On the Game-Based Approach to Optimal Design

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The problem addressed in this paper and proposed game theory approach to solving optimal deesign problem in structural systems is quite interesting, however, the poor presentation of this work makes it difficult to read and understand the actual contributions.

The author must address the following issues.

ABSTRACT:

Line 7: What is scalar criterion? Properly explain/expand new terms when introduced.

Line 8: This is not a good sentence. What about the "cardinal" players?

- Although the abstract correctly explains the research objective, the research gap is still missing. Why do you chose this method for Optimal design analyses.

To also make the research easily readable, it is important to mention the focus area (the types of systems) this applies to. For instance, structural systems is mentioned in keywords but not in abstract.

INTRODUCTION:

Line 35-40: Provide literature references for these claims

Line 44. All new terms have to have to be properly explained - "stratified game"

Line 54-56: add reference here.

Line 57: rephrase as: For the sake of clarity, it may be .....

Line 69: At this point it is confusing if the "designer" is a third player or you are inter-changing designer and operator. Best to stick to one term in order not to confuse the readers.

- References needed for the whole paragraph 4 of the introduction.

- The last paragraph of the introduction should summarize the rest of the sections

SECTION 2:

You earlier claimed Matrix games are all zero sums and when one player wins, the other loses. Does that also apply here for the payoff of the second player when the first player wins K[a](x,y)?
Line 153: You mean this paragraph since you already referred to the section in the first paragraph?

 

SECTION 3:

- It is not clear how sections 2 and 3 contribute to the research objective, generally making the paper difficult to read

-Line 267: What is the connection between bi-matrix games with problems already presented in section 1.

 

While the authors introduce new concepts in sections 2 and 3, it is not clear how they are related to the research objective and game theory concepts already established in previous sections.

 

SECTION 4: 

-Line 327: what aforementioned section?

 

Besides, how are the previous sections (2 and 3) considered results when they do not directly contribute to  solving the game problem already established in Section 1. I would have considered sections 2 and 3 related work but I dont see any literature reference to the formalization presented. Besides, these two sections will not count as contribution it is not clear how they are related to game problem in section 1.

 

SECTION 5: 

- Since the literature foundations of this work in Sections 2,3,4 and are not properly connected with the research problem, it is difficult to read the rest of the papers to understand the actual contribution of this work

- To also help with readability, every section should be properly introduced and expected outcomes from the sections summarized

Author Response

ABSTRACT:   Line 7: What is scalar criterion? Properly explain/expand new terms when introduced.  ANSWER: The definition "scalar criterion" with the citation to common sources is provided on Line 32 to 42 of the actual verison of manuscript.    Line 8: This is not a good sentence. What about the "cardinal" players? Line 35-40: Provide literature references for these claims ANSWER: The definition "cardinal players" with the citation to common sources is provided on Line 82 to 92 of the actual verison of manuscrip     - Although the abstract correctly explains the research objective, the research gap is still missing. Why do you chose this method for Optimal design analyses. ANSWER: The Introduction was completely reworked. The new texts are marked with the blue color. The new formulated sections are marked with the yellow color.    To also make the research easily readable, it is important to mention the focus area (the types of systems) this applies to. For instance, structural systems is mentioned in keywords but not in abstract. ANSWER: the keywords were reworked   INTRODUCTION:   Line 35-40: Provide literature references for these claims. ANSWER: the literature references were added    Line 44. All new terms have to have to be properly explained - "stratified game" ANSWER: See subsection 1.5° (Lines 109-125)   Line 54-56: add reference here. ANSWER: Citation added (Line 209)   Line 57: rephrase as: For the sake of clarity, it may be ..... ANSWER: corrected , Lines 198-199   Line 69: At this point it is confusing if the "designer" is a third player or you are inter-changing designer and operator. Best to stick to one term in order not to confuse the readers.   - References needed for the whole paragraph 4 of the introduction. ANSWER: this subsection is now 1.6° and the references were reworked   - The last paragraph of the introduction should summarize the rest of the sections ANSWER:All Sections got the final paragraph.    SECTION 2:   You earlier claimed Matrix games are all zero sums and when one player wins, the other loses. Does that also apply here for the payoff of the second player when the first player wins K[a](x,y)? ANSWER: The total payoff for both ordinal players on the lower level is zero. The goal function on the upper level is the payoff of an ordinal player, e.g. the "operator". This objective function is modified by the "designer" at the upper level (S. Lines 285-288)  Line 153: You mean this paragraph since you already referred to the section in the first paragraph? ANSWER: When there is only one cardinal player, the superstratum game reduces to the optimization problem. In contrast, when there are two or more cardinal players, their interests may be in opposition, resulting in what is known as an antagonistic game (Lines 282-284)       SECTION 3:   - It is not clear how sections 2 and 3 contribute to the research objective, generally making the paper difficult to read ANSWER: the explanation was given in Introduction, Liens 212-217   -Line 267: What is the connection between bi-matrix games with problems already presented in section 1.  ANSWER is given at Lines 218-225 of the Introduction         While the authors introduce new concepts in sections 2 and 3, it is not clear how they are related to the research objective and game theory concepts already established in previous sections. ANSWER: the sense was explained in the first introductory Section        SECTION 4:    -Line 327: what aforementioned section? ANSWER: aforementioned section is Section 3 (Lines 474-481)         Besides, how are the previous sections (2 and 3) considered results when they do not directly contribute to  solving the game problem already established in Section 1. I would have considered sections 2 and 3 related work but I dont see any literature reference to the formalization presented. Besides, these two sections will not count as contribution it is not clear how they are related to game problem in section 1.   ANSWER: the sections 2 and 3 introduce the general framework for the solution of exmaples, presented in Sections 5 to 7.         SECTION 5:    - Since the literature foundations of this work in Sections 2,3,4 and are not properly connected with the research problem, it is difficult to read the rest of the papers to understand the actual contribution of this work    ANSWER: the answers wege given in above replies    - To also help with readability, every section should be properly introduced and expected outcomes from the sections summarized   ANSWER: the short introductions and summaries were given to each section

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper is about a matrix game against nature, which is solved using Pontryagin's maximum principle. Included illustrations delve into a social game where the actions of the superstratum players shape the governing equations of the game, such as those related to taxation or ecological laws. Meanwhile, the players in the "substratum" adhere to the legislation that defines their objectives and the associated modus vivendi.

The article is interesting, but the numbers in the paragraphs are distracting, and several typos make the reading difficult. Please correct these errors. 

Please change the first section's title to "Introduction" and avoid enumerating the paragraphs.

Include a description of the remainder of the paper in the conclusion of the introduction.

Comments on the Quality of English Language

The article is interesting, but the numbers in the paragraphs are distracting, and several typos make the reading difficult. Please correct these errors. 

Author Response

The article is interesting, but the numbers in the paragraphs are distracting, and several typos make the reading difficult. Please correct these errors.    ANSWERS: 1. Each Section got the subsections (paragraphs). The paragraphs adress a single logical steps of the manuscript.  2: The typos were cleared and the citations updated   Please change the first section's title to "Introduction" and avoid enumerating the paragraphs.   ANSWER:  1. first section's title was changed to "Introduction" 2: The author prefer to divide the Introduction to paragraphs as well. The logical structure of the text need a fine division between different levels   Include a description of the remainder of the paper in the conclusion of the introduction.   ANSWER: a description of the remainder of the paper in the conclusion of the introduction was added (Lines 167- 254)

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

All previous comments have been addressed by the author(s). The paper can be accepted in present form

Reviewer 2 Report

Comments and Suggestions for Authors

My concerns have been addressed. Thank you!