Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article is very interesting, but the research conclusion lacks case support, and the article lacks management enlightenment, so it is hired after the research is revised.

Comments on the Quality of English Language

This article is very interesting, but the research conclusion lacks case support, and the article lacks management enlightenment, so it is hired after the research is revised.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

sustainability-3254244

This paper analyzed a competitive supply chain with one retailer and two manufacturers, focusing on how manufacturers' misreporting behaviors impact pricing and performance, influenced by the retailer's cooperate social responsibility (CSR). While it seemed that the authors invested considerable effort into the research, the presentation of the manuscript can be significantly improved for readability purposes. Some comments on improvements are as follows.

Abstract: please define the CSR.

Introduction. (1) Line 65 backward induction. Please give a brief description of the “backward induction” methods and why it is selected for this particular application. (2) Add more concrete statistics that involve misreporting. For example, X misreporting leads to Y% of loss, negative impact on decision making, or incorrect resources allocation. (3) Add explanation on how this work can contribute to the journal of Sustainability.

Section 2 is sufficient, but I would like to see more discussion of the previous methods or approach similar to the one proposed by the authors.

Section 3. (1) Line 151. Could you explain why the two manufacturers are denoted as i and 3-i? Also explain what does the “i" represent. (2) Line 155 before Figure 1. Also, explain the notations in Figure 1, for example, the Stackelberg game, leader, and follower. What do “wj” and “mi,e” represent? All of this should be clearly identified.  (3) Please carefully define all the variables, parameters and notations. Table 1 should be moved further up close to the first variables that were introduced in the text. (4) This section does not explain how “backward induction” were employed as mentioned in the Introduction line 65. (4) Providing a flowchart on how the methods in Section 3 related to or resulted in the 6 theorems in Section 4, would be helpful for readers. 

Section 4. (1) Should start with what the authors define by equilibrium analysis, what is the objective and how it is done before Case 1. (2) Line 224-242 should be separated and reorganized for ease of reading. (3) Theorem 1, the conditions in line 252-254 should also be included in Line 257-270 when explaining the theorem. Please do the same for Theorem 2 -6. (4) How Figure 3 and Figure 6. Since  τ and c are on the range of 0 to 1, a full range and combinations should be presented in a Table form. Additionally, instead of just presenting (τ=0.4, c=0.3), the authors can pick several combinations of τ and c or combine them into one figure.

No discussion section. Please add discussion, limitations, and future work session. Explain how this article can contribute to the Sustainability journal. Currently, there is no link to sustainability at all.

Format or presentation comments. (1) The presentation for Propositions 1 and 2 looks crowded. Please reorganize them or use bullet points for different conditions. (2) Check the in-text citation format. Follow the MDPI recommended format. (3) Check all the in-text variables; they may need to be italicized to follow the equation format. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper is devoted to a model of interaction of two manufacturers and one retailer. Manufacturers (followers in the Stackelberg game) produce substitutable products and a retailer (a leader) sell them. The paper consider different scenarios for manufacturers, where one of them or both are honest and disclose real costs or misreport them to retailer, increasing wholesale prices. Also retailer can be corporate social responsible, maximizing social welfare, or he can be selfish with an objective to increase his own pure profit. Retailer determines a retail price of manufacturers' products. Manufacturers' strategies are wholesale prices and misreporting factors deriving corresponding demands and profits. Authors consider the scenarios in combinations and analitically find and compare equilibria using simple algebra. In the conclusion they explain which scenario is beneficial to which side.

The article is clear and presents an original model, exploring the impact of misreporting and CSR behavior to players' interaction. There are some minor remarks.

1. The model assumes that both manufacturers have the same costs which are equal to c. This fact limites the possibility for misreporting in reality. Maybe it would be naturally to consider different c1 and c2.

2. The technical remark. From mathematical point of view it is not correctly to write:

"Max expression1 = expression2"

if expression2 is not a solution maximizing expression1. In eq. (2)-(5) you should write e.g. "maximize expression1, where expression1 = expression2".

3. Indexes "mi" in (2) and (3) for manufacturers in pi should be changed to "i".

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you for providing the response and addressing all the comments. Most of the comments were adequately addressed. One minor revision is to check the formatting of all the variables to ensure consistency. All the best with the publication!

Author Response

Please see the attachment.

Author Response File: Author Response.pdf