Game-Based Demand Feedback Reservation Parking Pricing

Round 1

Reviewer 1 Report

Dear authors,

I carefully read your article about parking reservation strategy and I have several comments:

- figure 1 should be exported in higher resolution, also Fig. 6
- literature review is fine, but you have the lowest number of sources I have ever seen
- I do not agree with the manipulation of the parking fee during the day. Especially in our country, in Eastern Europe, it would ultimately have nothing to do with parking policy, but it would degenerate into pure business.
- I don't understand if Table 2 is necessary, the factors would be enough in bullet points, and unify the formatting - capital letters at the beginning.
- You could use a smaller format for formulas to fit on one line - if possible.
- I appreciate that you made the conclusions graphically and thoroughly verbalized as well. However, I still do not think that the goal of the parking policy should be profit maximization. Can you take a position on this?

Thank you.

Author Response

Response to Reviewer 1 Comments

Dear reviewer，

Thank you very much for your professional and critical review. In this revised manuscript, we have added more than 1,000 characters, re-expanded the bibliography, listed the relevant parking methods and applicable situations in recent years, and improved the applicability and assumptions of the study. Thank you for correcting the scope of the article's application and communicating your position.Your suggestions have effectively pointed out the shortcomings of our manuscript and improved the quality of the content.

 

Point 1: figure 1 should be exported in higher resolution, also Fig. 6.

 

Response 1: Thanks to your meticulousness.This is our oversight and mistake.We have replaced all the images in the manuscript with 300 dpi.

 

Point 2: literature review is fine, but you have the lowest number of sources I have ever seen.

 

Response 2: With your suggestions, we have substantially increased the number of literature citations in recent years ([18-33]). References not listed in the previous content have been added([28-33]).

 

Point 3: I do not agree with the manipulation of the parking fee during the day. Especially in our country, in Eastern Europe, it would ultimately have nothing to do with parking policy, but it would degenerate into pure business. I appreciate that you made the conclusions graphically and thoroughly verbalized as well. However, I still do not think that the goal of the parking policy should be profit maximization. Can you take a position on this?

 

Response 3: I agree with you that profit should not be the primary consideration in the pricing of parking. Furthermore, after a preliminary research visit, I believe that parking pricing should take into account the characteristics of the facility and the needs of the facility's users, and here I would like to make two points in response to you.

1. For different facilities, their parking methods and purposes are different. For example, in hospitals, schools and other public welfare facilities attached to the parking lot, according to the characteristics of the facilities, their parking prices should be public welfare, mainly by the government and policy-led, while the designer is more to take into account the time-varying nature of the user, safety, and on the basis of which go to improve the occupancy rate of the parking lot as much as possible. In office buildings and residential areas, due to the nature of demand and supply and the obvious peak distribution of users, designers should consider the allocation of parking spaces during peak periods as well as the guidance to meet the demand of users at most and to reduce the number of long hours of parking as the first priority. On-street parking should focus on the planning of the location to avoid taking up road resources, and later go on to consider maximizing the use of parking spaces. And in our city visits, we have found that there is a great deal of flexibility among users in business districts, who are more in need of a stop-and-go parking option that can be booked at any time. On the other hand, shopping mall managers focus on price and cost, and at the same time prefer to drive traffic to their own commercial facilities through parking discounts or convenience. In this revision, some of the research objectives chosen by researchers in recent years under each category of parking lots are listed (Table 2), which hopefully can confirm this point.
2. Benefits should not be the only objective.We opted for a commercial zone parking facility and I understand your point of view and concern on the point of pricing in the commercial zone. However, as a commercial district facility, there are many constraints on setting fees. In our survey, the pricing of commercial parking lots in our neighborhood is not subject to policy or governmental restrictions, but they are also unable to change their prices at will. Because, like the traditional parking lots around, all parties are in a game of equilibrium, any price change will bring a decline in customer traffic, which they do not want to see. In the article we simulate the market competition with the restoration of this price constraint relationship, using a price game for the neighboring parking lots. At the same time, the price change affects the user's choice and the passenger flow. When the new optimal solution is finally reached, you can also see that the price per hour does not fluctuate too much compared to the original price, which is the result of optimizing the profitability by adding traffic and market competition. In fact, we only propose this pricing idealization model from the perspective of a commercial facility manager, and specific constraints need to be added when applying it, taking into account conditions such as government policies and occupancy indicators.

The above is the original intention and position of our study, and the explanation of the scope of application and application assumptions has also been strengthened in this revision(at line 117-148). We hope to gain your understanding and that of our readers.

 

Point 4: I don't understand if Table 2 is necessary, the factors would be enough in bullet points, and unify the formatting - capital letters at the beginning.

 

Response 4: Indeed, after your reminder, we found that the listing of factors in Table II duplicated the descriptions in the subsequent text and took up space, and we deleted the original Table II. At the same time, we have rechecked and standardized the writing of the factors, and we thank you for your rigor and professionalism.

 

Point 5: - You could use a smaller format for formulas to fit on one line - if possible.

 

Response 5: The article was edited so that we were writing in the font in the submission specifications, and the font size in the body of the article may not be adjustable against the published content. We have reduced the font size in the table to make it clearer and more intuitive.

 

Thank you very much for your attention and time with the editor. Your professional comments were very helpful to our manuscript. look forward to hearing from you.

 

Yours sincerely,

Bo Feng

29 Aug 2023.

 

Author Response File: Author Response.docx

Reviewer 2 Report

The article under review is of both scientific and practical interest, as it explores an important topic associated with the growth of motorization in cities - the lack of parking space, which exacerbates traffic. Therefore, the development of more efficient parking management methods is of paramount importance. The article title and keywords adequately reflect its content. In the abstract, the authors give the essence of the problem and its state, describe the methods and models of the study, the results obtained and conclusions on the work.

In the introduction, the authors provide a rationale for the relevance of the problem. The second section is devoted to a description and comparison of pricing methods for different types of parking lots, including a brief literature review on the topic of the article, and also formulates the tasks and the proposed research method, as well as its difference from previously used methods. The third part is devoted to describing the strategies and rules for booking parking lots. In the fourth section, the authors present nested logit and game modelling proposed. The fifth section contains a description of the experimental results, their interpretation, and experimental conclusions. In the "Conclusions" section, the authors summarize the results obtained and draw conclusions on the work.

The article is prepared in accordance with the instructions for the authors, corresponds to the topic that it explores and publishes. In our opinion, the article is in line with the theme of “improvement of parking space management based on mathematical models” and is in line with the Preliminary Study.

Comment.

The topic is interesting and actual, in general, the authors argue their models and conclusions well, but there are some minor comments that reduce the article quality.

1. At the end of the second chapter, the authors formulate the research tasks, the proposed method for solving them, but do not provide the conditions for application, limitations and practical significance (for example, for which cities this model is applicable, are there any restrictions on traffic flow parameters, traffic patterns, etc.).

2. It is not clear who is interested in applying the model proposed by the authors, how its practical application will be implemented.

3. References, in our opinion, are insufficient. In addition, there are few articles written in recent years. It is recommended to expand the list by adding new articles to it.

4. There are wishes to improve the quality of drawings up to 240 dpi so that the text on them is better readable.

Comments for author File: Comments.docx

Author Response

Response to Reviewer 2 Comments

Dear reviewer，

Thank you very much for your professional and critical review. In this revised manuscript, we have added more than 1,000 characters, re-expanded the bibliography, listed the relevant parking methods and applicable situations in recent years, and improved the applicability and assumptions of the study. Thank you very much for your appreciation of the article and your pertinent, spot-on advice. Your suggestions have effectively pointed out the shortcomings of our manuscript and improved the quality of the content.

 

Point 1: At the end of the second chapter, the authors formulate the research tasks, the proposed method for solving them, but do not provide the conditions for application, limitations and practical significance (for example, for which cities this model is applicable, are there any restrictions on traffic flow parameters, traffic patterns, etc.).

 

Response 1: With your reminder, we realized that our previous practice of showing the method model directly made the article content travel disconnected. We have refined this section by including a chapter after Chapter 2 that lists the applicability of existing research. After the overview, it is as natural as possible to draw out the limitations and applicable contexts of the research in this article(at line 117-146). At the same time, we included assumptions that fit the application context and experimental sites before presenting the model. We hope that our work can practically improve the rigor of the article.

 

Point 2: It is not clear who is interested in applying the model proposed by the authors, how its practical application will be implemented.

 

Response 2: We have highlighted the first description of a commercial facility's parking lot to be priced using a reservation mechanism in the newly added description. Also, subsequent modeling is presented from the perspective of the leader (the first parking lot manager to propose the adoption of reservations). Our model can bring more traffic and profit to the parking lot managers of commercial facilities. It is hoped that the descriptions included in the text will demonstrate the applicability of the research.

 

Point 3: References, in our opinion, are insufficient. In addition, there are few articles written in recent years. It is recommended to expand the list by adding new articles to it.

 

Response 3: With your suggestions, we have increased the number of literature citations in recent years ([18-33]). References not listed in the previous content have been added([28-33]).

 

Point 4: There are wishes to improve the quality of drawings up to 240 dpi so that the text on them is better readable.

 

Response 4: Thanks to your meticulousness, we have replaced all the images in the manuscript with 300 dpi.

 

Thank you very much for your attention and time with the editor. Your professional comments were very helpful to our manuscript. look forward to hearing from you.

 

Yours sincerely,

Bo Feng

29 Aug 2023.

 

 

Author Response File: Author Response.docx

Reviewer 3 Report

The article is about the application of game theory to the problem of determining the price of parking, which uses two types of Stackelberg and Nash games. The objective function of the game leader has been obtained and maximized, and the price has been obtained, but I did not understand how the game balance point is obtained, the only thing I understood is the maximization of the profit function of the game leader, and it is better to explain in detail which methodology exactly is used . The game used is Nash or Stackelberg?

Author Response

Response to Reviewer 3 Comments

Dear reviewer，

Thank you very much for your professional and critical review. In this revised manuscript, we have added more than 1,000 characters, re-expanded the bibliography, listed the relevant parking methods and applicable situations in recent years, and improved the applicability and assumptions of the study. Thank you for your corrections regarding the application of models and methods to the article. With your suggestions, we have actually improved the quality of the article and removed ambiguities, and we hope that our work is useful for readers' understanding.

 

Point 1: The article is about the application of game theory to the problem of determining the price of parking, which uses two types of Stackelberg and Nash games. The objective function of the game leader has been obtained and maximized, and the price has been obtained, but I did not understand how the game balance point is obtained.

 

Response 1: Thank you for your professional comments. Stackberg game model was used in this study. In this model, the reservation parking lot acts as a leader with a known response function for traditional parking lots and sets its own optimal price based on its response function. There are reasons for using this model:

1. The first parking lot to adopt the new type of reserved parking will redefine its pricing scheme, and the traditional parking lots will adjust their own prices after the new type of reserved parking is announced. In terms of strategy and price, there are advantages over other parking lots. More consistent with the characteristics of the leader in the model, the Stackberg model is more consistent with the actual game.
2. At the level of the model and reaction function, the study in this paper uses a mathematical derivation to solve for the price of applying Stackberg. The process is complex to compute and derive (it constitutes a transcendental function, which needs to be solved by invoking the Burrang W-function) and takes up too much space and work. According to the research direction of the article, it is only necessary to find the price of the reservation parking lot side of the price based on the consideration of the price of the traditional parking lot, and the Stackberg model in the assumption that there is no need to find the response function of the reservation parking lot itself, so the Stackberg model is used.

In the manuscript, this part was incorrectly omitted. With your correction, we have added a paragraph（at line 323-332） explaining the reason for not solving for the traditional parking lot on the other side, in the hope that the reader will better understand the logic of the article.

 

Point 2: It is better to explain in detail which methodology exactly is used . The game used is Nash or Stackelberg?

 

Response 2: Thank you for your rigor and care. In our checking, we found that there are several places in our text where the "equilibrium point" is incorrectly described as the "Nash equilibrium point". This error of ours caused misinformation and problems for the readers, and we have corrected the text accordingly（at line 270、302、311、317）, applying only the Stackberg game model in the study. Again, we apologize for the problems caused by our error.

 

Thank you very much for your attention and time with the editor. Your professional comments were very helpful to our manuscript. look forward to hearing from you.

 

Yours sincerely,

Bo Feng

29 Aug 2023.

 

Author Response File: Author Response.docx

Reviewer 4 Report

Dear authors, 

very interesting work on parking issue. My concern is how methodology and results interpretation can take into account sustainability issues that are the most important concurrent issue. Please add your considerations. 

I would also like to see/understand:

* Which is the main innovation point compared to other dynamic parking approaches? please add a discussion session where you can show the added value compared to other scientific approaches and applied strategies. In discussion session a link to literature review findings should be made

* It would be good to substantially increase the references, not only in number but also from global experience and proposals

* practical & policy implications can be improved/clarified

* next steps to be added

* 

Author Response

Response to Reviewer 4 Comments

Dear reviewer，

Thank you very much for your professional and critical review. In this revised manuscript, we have added more than 1,000 characters, re-expanded the bibliography, listed the relevant parking methods and applicable situations in recent years, and improved the applicability and assumptions of the study. Thank you very much for your suggestions regarding the article review section and the literature citation section. Your suggestions have effectively pointed out the shortcomings of our manuscript and improved the quality of the content.

 

Point 1: Which is the main innovation point compared to other dynamic parking approaches? please add a discussion session where you can show the added value compared to other scientific approaches and applied strategies. In discussion session a link to literature review findings should be made.  

 

Response 1: With your reminder, we realized that the methodology and scope of the application were not well described in the manuscript(at line 117-128). We have added a new section that lists the main research directions, applications, and contexts in recent years to help readers better understand the issue. At the same time, the innovative methods and strategies of this paper are introduced through the research of the articles. The DOIs and hyperlinks of all the literature have been added, thanks again for your suggestions.

 

Point 2: It would be good to substantially increase the references, not only in number but also from global experience and proposals.

 

Response 2: With your suggestions, we have increased the number of literature citations([18-33]). References not listed in the previous content have been added([28-33]), and a new Table 2 has been added to summarize the policies and methods of each research direction.

 

Point 3: practical & policy implications can be improved/clarified.

 

Response 3: In the textual description of the modification paragraph, we detail the scenarios and objectives of the subsequent policy application(at line 129-146). It is hoped that these clarifications will enable readers to better understand the scope of our study and its application.

 

Thank you very much for your attention and time with the editor. Your professional comments were very helpful to our manuscript. look forward to hearing from you.

 

Yours sincerely,

Bo Feng

29 Aug 2023.

 

Author Response File: Author Response.docx

Reviewer 5 Report

This research is good and will be highly useful to aspiring researchers even though it is not fully new. The manuscript's writing is excellent and well-organized. I'd like to offer the following brief suggestions:

 

• A novel reservation parking approach based on the Stackberg and nested logit models has been proposed for commercial districts, which was used to analyse the cost, demand, and price aspects systematically in accordance with the user's choosing behavior that are clearly organized and presented in the manuscript.
• In equation 26. at line 373, the factors used in the equation should be in brackets, and add units to each factor. Do these changes throughout the manuscript.  
• In Fig. 1, line no. 121; Fig. 2, line no. 137, authors used h, and N, but both are not mentioned in Section 3.1, page no. 3.
• Figure 3. Line no. 185, data, is not properly visible; therefore, replace it with 300 dpi.
• In Figs. 4 and 5, add units of parameters used on both axes.
• Remove the typographical errors.
• It is advised to the authors to add some relevant research papers for 2022 and 2023.
• Hanzl et al.'s (2021) work was present in Table 1 but absent in Literature Review Section 2 on Page No. 2, Line No. 51.
• In the Reference section, all references are available without a DOI [1–17].

Remove the typographical errors

Author Response

Response to Reviewer 5 Comments

 

Dear reviewer，

Thank you very much for your professional and critical review. In this revised manuscript, we have added more than 1,000 characters, re-expanded the bibliography, listed the relevant parking methods and applicable situations in recent years, and improved the applicability and assumptions of the study. Thank you for your comments on the formatting and citation of the article, and through your suggestions, we hope that our manuscript can be more clearly and professionally presented to the readers.

 

Point 1: In equation 26. at line 373, the factors used in the equation should be in brackets, and add units to each factor. Do these changes throughout the manuscript.  

 

Response 1: Thank you for your professional comments. We have corrected formula errors in the text (equation 26、27、29、31）and added parenthetical labeling for each factor. On the other hand, we have added the units of the factors and further explanations of each factor in the paragraphs where the factors are first presented in the text(at line 189-199）.

 

Point 2: In Fig. 1, line no. 121; Fig. 2, line no. 137, authors used h, and N, but both are not mentioned in Section 3.1, page no. 3.

 

Response 2: Thank you for your rigor and care. In our initial idea, we used Figures 1 and 2 to go for a schematic illustration of appointment staging. However, due to our omission and carelessness, there is less description of the images. We have re-added this section to the textual description following Figure 1 where it first appeared (at line 123), which we hope will help readers understand.

 

Point 3: Figure 3. Line no. 185, data, is not properly visible; therefore, replace it with 300 dpi.

 

Response 3: We replaced all the images in the article (Figure 1-9) with higher resolution, increasing the dpi to 300 in the hope of presenting clearer images.

 

Point 4: In Figs. 4 and 5, add units of parameters used on both axes.

 

Response 4: Thanks to your correction, we have increased the units of the horizontal and vertical axes (times and yuan) and replaced the images (Figures 4-6).

 

Point 5: Remove the typographical errors.

 

Response 5: We have done our best to recheck the entire text and correct some grammatical and spelling errors.

 

Point 6: It is advised to the authors to add some relevant research papers for 2022 and 2023.

 

Response 6: We have reintroduced a section after the literature citation(at line 111-153), focusing on the detailed analysis of the relevant parking models and methodological applications in recent years, which expands the literature references and at the same time enhances the scientific soundness of the article.

 

Point 7: Hanzl et al.'s (2021) work was present in Table 1 but absent in Literature Review Section 2 on Page No. 2, Line No. 51.

 

Response 7: After your reminder, we realized that our approach was abrupt and disrespectful to the citing authors. We have reintroduced the description and introduction of the articles used in Table 1 (at line 84) in the previous literature review section.

 

Point 8: In the Reference section, all references are available without a DOI [1–17].

 

Response 8: Your reminder is professional, We have included the article's DOI and hyperlink after each literature citation in the References section. We hope that your reminder will make our articles more professional and standardized.

 

Thank you very much for your attention and time with the editor. Your professional comments were very helpful to our manuscript. look forward to hearing from you.

 

Yours sincerely,

Bo Feng

29 Aug 2023.

 

 

 

Author Response File: Author Response.docx

Round 2

Reviewer 3 Report

The authors have answered my questions, but I have not yet understood the use of the Stackelberg game, and everything is unclear to me, because as far as I know, in the Stackelberg game, the problem of the follower player turns into the condition of Kan Tucker and is placed in the problem of the leader of the game. And the answer obtained is optimal for both and will be the balance point, but there is no such approach in the article, but this issue is not in my scientific expertise, and I suggest that the article be sent to Dr.Mahboobe Honarvar