Rough Set-Game Theory Information Mining Model Considering Opponents’ Information

Round 1

Reviewer 1 Report

The main contribution of the paper is the RS-GT algorithm. However, there is no evidence presented regarding the correctness and the efficiency of the algorithm except an example. The numerical analysis merely states how to apply the algorithm steps in case of a two-player game. Simulation studies are missing that could have been done to show how this algorithm fares against other methods. Without those results, it is hard to conclude about the effectiveness of the proposed research.

Author Response

Thank you for the endorsement to our work and for the invaluable suggestion.

In this paper, we utilized an example to presenting the efficiency of RS-GT model. The numerical analysis stated how to apply the algorithm steps in case of a two-player game. Theoretical proof is not provided, which is not perfect. Here, simulation studies were provided to show how this algorithm fares against game theory.  Combined with your Suggestions, we increased the description about the example:  “In this game, B₁ has a non-disadvantage strategy , and B₂ has no advantage strategy. ……”.

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper presents a rough set-game theory model to handle the uncertain information and the opponent's decision rules.

 

The paper has many concerns that should be carefully addressed before further consideration as follows:

 

The paper writing and presentation are poor.

 

The paper's contribution is not clear.

 

It is recommended to the authors to add a table of notations to facilitate the paper's readability.

 

The basic game metrics are not clear. What are the physical definitions of the players, players' actions, strategies, utility function, etc?

 

What is the incentive to the authors to use game theory as compared to the other methodologies in the literature?

 

What are the outperforming features of the proposed game approach among the existing game models in the literature?

 

The system model is not clear.

 

It seems that the adopted model handles a two players' scenario. Can the proposed model represent a game of more than two players?

 

Although the proposed game seems like a Stackelberg game, the authors have relied on the repeated game. However, the Pareto optimality is not clear in this approach. It is well known that the Pareto optimality is a solution to a repeated game.

 

Why did not the authors adopt this game type?

 

The Nash equilibrium proof and its uniqueness is not clearly mentioned in the manuscript. It is recommended to the authors to do more surveys on game theory and its parameters and how to handle the above-mentioned essential issues. The following papers are recommended to discuss in related work that can assist the authors to overcome those issues:

- Game theory meets wireless sensor networks security requirements and threats mitigation: A survey

- Using repeated game for maximizing high priority data trustworthiness in wireless sensor networks

- An effective stackelberg game for high-assurance of data trustworthiness in wsns

- A game-theoretic approach for enhancing security and data trustworthiness in IoT applications

- Employing game theory and TDMA protocol to enhance security and manage power consumption in WSNs-based cognitive radio

- Non-zero-sum game-based trust model to enhance wireless sensor networks security for IoT applications

- Using Stackelberg game to enhance cognitive radio sensor networks security

The numerical results are not supported by visual results showing the model performance, when the NE exists, comparison with the corresponding models, etc.

The paper is without a conclusion section. The authors should split the discussion from the conclusion.

Mostly, the used references are outdated. The authors should focus more on the recent works.

Author Response

Thank you for the endorsement to our work and for the invaluable suggestion.

The paper presents a rough set-game theory model to handle the uncertain information and the opponent's decision rules.

 The paper has many concerns that should be carefully addressed before further consideration as follows:

1 The paper writing and presentation are poor.

 Re: In the revised version, we have re-written the paper throughout and have checked the English carefully. All the following changes were marked in the revised manuscript.

2 The paper's contribution is not clear.

 Re: The article constructs a rough set-game model, based on the outstanding ability in dealing with uncertain and fuzzy data of rough set, and not requiring any prior knowledge. The rough set obtain the decision rules of competitors by mining historical information. This model examines the decision-makers' preferences in different environments. The player determines strategies by predicting the opponent's behavior, to eliminate unfavorable situations.  The method model proposed in the article is a new exploration applications of game theory and rough set theory to combine the two methods advantages pursue better results.

3 It is recommended to the authors to add a table of notations to facilitate the paper's readability.

 Re: We have add Table 1 in the revised revised manuscript, which present parameters and definition.

4 The basic game metrics are not clear. What are the physical definitions of the players, players' actions, strategies, utility function, etc?

Re: Here, physical definitions of the players, players' actions, strategies, utility function were not presented. In this paper, we utilized an example to presenting the efficiency of RS-GT model. The numerical analysis stated how to apply the algorithm steps in case of a two-player game. Here, simulation studies were provided to show how this algorithm fares against game theory.

5 What is the incentive to the authors to use game theory as compared to the other methodologies in the literature?

 Re: rough set can get the opponent's decision-making rules, while it can't give an exact solution. Game theory can give an equilibrium solution. However, the calculation will become difficult when the type of players and the strategies are uncertain. The method model proposed in the article is a new exploration applications of game theory and rough set theory to combine the two methods advantages pursue better results.

6 What are the outperforming features of the proposed game approach among the existing game models in the literature?

 Re: Game theory can give an equilibrium solution. However, the calculation will become difficult when the type of players and the strategies are uncertain. The article constructs a rough set-game model, based on the outstanding ability in dealing with uncertain and fuzzy data of rough set, and not requiring any prior knowledge. The rough set obtain the decision rules of competitors by mining historical information. This model examines the decision-makers' preferences in different environments. The player determines strategies by predicting the opponent's behavior, to eliminate unfavorable situations.

7 The system model is not clear.

 Re: We combed the steps of the model. The changes were marked in the revised manuscript.

8 It seems that the adopted model handles a two players' scenario. Can the proposed model represent a game of more than two players?

Re: We discussed two players' scenario in multiplayer game. We class players into one person and an union in the multiplayer game in this paper. In the future, we will discuss multiplayer game further.

9 Although the proposed game seems like a Stackelberg game, the authors have relied on the repeated game. However,the Pareto optimality is not clear in this approach. It is well known that the Pareto optimality is a solution to a repeated game. Why did not the authors adopt this game type?

 Re: We discussed the non-cooperative game. Non-cooperative game research focuses on individual behavior characteristics. So the Pareto optimality is not prominent. Here we assume that the history of the same game can be observed and utilized to mining and predict the behavior of rivals based on the history of game data. Participants’ action depends on the others before action in order to gain more profits.

10 The Nash equilibrium proof and its uniqueness is not clearly mentioned in the manuscript. It is recommended to the authors to do more surveys on game theory and its parameters and how to handle the above-mentioned essential issues. The following papers are recommended to discuss in related work that can assist the authors to overcome those issues:

- Game theory meets wireless sensor networks security requirements and threats mitigation: A survey

- Using repeated game for maximizing high priority data trustworthiness in wireless sensor networks

- An effective stackelberg game for high-assurance of data trustworthiness in wsns

- A game-theoretic approach for enhancing security and data trustworthiness in IoT applications

- Employing game theory and TDMA protocol to enhance security and manage power consumption in WSNs-based cognitive radio

- Non-zero-sum game-based trust model to enhance wireless sensor networks security for IoT applications

- Using Stackelberg game to enhance cognitive radio sensor networks security

The numerical results are not supported by visual results showing the model performance, when the NE exists, comparison with the corresponding models, etc.

Re:　Thank you for your suggestion. Those references recommended are helpful to us, especially “Game theory meets wireless sensor networks security requirements and threats mitigation: A survey” and “An effective stackelberg game for high-assurance of data trustworthiness in WSNs”.

11 The paper is without a conclusion section. The authors should split the discussion from the conclusion.

Re： Thank you for your suggestion. We adjusted the discussion from the conclusion.

12 Mostly, the used references are outdated. The authors should focus more on the recent works.

Re：Thank you for your suggestion. We have added some recent works in the Reference section.

All the above changes were marked in the revised manuscript. Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

In this paper, the authors proposed on the rough set-game theory model and presented its application. The idea is very interesting and well presented. The readability of this manuscript is good. I think the manuscript needs a major revision before going to the next step. The following are the suggestions to include in the manuscript.

1. The concept of rough set presented on page 3 should be given in more detail. Also, the notation should be explained.
2. The RS-GT algorithm (line 231) should be clearly written (mathematical formulas for steps can be given or others). That is, it is not attractive. Also, add a flow chart for the RS-GT algorithm.
3. The authors claim that the introduction offers a more comprehensive approach than existing game theory approaches based on uncertainty. They should support this claim by adding a comparison section. What is the advantage of the new approach?
4. You can improve the introduction section by including the concepts of soft rough set, hypersoft rough set, soft game theory and linguistic single‐valued neutrosophic soft sets based game theory and expand the literature review.
5. Please mention the effect of this paper on the future and future work.
6. Revise the symbol B-1 in line 257. Also, different notations are used for the same terms. Correct these. For example, B1, B2 and B_1 and B_2 in lines 257 and 260. Also, in Tables 3,4,5, X1, X2,… and x_1,x_2,… in line 280. And others. Check the symbols throughout the paper. Further improve the presentation of the paper.

Author Response

1 The concept of rough set presented on page 3 should be given in more detail. Also, the notation should be explained.

Re: Thank you for your suggestion. We have added Table 1 in the revised revised manuscript, which present parameters and definition.

2 The RS-GT algorithm (line 231) should be clearly written (mathematical formulas for steps can be given or others). That is, it is not attractive. Also, add a flow chart for the RS-GT algorithm.

Re: In our revision, the numerical analysis states how to apply the algorithm steps in case of a two-player game.

3 The authors claim that the introduction offers a more comprehensive approach than existing game theory approaches based on uncertainty. They should support this claim by adding a comparison section. What is the advantage of the new approach?

Re: In this paper, we utilized an example to presenting the efficiency of RS-GT model. The numerical analysis stated how to apply the algorithm steps in case of a two-player game. Here, simulation studies were provided to show how this algorithm fares against game theory.

4 You can improve the introduction section by including the concepts of soft rough set, hypersoft rough set, soft game theory and linguistic single‐valued neutrosophic soft sets based game theory and expand the literature review.

Re: Thank you for your suggestion. We will introduce soft rough set, hypersoft rough set, soft game theory and linguistic single‐valued neutrosophic soft sets based game theoryin the future work.

5 Please mention the effect of this paper on the future and future work.

Re: The article constructs a rough set-game model, based on the outstanding ability in dealing with uncertain and fuzzy data of rough set, and not requiring any prior knowledge. The rough set obtain the decision rules of competitors by mining historical information. This model examines the decision-makers' preferences in different environments. The player determines strategies by predicting the opponent's behavior, to eliminate unfavorable situations.  The method model proposed in the article is a new exploration applications of game theory and rough set theory to combine the two methods advantages pursue better results.

6 Revise the symbol B-1 in line 257. Also, different notations are used for the same terms. Correct these. For example, B1, B2 and B_1 and B_2 in lines 257 and 260. Also, in Tables 3,4,5, X1, X2,… and x_1,x_2,… in line 280. And others. Check the symbols throughout the paper. Further improve the presentation of the paper.

Re: Thank you for your attention. In the revised version, we have re-written the paper throughout and have checked the English carefully.

All the above changes were marked in the revised manuscript. Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 4 Report

The paper concerns a rough set-game theory model. A rough set model accounts for the uncertainty endowed with the strategic competition.

The authors focus on non-cooperative games. There exist cooperative games too. There, the informational structure is very different. This distinction should be made in the third paragraph of the Introduction.

A major limitation of the study is that not all games can be repeated. Here the authors assume that there is a backlog of data about previous instances of the same game (and lines 227-8 explain this feature in technical terms). This shortcoming should be emphasized, probably the Discussion is the right place.

Other minor comments:

First sentence of Abstract: “In order to maintain an advantage and obtain profits in a competitive situation,” introduces the topic better.

Line 210: delete “that”

Line 225: “In this article” is better.

Line 296: wishes equilibrium ?

Typos in two references: the respective journals are Econometrica (ref. 9) and Economica (ref. 21).

Author Response

Thank you for the endorsement to our work and for the invaluable suggestion. 

The paper concerns a rough set-game theory model. A rough set model accounts for the uncertainty endowed with the strategic competition.

1 The authors focus on non-cooperative games. There exist cooperative games too. There, the informational structure is very different. This distinction should be made in the third paragraph of the Introduction.

Re: Thank you for your suggestion. We have added description in Introduction as your recommend.

2 A major limitation of the study is that not all games can be repeated. Here the authors assume that there is a backlog of data about previous instances of the same game (and lines 227-8 explain this feature in technical terms). This shortcoming should be emphasized, probably the Discussion is the right place.

Re: Thank you for your attention. Here we assume that the history of the same game can be observed and utilized to mining and predict the behavior of rivals based on the history of game data. Participants’ action depends on the others before action in order to gain more profits.

Other minor comments:

(1) First sentence of Abstract: “In order to maintain an advantage and obtain profits in a competitive situation,” introduces the topic better.

Re: Thank you for your suggestion. We have adjusted the Abstract as your recommend.

(2)Line 210: delete “that”

Re: We have deleted “that” from Line 210.

 (3)Line 225: “In this article” is better.

Re: We have changed as your recommend in Line 210.

 (4)Line 296: wishes equilibrium ?

Re: We have changed “wishes equilibrium” to “expectation”

(5)Typos in two references: the respective journals are Econometrica (ref. 9) and Economica (ref. 21).

Re: Thank you. We have changed as your pointed.

All the above changes were marked in the revised manuscript. Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors added a section on cooperative and non-cooperative games in the introduction which makes that part only a tad better. Therefore I changed the rating of "Introduction". Some new references are cited. But apart from those, no substantial change has been made. The main concern has not been addressed.

Author Response

Re: Thank you for your suggestion. Combined with your Suggestions, we increased presentation about the example, which are from Line 318 to 322 in Section 5 and Line 369 to 374  in Section 6.  In the revised manuscript, we make Text highlighting about changes. 

Author Response File: Author Response.pdf

Reviewer 2 Report

General comment:

The authors should clearly mention in their responses what and where exactly their updates have been reflected in the revised version.

 

The table of parameters and definitions mentioned in the revised version should be Table 7, not 1.

 

In comment 4, the authors have been asked about the basic game metrics and their physical meaning of the proposed game model. However, their response does not meet the comment.

 

The authors have been asked to support the numerical results by visual results showing the model performance when the NE exists. In addition, they need to compare their results with the corresponding models in the literature. Unfortunately, they did not reflect that in the revised version.

 

The authors in their responses have mentioned "The method model proposed in the article is a new exploration applications of game theory and rough set theory to combine the two methods advantages pursue better results." However, without a comparison, how do they judge whether their results are sufficient and efficient or not?

 

The authors have been asked to present the Nash equilibrium proof and its uniqueness based on the proposed approach. In the revised version, these two main points are still missing.

 

The conclusion should focus on the paper's insights and findings not to mention some introductory points.

Author Response

 The authors should clearly mention in their responses what and where exactly their updates have been reflected in the revised version.

Re: Thank you for your suggestion. In the revised manuscript, we make Text highlighting about changes.

The table of parameters and definitions mentioned in the revised version should be Table 7, not 1.

Re: Thank you. We have changed Table 1 in Appendix A to Table 7 in Line 392.

In comment 4, the authors have been asked about the basic game metrics and their physical meaning of the proposed game model. However, their response does not meet the comment.

The authors have been asked to support the numerical results by visual results showing the model performance when the NE exists. In addition, they need to compare their results with the corresponding models in the literature. Unfortunately, they did not reflect that in the revised version.

Re: Thank you for your suggestion. In the revised version, we have changed pay-off matrix, which is in Table 6. We increased presentation about the example, which are from Line 318 to 322 in Section 5. In this game, both strategies may be selected in a specific market environment,.  There are two pure strategy equilibriums in this game (9, 9), (7, 7). In the above example, it has been predicted that the strategy of B₂ is . In the discussion of classic game theory, the equilibrium point is (7, 7). However, the equilibrium is not the expectation of enterprise B₁.

The authors in their responses have mentioned "The method model proposed in the article is a new exploration applications of game theory and rough set theory to combine the two methods advantages pursue better results." However, without a comparison, how do they judge whether their results are sufficient and efficient or not?

Re: In the manuscript, we applied rule extracting from Rough Set to Game theory. The example presents the result of RS-GT, which is noted from Line 318 to 334.

The authors have been asked to present the Nash equilibrium proof and its uniqueness based on the proposed approach. In the revised version, these two main points are still missing.

Re: In Table 6, There are two pure strategy equilibriums (9, 9) and (7, 7) in this game and the result of the game is (7,7). We presented explanation from Line 318 to 334.

The conclusion should focus on the paper's insights and findings not to mention some introductory points.

Re: Thank you for your suggestion. In the revised version, we increased presentation in Section 6, which is from Line 369 to 374 in Section 6. 

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors succeeded in some of the revisions. But for the following comments, I could not see the necessary changes and additions in the paper.

1. The RS-GT algorithm (line 231) should be clearly written (mathematical formulas for steps can be given or others). That is, it is not attractive. Also, add a flow chart for the RS-GT algorithm.

2. The authors claim that the introduction offers a more comprehensive approach than existing game theory approaches based on uncertainty. They should support this claim by adding a comparison section. What is the advantage of the RS-GT?

3. You can improve the introduction section by including the concepts of soft rough set, hypersoft rough set, soft game theory and linguistic single‐valued neutrosophic soft sets based game theory and expand the literature review.

These comments are intended to improve the quality of the paper. I hope to see them in the next revision file.

Author Response

The authors succeeded in some of the revisions. But for the following comments, I could not see the necessary changes and additions in the paper.

1. The RS-GT algorithm (line 231) should be clearly written (mathematical formulas for steps can be given or others). That is, it is not attractive. Also, add a flow chart for the RS-GT algorithm.

Re: Thank you for your suggestion. In the revised version, we increased presentation from Line 253 to Line 263 in Section 3.

2. The authors claim that the introduction offers a more comprehensive approach than existing game theory approaches based on uncertainty. They should support this claim by adding a comparison section. What is the advantage of the RS-GT?

Re: In the manuscript, we applied rule extracting from Rough Set to Game theory. The example presents the result of RS-GT, which is noted from Line 318 to 334.

3. You can improve the introduction section by including the concepts of soft rough set, hypersoft rough set, soft game theory and linguistic single‐valued neutrosophic soft sets based game theory and expand the literature review.

Re: Thank you for your suggestion. In the manuscript, we research rough set-game theory model (RS-GT) considering uncertain information and the opponent's decision rules. We will introduce soft rough set, hypersoft rough set, soft game theory and linguistic single‐valued neutrosophic soft sets based game theoryin the future work.

These comments are intended to improve the quality of the paper. I hope to see them in the next revision file.

Author Response File: Author Response.pdf

Round 3

Reviewer 1 Report

With the addition of flowchart (and a new example), now the algorithm and its implication is a bit more clearly conveyed. 

Minor revisions are suggested for English grammars - for example, the last sentence of the numerical analysis section ends abruptly.   

Author Response

The authors wish to thank you for your comments and suggestions, which are invaluable for significant improvement of the readability and quality of the manuscript. In the revised version, we have checked the English carefully. We have done three changes about English in the revised manuscript.

1 In Section Abstract, “In multi-strategy games, the increase in the number of strategies is more difficult to make solution.” was changed to “In multi-strategy games, the increase in the number of strategies is difficult to make solution.” From Line 9 to Line 10.

2 In Section 5, “Ensure greater gains in the competition and maintain market competitive advantages.” was changed to “From numerical analysis, we find it can ensure greater gains in the competition and maintain market competitive advantages.” From Line 345 to Line 346.

3 In Section 6, “The method model proposed in the article is a new exploration applications of game theory and rough set theory to combine the two methods advantages pursue better results.” was changed to “The method model proposed in the article is a new exploration application of game theory and rough set theory, which combines the two methods advantages to attain better results.” From Line 372 to Line 374.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors have improved their manuscript. I would like to recommend acceptance to the paper.

Author Response

The authors wish to thank you for your comments and suggestions, which are invaluable for significant improvement of the readability and quality of the manuscript. In the revised version, we have checked the English carefully. We have done three changes about English in the revised manuscript.

1 In Section Abstract, “In multi-strategy games, the increase in the number of strategies is more difficult to make solution.” was changed to “In multi-strategy games, the increase in the number of strategies is difficult to make solution.” From Line 9 to Line 10.

2 In Section 5, “Ensure greater gains in the competition and maintain market competitive advantages.” was changed to “From numerical analysis, we find it can ensure greater gains in the competition and maintain market competitive advantages.” From Line 345 to Line 346.

3 In Section 6, “The method model proposed in the article is a new exploration applications of game theory and rough set theory to combine the two methods advantages pursue better results.” was changed to “The method model proposed in the article is a new exploration application of game theory and rough set theory, which combines the two methods advantages to attain better results.” From Line 372 to Line 374.

Reviewer 3 Report

The authors achieved the proposed revisions. In the current form, this paper deserves to be published in your journal.

Author Response

The authors wish to thank you for your comments and suggestions, which are invaluable for significant improvement of the readability and quality of the manuscript. In the revised version, we have checked the English carefully. We have done three changes about English in the revised manuscript.

1 In Section Abstract, “In multi-strategy games, the increase in the number of strategies is more difficult to make solution.” was changed to “In multi-strategy games, the increase in the number of strategies is difficult to make solution.” From Line 9 to Line 10.

2 In Section 5, “Ensure greater gains in the competition and maintain market competitive advantages.” was changed to “From numerical analysis, we find it can ensure greater gains in the competition and maintain market competitive advantages.” From Line 345 to Line 346.

3 In Section 6, “The method model proposed in the article is a new exploration applications of game theory and rough set theory to combine the two methods advantages pursue better results.” was changed to “The method model proposed in the article is a new exploration application of game theory and rough set theory, which combines the two methods advantages to attain better results.” From Line 372 to Line 374.