairness in the game. Concentrating fairness concerns on retailers therefore helps highlight the core mechanism of our study while avoiding excessive model complexity that could undermine interpretability.

In terms of specific revisions, we added an explanation of the research boundary in Section 3.1 Model Description, clarifying the rationale for considering only retailer fairness concerns and citing related literature (e.g., Chen & Xiao, 2015; Wu et al., 2020) to show consistency with mainstream modeling practices. In addition, in Section 3.2 Assumptions, we inserted a paragraph acknowledging the potential existence of supplier fairness concerns, and we positioned this as a future research extension, suggesting that bilateral fairness concerns could be incorporated in future studies.

These revisions are mainly reflected in Sections 3.1–3.2 of the Model Construction and Assumptions, and have been highlighted in the revised manuscript.

 

Comments3:

In the scenario of information asymmetry, the paper assumes that retailers have a grasp of the real market demand, while suppliers only know its probability distribution, but does not consider the information transmission strategy of retailers. In the current supply chain, retailers may convey demand information through signals such as order volume and pricing, and fairness concerns may affect the authenticity of their signal transmission. Then, does the magnitude of the fairness concern coefficient θ affect the information transmission strategy of retailers? What specific impacts does this strategic information behavior have on suppliers' channel encroachment decisions and the level of green investment?

 

Response3:

We sincerely thank you for raising this forward-looking question. We agree that under information asymmetry, retailers not only hold the real market demand information but may also influence supplier decisions through information transmission strategies, with fairness concerns directly affecting the authenticity of such transmission.

In terms of revision logic, we clarified the relationship between the fairness concern coefficient θ and the authenticity of retailer information transmission: when θ is relatively high, retailers are more sensitive to unfair profit distribution, which may reduce the authenticity of the transmitted information; when θ is lower, their transmission tends to reflect real demand more faithfully. This indicates that fairness concerns and information asymmetry jointly affect suppliers' channel encroachment decisions and their level of green investment.

The specific revisions are as follows: in Section 3.2 Assumptions, we added a description of the relationship between fairness concerns and information authenticity; in Sections 5.1–5.2 propositions and interpretations, we further elaborated on how θ influences suppliers' channel encroachment and green investment decisions under information asymmetry; and finally, in Section 8 Conclusion, we summarized that the coupling effect of fairness concerns and information asymmetry represents an important direction for future research.

These revisions have been made in Sections 3.2, 5.1–5.2, and Section 8 Conclusion, and are highlighted in the revised manuscript.

 

Comments4:

In the parameter assignment, the setting of vh=12 and vl=4 is based on the principle that "rural e-commerce accounts for 27.6%", but the data source year and regional representativeness are not specified. For instance, does this proportion apply to high-priced low-carbon products?

 

Response4:

We sincerely thank you for the detailed comment on parameter settings, and we fully agree that it is necessary to provide clearer explanations of the data sources, the year of reference, and the applicability of these values in order to enhance the transparency and credibility of the study.

In revising this part, our approach was to first supplement the explanation of the data source, specifying that the proportion was drawn from national statistics and related studies, and indicating the reference year and context. Second, we clarified the representativeness of this proportion across different regions and product types, particularly its relation to the demand distribution of high-priced low-carbon products. These additions make the parameter assignment more evidence-based and reasonable.

The specific revisions were made in the parameter assignment section of Section 6, Simulation Analysis: when explaining the basis for setting vh=12 and vl=4, we added the year of the data source and indicated that the proportion comes from rural e-commerce development statistics, reflecting urban–rural consumption differences. At the same time, we clarified its applicability to high-priced low-carbon products by stressing the relative rather than absolute nature of the ratio, thereby ensuring the robustness and interpretability of the model results.

These revisions are located in Section 6, Simulation Analysis – parameter assignment, and are highlighted in the revised manuscript.

Parameter	Value (Base)	Sensitivity (Low)	Sensitivity (High)	Source & Explanation
b	2	1.5	3	Typical price-elasticity of consumer goods ranges from –1.5 to –3, so we use 2 [38].
r	0.5	0.42	0.6	Survey reports show ~42–60% of consumers willing to pay more for sustainable products; we set r≈0.5, .
λ	0.6	0.5	0.7	Asia-Pacific accounted for >57% of global e-commerce value in 2024, so λ≈0.6.
d	4	3	5	Average shipping cost is 10–15% of order value; for a $40 average order, cost ≈$4.
η	0.1	0.05	0.15	Fortune Global 500 firms spend ~$20 billion/year on CSR, ~0.1% of total revenues, so η≈0.1.
e	0.3	0.1	0.5	Cao et al. (2022) and Ghosh & Shah (2015), who model low-carbon supply chains with investment levels between 0.1 and 0.5 after normalization [39, 40]. So we set e = 0.3.
θ	0.4	0.1	0.6	The fairness concern coefficient θ draws on behavioral supply chain literature, where typical values range from 0.1 to 0.6. We set 0.4 as the base [35, 41, 42].

35.Cui, T.H.; Raju, J.S.; Zhang, Z.J. Fairness and channel coordination. Manag. Sci. 2007, 53(8), 1303–1314. https://doi.org/10.1287/mnsc.1060.0697.

38.Tellis, G.J. The price elasticity of selective demand: A meta-analysis of econometric models of sales. J. Mark. Res. 1988, 25(4), 331–341. https://doi.org/10.1177/002224378802500401

39.Cao, K.; Zhang, Q.; He, P. Low-carbon supply chain coordination with green investment under different channel power structures. Int. J. Prod. Econ. 2022, 247, 108429. https://doi.org/10.1016/j.ijpe.2022.108429.

40.Ghosh, D.; Shah, J. Supply chain analysis under green sensitive consumer demand and cost sharing contract. Int. J. Prod. Econ. 2015, 164, 319–329. https://doi.org/10.1016/j.ijpe.2014.11.009.

41.Ho, T.H.; Su, X. Peer-induced fairness in games. Am. Econ. Rev. 2009, 99(5), 2022–2027. https://doi.org/10.1257/aer.99.5.2022

42.Katok, E.; Pavlov, V. Fairness in supply chain contracts: a laboratory study. J. Oper. Manag. 2013, 31(3), 129–137. https://doi.org/10.1016/j.jom.2013.01.001

 

Comments5:

The conclusion mentioned that "the green premium is mainly captured by suppliers and retailers' profits are compressed", but did not delve deeply into the channel power mechanism behind it. In a low-carbon supply chain, retailers may enhance the low-carbon premium of their products through green marketing, consumer education and other behaviors. If the green marketing investment of retailers is incorporated into the model, will the distribution structure of the green premium change? Will retailers' concerns about fairness vary in intensity due to their contributions to green value creation?

 

Response5:

We sincerely thank you for the insightful comment on the conclusion section. We fully agree that in the context of a low-carbon supply chain, the distribution of the green premium is not only related to suppliers' green investment but may also be influenced by retailers' green marketing efforts and consumer education activities. Therefore, it is necessary to further elaborate the underlying channel power mechanism in the conclusion.

In terms of revision logic, we first extended the discussion of the conclusion "the green premium is mainly captured by suppliers' and retailers' profits are compressed" by analyzing the underlying mechanism, namely the suppliers' bargaining advantage and channel control power. We then addressed your suggestion by theoretically exploring the possibility that if retailers' green marketing investment were incorporated into the model, the distribution structure of the green premium might change: retailers could not only enhance the low-carbon added value of products but also secure a more equitable share in profit distribution. At the same time, this additional contribution might alter the intensity of retailers' fairness concerns, thereby affecting their sensitivity to profit allocation outcomes.

The specific revisions were made in Section 8 Conclusion: we added a paragraph elaborating on the mechanism of green premium distribution, highlighting the different roles of suppliers and retailers in green value creation, and suggesting the incorporation of retailers' green marketing investment as a potential future extension to enrich the analysis of the relationship between fairness concerns and green premium allocation.

These revisions are located in Section 8 Conclusion, and have been highlighted in the revised manuscript.

 

Once again, we extend our most sincere gratitude to you. Your careful review and constructive feedback have greatly contributed to the improvement of this paper and have guided us to be more rigorous and comprehensive in both research perspective and presentation. We sincerely hope that the revised manuscript meets your expectations, and we look forward to receiving your valuable guidance and advice in the future.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Author(s)

Your topic is timely, and the “fairness × green × information” triad is worthwhile. The manuscript would benefit from sharpening the theoretical architecture, cleaning several modelling choices, and strengthening empirical credibility in the simulation design.

 

Key comments

1)

1. Equation (1) writes the retailer’s utility as πr=πr±θ(πs−πr). The “±” leaves the definition ambiguous (advantageous vs. disadvantageous inequality). Please specify the exact piecewise form (e.g., Fehr–Schmidt style) and the fairness reference under each scenario (encroachment vs. not). As written, readers cannot reproduce comparative statics. Cite and align with a standard formulation or justify departures.

1. Earlier, you defined four scenarios as SN/SE/AN/AE, yet later, Section 4 refers to “NN/NE,” and subsection 4.1 is titled “No Supplier Encroachment (SN)” but uses pNNp ​ in equations. Please fix the label system and maintain it throughout the proofs, propositions, figures, and tables.

2)

1. “Green input” e shifts demand additively via re, raises costs via ηe² and critically has no explicit emissions or social-welfare link. Given the low-carbon framing, consider adding an emissions function C(e) (e.g., decreasing and convex), a social planner or regulatory view (carbon tax/subsidy), or at least report environmental outcomes alongside profits to avoid a purely private-benefit framing.

1. Equal sharing of green costs is assumed “for fairness and incentive compatibility.” That choice drives several results (retailer’s profit compression under higher eee). Provide a contract section that compares equal sharing with alternative schemes (two-part tariffs, revenue sharing, cost-plus, or green-bonus contracts) and show which yields channel coordination across scenarios.

3)

1. Reference profit under fairness: When encroachment occurs, the retailer’s fairness reference switches to the supplier’s direct-channel profit (not total supplier profit). Provide a clear behavioural rationale and cite sources; otherwise, the fairness target looks ad hoc and mechanically pushes some comparative statics.

4)

1. Several simulation inputs come from Wikipedia elasticity pages, a 2015 Nielsen blog, Apple’s gross margin, and generic shipping costs; these are not suitable for calibration in a journal article. Replace with peer-reviewed or official datasets, justify mappings to your abstract parameters, and add sensitivity sets (high/low b,r,η,d,λ).

1. Share the MATLAB code (or Python) and random seeds as supplementary material, along with a README describing how each figure is generated for reproducibility

5)

1. The literature review is well organised, but several paragraphs are repeated verbatim in the “Research Gap” subsection; this should be tightened and deduplicated.

1. Strengthen links between your results and prior dual-channel and fairness models: when do your thresholds reduce to known results if e=0 or θ=0? A comparative table would help anchor what is genuinely new versus a parameterised special case.

6)

1. The implications section states that green premiums are captured upstream and urges suppliers to “scientifically grasp” investment boundaries, while encouraging better information sharing and incentive design. Turn these into actionable prescriptions: propose a minimal information-sharing mechanism that improves expected channel profit under asymmetry (e.g., cheap-talk thresholds or a screening contract).

7)

1. There are duplicated sentences in the research gap; several terms alternate (encroachment vs. invasion); and some typos (e.g., “non-encroachment model (NN)” vs. “SN” in the same section). Clean thoroughly and standardise the terminology.

1. The Nike/Moutai examples use non-archival links with trailing question marks and mixed formatting. Please replace with citable reports or academic sources and ensure URLs are stable; otherwise, move such material to an appendix.
2. Add a notation table early (complete, consistent), a scenario map (flow diagram with timing), and for simulations, provide figure captions that state parameter values and the main takeaway.
3. Use consistent titles for the four scenarios across text, equations, and figures (SN/SE/AN/AE only, or NN/NE/AN/AE, but not both).

 

Author Response

We sincerely thank you for the careful review and the constructive comments. We are deeply grateful for your thoughtful feedback, which has been invaluable in helping us identify and address the shortcomings of the original manuscript while also providing clear guidance for further improvement. In response, we have carefully revised and supplemented the paper point by point, with all modifications highlighted in red in the revised manuscript to facilitate verification.

 

Comments1:

Equation (1) writes the retailer's utility as πr=πr±θ(πs−πr). The "±" leaves the definition ambiguous (advantageous vs. disadvantageous inequality). Please specify the exact piecewise form (e.g., Fehr–Schmidt style) and the fairness reference under each scenario (encroachment vs. not). As written, readers cannot reproduce comparative statics. Cite and align with a standard formulation or justify departures.

 

Response1:

We sincerely thank you for raising this crucial point on the retailer's utility function. We fully agree that the "±" symbol in the original manuscript created ambiguity and did not clearly distinguish between disadvantageous and advantageous inequality.

During revision, we followed Fehr and Schmidt (1999) and Cui et al. (2007) and rewrote the retailer's utility function in the standard disadvantageous-inequity aversion form, explicitly expressed in Eq. (2) as

 

This formulation clearly shows that when the retailer's profit is lower than the supplier's, its utility decreases according to the fairness concern coefficient θ. We further explained that in the low-carbon supply chain scenarios considered here, suppliers are the dominant players and rarely earn less than retailers; thus, advantageous-inequity aversion is negligible. In addition, in Section 3.2 Assumptions, we explained the rationale for this assumption: focusing only on retailers' disadvantageous inequity aversion keeps the model tractable and aligns with established practices in the literature. We also noted that this is a simplifying assumption, and future research could extend the framework to consider bilateral fairness concerns.

These revisions are located in Section 3.2 Assumptions, and are highlighted in the revised manuscript.

 

Comments2:

Earlier, you defined four scenarios as SN/SE/AN/AE, yet later, Section 4 refers to "NN/NE," and subsection 4.1 is titled "No Supplier Encroachment (SN)" but uses pNNp ​ in equations. Please fix the label system and maintain it throughout the proofs, propositions, figures, and tables.

 

Response2:

We sincerely thank you for pointing out the inconsistency in scenario labeling, and we fully agree that the coexistence of “SN/SE/AN/AE” and "NN/NE" in the original manuscript was confusing and undermined the clarity and readability of the paper.

In our revision, we systematically reviewed the entire manuscript and unified all scenario labels as SN (Symmetric information, No encroachment), SE (Symmetric information, Encroachment), AN (Asymmetric information, No encroachment), and AE (Asymmetric information, Encroachment). This labeling scheme was defined in Section 3 (Model Construction) and is now consistently applied throughout Section 4 and the subsequent derivations, propositions, simulation analysis, figures, and tables, ensuring logical coherence and notational consistency.

These revisions span the entire manuscript, with particular focus on Section 4 and subsequent sections, and have been comprehensively unified in the revised manuscript.

 

Comments3:

"Green input" e shifts demand additively via re, raises costs via ηe2 and critically has no explicit emissions or social-welfare link. Given the low-carbon framing, consider adding an emissions function C(e) (e.g., decreasing and convex), a social planner or regulatory view (carbon tax/subsidy), or at least report environmental outcomes alongside profits to avoid a purely private-benefit framing.

 

Response3:

We sincerely thank you for this highly constructive comment. We fully agree that the original manuscript placed excessive emphasis on profit outcomes while lacking an explicit presentation of environmental performance, which could lead to a "purely private-benefit framing."

In terms of revision logic, we adopted your suggestion by introducing an environmental linkage assumption into the model and supplementing environmental performance outcomes in the simulations. Specifically, in Section 3.2 Assumptions, we added Assumption 5, defining an emissions function  which is decreasing and convex in e, to capture diminishing marginal abatement. This retains tractability while adding an explicit environmental reference alongside profit outcomes. Then, in Section 6.5 Simulation Analysis, we reported environmental indicators in addition to profit results, namely emissions , abatement , and abatement rate  presented in Table 3. These revisions avoid a purely private framing and strengthen the alignment of our model with the low-carbon context.

These revisions are mainly reflected in Section 3.2 Assumptions (Assumption 5) and the end of Section 6 (Subsection 6.5 and Table 3), and are highlighted in the revised manuscript.

 

Comments4:

Equal sharing of green costs is assumed "for fairness and incentive compatibility." That choice drives several results (retailer's profit compression under higher e). Provide a contract section that compares equal sharing with alternative schemes (two-part tariffs, revenue sharing, cost-plus, or green-bonus contracts) and show which yields channel coordination across scenarios.

 

Response4:

We sincerely thank you for highlighting that relying only on equal sharing (ES) of green costs limits the generality of the results and for requesting comparisons with alternative contracts. We fully agree. Accordingly, we added a dedicated Section 7 "Extension" that systematically compares alternative mechanisms to more comprehensively link cost allocation, fairness concerns, and channel coordination in a low-carbon setting.

In terms of the revision logic, within a unified framework we introduced and compared Equal Sharing (ES), Two-Part Tariffs (TPT), Revenue Sharing (RS), Cost-Plus (CP), and Green-Bonus (GB) across the four scenarios (SN/SE/AN/AE). To ensure comparability and reproducibility, we reported the functional forms and parameter settings, and presented side-by-side outcomes for price, quantity, profit, and green investment.

The concrete revisions and main findings are presented in Sections 7.1–7.3 with supporting figures: Figures 11–14 provide head-to-head comparisons and sensitivity sweeps. The text states that ES, while a clean baseline, cannot by itself remove inefficiencies from double marginalization; TPT and properly parameterized RS can replicate the centralized (First-Best) outcome, eliminate double marginalization, and achieve channel coordination; CP improves cost pass-through but does not guarantee full coordination; GB works as a complementary incentive that stabilizes cooperation in the presence of fairness concerns. Section 7.3 summarizes these results and offers managerial implications.

These additions appear in Section 7 (7.1 Mechanism Introduction, 7.2 Simulation Analysis, 7.3 Conclusion of the Extension), highlighted in the revised manuscript.

 

Comments5:

Reference profit under fairness: When encroachment occurs, the retailer's fairness reference switches to the supplier's direct-channel profit (not total supplier profit). Provide a clear behavioural rationale and cite sources; otherwise, the fairness target looks ad hoc and mechanically pushes some comparative statics.

 

Response5:

We sincerely thank you for raising this crucial point regarding the "reference profit under fairness." We fully agree that without a clear behavioral rationale and supporting citations, the choice of reference could appear ad hoc and mechanically affect the comparative statics.

During revision, we strengthened the explanation of fairness reference in Sections 3.1–3.2. Specifically, we clarified that when channel encroachment occurs, the retailer takes the supplier's direct-channel profit as the fairness reference, rather than the supplier's total profit. This is because the supplier's direct channel competes directly with the retailer, making it the most salient and relevant benchmark for relative position in profit distribution.

In addition, we added theoretical and empirical support. Drawing on fairness preference theory (Fehr & Schmidt, 1999) and supply chain fairness studies (Cui et al., 2007), we noted that fairness concerns are typically anchored to the outcomes of the most salient competitor. For retailers, this salient comparator is the supplier's direct channel rather than the supplier's total profit. Thus, the choice of reference is both behaviorally grounded and literature-supported. (Fehr, E.; Schmidt, K.M. A theory of fairness, competition, and cooperation. Q. J. Econ. 1999, 114, 817–868. https://doi.org/10.1162/003355399556151Cui, T.H.; Raju, J.S.; Zhang, Z.J. Fairness and channel coordination. Manag. Sci. 2007, 53, 1303–1314. https://doi.org/10.1287/mnsc.1060.0679)

Finally, we acknowledged that in real low-carbon supply chains, suppliers may also pay attention to fairness in profit allocation. However, for tractability and to isolate the marginal effects of retailer fairness concerns, our study focuses solely on the retailer's fairness concerns. We emphasized that this is a reasonable simplifying assumption and noted that future research could extend the analysis to bilateral fairness.

These revisions are located in Sections 3.1–3.2, and are highlighted in the revised manuscript.

 

Comments6:

Several simulation inputs come from Wikipedia elasticity pages, a 2015 Nielsen blog, Apple's gross margin, and generic shipping costs; these are not suitable for calibration in a journal article. Replace with peer-reviewed or official datasets, justify mappings to your abstract parameters, and add sensitivity sets (high/low b, r,η, d,λ).

 

Response6:

We sincerely thank you for raising this important point regarding the sources of simulation input parameters. We fully agree that relying on non-academic or non-official data (e.g., Wikipedia, blogs, or company gross margins) was not suitable for a journal article.

In our revision, we systematically updated the parameter settings: first, we replaced the previous informal sources with peer-reviewed studies, official statistics, and authoritative market reports; second, we provided detailed justifications for how each dataset maps to our abstract parameters; and finally, we added sensitivity sets (high/low values) for each key parameter to verify the robustness of our main conclusions. In addition, we reported Base/Low/High values for these parameters in Table 2, and noted in both the table footnotes and the text that "most results remain consistent within this range, thereby supporting the robustness of our conclusions."

These revisions are located in Section 6 Simulation Analysis – Parameter Assignment (Table 2 and accompanying explanation), and are highlighted in the revised manuscript.

 

Comments7:

Share the MATLAB code (or Python) and random seeds as supplementary material, along with a README describing how each figure is generated for reproducibility.

 

Response7:

We sincerely thank you for the valuable suggestion on reproducibility and fully agree that the research results should be verifiable. In response, we have prepared a compressed package containing the MATLAB codes used to generate all results in the paper as well as the original figure files. This package will be uploaded as supplementary material together with the revised manuscript, enabling reviewers and readers to reproduce our study.

 

Comments8:

The literature review is well organised, but several paragraphs are repeated verbatim in the "Research Gap" subsection; this should be tightened and deduplicated.

 

Response8:

We sincerely thank you for the careful comment on the structure of the literature review. We fully agree that in the original manuscript, some paragraphs in the "Research Gap" subsection were repeated verbatim from earlier sections, which reduced conciseness.

In response, we carefully reviewed the literature review, deleted the redundant content, and merged/condensed overlapping statements. The revised "Research Gap" subsection now directly highlights the novelty and contribution of this paper without repeating earlier discussions.

These revisions are located in the literature review section, particularly the "Research Gap" subsection, and are highlighted in the revised manuscript.

 

Comments9:

Strengthen links between your results and prior dual-channel and fairness models: when do your thresholds reduce to known results if e=0 or θ=0? A comparative table would help anchor what is genuinely new versus a parameterised special case.

 

Response9:

We sincerely thank you for this constructive suggestion, and we fully agree that our results should be linked to prior dual-channel and fairness models to emphasize both novelty and consistency with established work.

In the main text, we chose not to add the full derivations and comparative tables for the limiting cases, primarily to avoid excessive length and redundancy. To address your concern, we consolidated the relevant material in Appendix A, where we explicitly show:

Appendix A: Proof Sketches for Limiting Cases

A.1 No Greening (): Back to DM-relief vs. Cannibalization

When green investment is absent (), demand reduces to  and the green cost vanishes. This reproduces the classical linear-demand dual-channel model.

Centralized benchmark:

Maximize . First-order condition yields:

Wholesale-only (no encroachment, SN):

Retailer best response p Quantity  Supplier maximizes . FOC gives w Thus q the classic double marginalization result.

Direct-only (encroachment extreme):

Supplier monopoly: max. Solution: p  Compare to wholesale profit  Thus  positive when downstream cost  is high, recovering the classic DM-relief vs. cannibalization trade-off.

A.2 No Fairness (): Back to Classic Coordination

Retailer utility U. Setting  collapses utility to pure profit: U Then:

- Wholesale-only returns to Stackelberg result of A.1.
- Two-part tariff (TPT) with , fixed fee  coordinates fully, achieving centralized outcome.
- Revenue sharing (RS) at  with suitable share also coordinates.
- Cost-plus (CP) remains distorted.

Thus  eliminates all fairness-driven comparative statics, leaving only classic coordination contracts as in Cachon & Lariviere (2005).

A.3 One-line Anchors for Main Text

When greening is shut down (), our encroachment thresholds collapse to the standard dual-channel DM-relief vs. cannibalization result. When fairness vanishes (), retailer utility reduces to profit and coordination aligns with two-part tariff or revenue-sharing contracts.

Case	Our model	Reduced form	Anchor literature
e>0, θ>0	Green + fairness + info asymmetry	New interaction	—
e=0	No green effort	Dual-channel DM vs. cannibalization	Chiang et al. (2003); Arya et al. (2007)
θ=0	No fairness	Classic coordination contracts	Cachon & Lariviere (2005)

With this arrangement, we avoided inflating the length of the main text while ensuring that interested readers and reviewers can clearly see in the appendix how our model reduces to established results in the limiting cases.

 

Comments10:

The implications section states that green premiums are captured upstream and urges suppliers to "scientifically grasp" investment boundaries, while encouraging better information sharing and incentive design. Turn these into actionable prescriptions: propose a minimal information-sharing mechanism that improves expected channel profit under asymmetry (e.g., cheap-talk thresholds or a screening contract).

 

Response10:

We sincerely thank you for this valuable comment and fully agree that the "Implications" section should not remain at the level of general principles but instead offer more actionable prescriptions.

In terms of revision logic, following your suggestion, we expanded Section 7 Extensions to introduce and compare different information-sharing and incentive mechanisms, particularly threshold-based signaling and contract screening under information asymmetry, showing how they can improve expected channel profit while accounting for fairness concerns. We then distilled these analyses in Section 8 Conclusion, offering actionable prescriptions such as:(1) adopting minimal information-sharing mechanisms (e.g., threshold-based demand signals) to partially mitigate efficiency losses under asymmetric information;(2) implementing contract screening mechanisms (e.g., differentiated contracts based on green investment or sales volume) to enhance incentive compatibility and thereby achieve higher levels of green investment and channel profit.

These revisions are located in Section 7 Extensions and Section 8 Conclusion, and are highlighted in the revised manuscript.

 

Comments11:

There are duplicated sentences in the research gap; several terms alternate (encroachment vs. invasion); and some typos (e.g., "non-encroachment model (NN)" vs. "SN" in the same section). Clean thoroughly and standardise the terminology.

 

Response11:

We sincerely thank you for the reminder. We have thoroughly cleaned and standardized the manuscript: deduplicated the "Research Gap" subsection; unified terminology to encroachment (no longer alternating with invasion); corrected all label/typo issues (e.g., "NN" vs. "SN" inconsistencies), and updated section titles, figure captions, and table titles accordingly. All changes are highlighted in the revised manuscript for easy verification.

 

Comments12:

The Nike/Moutai examples use non-archival links with trailing question marks and mixed formatting. Please replace with citable reports or academic sources and ensure URLs are stable; otherwise, move such material to an appendix.

 

Response12:

We sincerely thank you for pointing out the citation issues in the introduction. We fully agree that the use of non-archival links with unstable formats in the original manuscript was not appropriate for academic writing.

In the revision, we thoroughly updated the Nike and Moutai case citations: replacing the previous dynamic web links with stable, citable sources such as official annual reports and authoritative datasets, and standardizing their formatting in the reference list. The narrative of the examples was retained to highlight the practical relevance of our research.

These revisions are located in Section 1 Introduction and are highlighted in the revised manuscript.

 

Comments13:

Add a notation table early (complete, consistent), a scenario map (flow diagram with timing), and for simulations, provide figure captions that state parameter values and the main takeaway.

Use consistent titles for the four scenarios across text, equations, and figures (SN/SE/AN/AE only, or NN/NE/AN/AE, but not both).

 

Response13:

We sincerely thank you for these specific and constructive suggestions, and we fully agree that the original manuscript lacked completeness and consistency in the notation, scenario presentation, and figure interpretation.

In the revision, we made the following improvements: first, we added a complete and consistent notation table (Table 1) at the beginning of the paper, which explains all variables and parameters; second, we introduced a scenario flow diagram (Figure 1) in timeline form to clearly illustrate the decision sequence and information structure differences across the four scenarios (SN/SE/AN/AE); and finally, we rewrote all simulation figure captions, specifying the key parameter values and highlighting the main takeaways so that readers can immediately grasp the message of each figure. In addition, we thoroughly standardized the scenario labeling throughout the manuscript, consistently using only SN/SE/AN/AE, and eliminating the mixed use of NN/NE, thereby improving overall clarity and readability.

These revisions are mainly reflected in Table 1, Figure 1, and the captions of all simulation figures in Section 6, and are highlighted in the revised manuscript.

 

Once again, we sincerely thank you for your thoughtful review and valuable guidance. Your comments have greatly strengthened the rigor of our work in terms of model assumptions, simulation design, and result interpretation, while also improving the clarity and consistency of the overall presentation. We truly hope that the revised manuscript meets your expectations, and we would be most grateful to receive any further feedback you may have.

Author Response File: Author Response.docx