Sustainability of Intertwined Supply Networks: A Game-Theoretic Approach

Round 1

Reviewer 1 Report

This paper proposes a formal game-theoretic model of an intertwined supply network in a simplified version. Conditions for the sustainable development of an active system have been presented in general form and then specified in the case of intertwined supply networks. An example of the model of Social and Private Interests Coordination Engines (SPICE-model) for a marketing network has been illustrated and analytically investigated. The idea is interesting. But, the paper lacks in terms of scientific innovation and technical representation. However, the paper can be improved by considering the following issues.

1. The Abstract part should be revised carefully. Please mention the objective, methodology, significance, and novelty of the paper.
2. The introductory section must appropriately highlight the objectives of this research.
3. In the literature review, it is suggested to add the latest frontiers of literature and analyze their main contributions and their value and usefulness for this study.
4. To show the novelty, insert a Table at the end of the Introduction section showing related publications chronologically from the updated literature study. This part would basically focus on the hierarchy of literature study in brief showing your work’s novelty.
5. The motivation for this is not highlighted in the manuscript. The manuscript's value is hidden to the reader. It needs to be emphasized in a paragraph clearly.
6. The contributions of the paper should be written in a bulleted list.
7. The description of the method section seems a bit confusing, and the basic concepts and definitions of the method need to be clarified.
8. It is difficult to figure out the practical importance of this study. What practical implications and insights can this study give to companies?
9. This work supplements the work of Ivanov and Dolgui [12]. But, there is no conceptual comparison with existing approaches and no discussion on the benefits and drawbacks of the new approach.
10. Would it be possible to reflect and describe the limitations of the paper? And what future avenues of research do these limitations open up?

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

This paper proposes a new game-theoretic approach for sustainability of intertwined supply networks. It is original and innovative. It is based on sound theoretical formulaes. 

1. Some abbreviations should be detailed. The readers may not know the meaning of these abbreviations. For instance, in line 158, arc(i,j) (arc=?); in line 318, Arg (Arg=?, state that Arg means that argument); and so on.
2. The author(s) said that “?=||?_??|| is the matrix of links between agents”. Do the notations ||f(x,u,t)|| and ||x|| in line 270 also represent the matrix? The notation [?_??] is usually used for the matrix.
3. Explain what is meant by “--> max” in Eq. (7) in line 196. This is important. Because similar situations exist in Eqs. (9), (10), (12), (19), (20), and (22).
4. The arrows in Figure 2 are randomly placed. Edit this Figure.
5. Pay attention to the notations. For example, in line 156, “g_i: UxY_i --> R” (here, explain R). Change X * in Eq. (11) and U * in line 282 as X* and U*. Because you use these notations in the rest of the article (see line 427, line 350, …). Also, the description of U * in line 282 should be revised. This description is not understood.
6. See “Место для уравнения.(16)” in line 294 and Место для уравнения.(23) in line 333. Delete them.
7. The conclusion section should be improved by referring to the future work of the author(s).

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

This paper discussed the sustainability of intertwined supply networks through a game-theoretic approach. Specifically, a formal game-theoretic model of an intertwined supply network is presented.  

The findings in this paper are of considerable interest. Here are some comments which may improve this paper further:

(i) There exists some typos in this paper: i) ii) Many formulas in this paper are not punctuated, for example, there is a lack of ``.'' at the end of the formula (1). Please check the whole paper carefully and correct them. iii) Please delete ``Место для уравнения'' in Line 294.

(ii) It is better to supply some recent references to introduce intertwined supply networks in Section I.

(iii) Please explain the rationality of the assumption in Line 267-268.

(iv) Please adjust the size of the formula in Line 350-352.

(v) The format of the references cited in this paper is not uniform. Please refer to the journal standards and unify the literature format.

(vi)  Please compare the results in this paper with other relevant papers.

Author Response

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Author Response File: Author Response.docx

Reviewer 4 Report

-Though the ISN concept is interesting and the role of strategic agents is certainly a valid consideration in that context, this paper may be better suited to an OR or Production/Management journal.

-Given that the notions of sustainability/viability are established in the game theory literature, as appropriately cited in the paper, and more broadly are contained in the ``folk theorem''-type results from repeated games or long-run steady states of dynamic models, it seems section 4 could be presented more clearly.  In particular the networked aspect of the ISN application could be emphasized more in the general treatment.

-The paper's main conclusion is, "...is that the sustainable development of the active system is possible only under the viability conditions satisfied simultaneously with coordinating the interests of all active agents of the system."  Is this a surprise?  Are there any conditions when that is not true? 

Author Response

The answer is attached

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors have addressed all the issues raised by the reviewer.  The paper may be accepted for publication in its present form. 

Reviewer 3 Report

This paper considered an intertwined supply network via a formal game-theoretic approach, which involved full and simplified versions. The findings in this paper are of considerable interest. Here are some minor comments which may improve this paper further:

(i)  Too many formulas in this paper are not in an appropriate position. Please check the whole paper carefully and correct them.

(ii) Please compare the results obtained in the paper with the existing relevant results, and state the method used in this paper with reference [43].

~~(iii) Before submitting a revision be sure that your material is properly prepared and formatted.

(iv) There exist some typos in the current version. For example, the expression of notation $\sqrt$ is non-standard. Please check the whole paper carefully and correct all the typos.

Reviewer 4 Report

The specified goals of the paper in the introduction have clarified its contributions.