Promoting Entry and Efficiency via Reserve Prices

Round 1

Reviewer 1 Report

This paper presents a nice example of how reserve price can prevent a more detailed information revelation, resulting in higher participation rate, expected selling price and expected social surplus. The idea of the model is based on the assumption that once the bidder is out of the auction, he cannot return back. Thus, in case of no reserve price it is not possible for all but one entrant to remain in the auction when price reaches 9/10 and, if the incumbent does not drop out, the others can join the auction when price reaches 11/10. I believe the paper should be published with minor addition to the introduction. In particular,

1) A better intuitive explanation of how the model works should be included (along the lines discussed above)

2) I believe, there are some papers that discuss situation when the bidders want to drop in the middle price range and get back to auction when price becomes higher. On the top of my head, I do not remember these papers, but I am certain I read one about 10 years ago. If such research exists, it should be cited.

3) The authors mention some research on how reserve price can discourage entry. I think, another relevant research stream that deals with jump bid signalling that affects entry should also be mentioned. E.g., Dodonova A., “Preemptive Bidding and Pareto Efficiency in Takeover Auctions”, Economics Letters 159, 214-216, 2017 discusses its effect in case when there is a common value component in the object;s value (like in this paper)

Author Response

Dear reviewer,

Thanks for your comments that helped me improved the paper.

Let me point out to you the changes introduced following your comments.

1) A better intuitive explanation of how the model works should be included (along the lines discussed above).

I have added better intuitive explanations of how the model works in the last paragraph of the introduction, and in the final part of the conclusions. I am also more clear about the fact that reentry is not allowed. 

2) I believe, there are some papers that discuss situation when the bidders want to drop in the middle price range and get back to auction when price becomes higher. On the top of my head, I do not remember these papers, but I am certain I read one about 10 years ago. If such research exists, it should be cited.

The only paper I am aware of is the one by Izmalkov, which I now cite. The paper is from 2003, it has not been published but it is easy to download. I hope it is the one you also had in mind. Thanks for suggesting to add this paper.

3) The authors mention some research on how reserve price can discourage entry. I think, another relevant research stream that deals with jump bid signalling that affects entry should also be mentioned. E.g., Dodonova A., “Preemptive Bidding and Pareto Efficiency in Takeover Auctions”, Economics Letters 159, 214-216, 2017 discusses its effect in case when there is a common value component in the object;s value (like in this paper)

You are right about this. I know those papers. Initially I had not cited them as they are based on the signaling explanation, and I did not realize the connection based on deterring entry. They provide an additional reason why entry can be low in the English auction so thanks for suggesting them. I have added the paper you mentioned, the seminal paper by Fishman (1988) and a paper by Khoroshilov and Dodonova (2013) that provides experimental evidence on preemptive bids.

Finally, notice that I rewrote the introduction adding many more citations as this was asked also by another reviewer. I have also edited the text of the first proposition and added further comments in the second part of page 4 to explain more clearly why it cannot be strictly profitable for more than one entrant to enter. Finally, I have expanded the conclusions to put this contribution more into perspective and to point out how new research should focus more into less canonical settings like this paper and those cited through the introduction do.

I hope you will find that the revised version improved compared to the original submission.

Thanks again, and I look forward to any further comments you might have.

Reviewer 2 Report

Please allow me a few remarks to improve the final aspect of this article.
The manuscript seems to be an original work, proved by the tiny precent of similarity in anti-plagiarism software (2%).
From what I see, the manuscript is written in LaTeX format, a supplementary work for authors, not quite easy. Nevertheless, from what I see the format does not comply at all with the standard MDPI format, which can be downloaded from here https://www.mdpi.com/journal/games/instructions, or you can work directly here too https://www.overleaf.com/gallery/tagged/mdpi-official
I quote from instructions for authors / templates (some important issues):
"References should be numbered in order of appearance and indicated by a number or numbers in square brackets, for example, [1] or [2,3] or [4-6]."
"We do not have strict formatting requirements, but all manuscripts must contain the necessary sections: Author Information, Abstract, Keywords, Introduction, Materials and Methods, Results, Conclusions" ...
I recommend that equations, mathematical formulas should be numbered (1), (2) ... etc. in the order of their appearance. Also, make sure that the important equations do not appear directly intermingled in the sentence (for example, Proposition 2 seems to come out of the edges of the page, etc.).
I don't know if it's suitable to put footnotes in the manuscript, I haven't encountered MDPI articles with footnotes.
The abstract seems too swift, too brief to attract the interest of potential readers of this article. I suggest the authors to improve it.
The manuscript gives the impression to be written/intended for another journal, possibly from the field of business / economics (JEL Classification Numbers?)
I recommend a broader theoretical fundament of the study conducted by the authors, with the addition of other bibliographic references, perhaps even newer (There are 12 bibliographic references, the newest from 2016; 4 of them from 1980s).
I also recommend, based on the state of the art (missing), that the authors emphasize more their contribution, what they bring up new, improved in comparison to what has already been done (in a period closer to 2022).
I recommend a larger section of conclusions, to enclose a little bit about the authors’ plan to improve their current study, and their future intends for continuing their research.

Author Response

Dear reviewer,

Thanks for your comments that helped me improve the paper.

Let me point out to you the changes introduced following your comments.

First, I have now used the MDPI format. Thanks for pointing out precisely where to find it. 

I recommend that equations, mathematical formulas should be numbered (1), (2) ... etc. in the order of their appearance. Also, make sure that the important equations do not appear directly intermingled in the sentence (for example, Proposition 2 seems to come out of the edges of the page, etc.).

I now number the main equations. Also, I have corrected the line that was misplaced. I am sorry it did not come out correctly in the previous version. I should have noticed.

I don't know if it's suitable to put footnotes in the manuscript, I haven't encountered MDPI articles with footnotes.

I found some paper in games with footnotes. I tried to use them with parsimony. If really needed I can of course put them in the main text.

The abstract seems too swift, too brief to attract the interest of potential readers of this article. I suggest the authors to improve it.

Thanks for this comment. My goal was to have a very short abstract that could catch the reader attention by highlighting the result that may appear surprising in light of the standard and very well known analysis on reserve prices. I do agree with you that it was too swift as it is important to add a few lines to tell the reader that the result provided it is not just a curiosity but it is relevant for important applications. I have thus added the following lines:

Such feature is realistic for applications characterized by the presence of an incumbent who is better informed about some common characteristics of the object for sale.

The manuscript gives the impression to be written/intended for another journal, possibly from the field of business / economics (JEL Classification Numbers?)
I recommend a broader theoretical fundament of the study conducted by the authors, with the addition of other bibliographic references, perhaps even newer (There are 12 bibliographic references, the newest from 2016; 4 of them from 1980s).

Thanks for prompting me to work more on this. Now I have more than double of the initial references (26, before 12). This means that the introduction is much longer and I hope it highlights better the theoretical contribution, and how it is related to existing results. 

I also recommend, based on the state of the art (missing), that the authors emphasize more their contribution, what they bring up new, improved in comparison to what has already been done (in a period closer to 2022).

Again now I have 26 references some of which are more recent. There are even more recent contributions on reserve prices but they are not sufficiently related to be added (at least the ones I am aware of).

I recommend a larger section of conclusions, to enclose a little bit about the authors’ plan to improve their current study, and their future intends for continuing their research.

Thanks for suggesting this. I have now a larger section. I use the conclusions now to provide an intuitive explanation of the main findings, as well as to emphasize how this contribution as well as the other cited in the paper have looked beyond the more canonical auction framework. The message I wanted to leave is that further research along this line is welcomed.

Finally, notice that I have also edited the text of the first proposition and added further comments in the second part of page 4 to explain more clearly why it cannot be strictly profitable for more than one entrant to enter. 

I hope you will find that the revised version improved compared to the original submission.

Thanks again, and I look forward to any further comments you might have.

Best wishes.

..

Reviewer 3 Report

The authors state textually (1st line of the Abstract) that:
-We show that the introduction of a reserve price may promote entry, increase social welfare, and also induce higher revenues.
A result with "may" is evidently a "weak result", a lot can happen...
Furthermore, the entire argumentative defense of this result is based on a single, very particular example.
According to the authors, this result is in contradiction with the literature that focuses on these issues, which may arouse interest in considering them.
It also happens that the authors try to find an explanation for this fact in reasoning in the field of economics.
Thus, at the very least, the example should be formulated in abstract terms (with parameters) and solved in order to obtain conditions (relationships between parameters) that guarantee what the authors have stated. Then one would try to interpret these relationships in economic terms.
In my opinion, this text should be rejected and resubmitted after being redone according to the guidelines recommended above.

Author Response

Dear reviewer,

Thanks for your comments. 

I have now revised my manuscript according to the requests of the editor. 

I hope you will find that the revised version improved compared to the original submission. 

Thanks again, and I look forward to any further comments you might have.

Best wishes.

Reviewer 4 Report

I like this paper. It does exactly what it claims it does: provide a simple yet important example of how reserve price can increase competition when most existing literature claims otherwise. It does not go beyond it and did not try to include any comparative analysis or make any predictions, and it is a good thing: the main contribution of the paper is pointing out (with numerical example) that existing view of the effect of the reserve price on the competition may not be correct all the time. 

The only suggestion I have is to expand the literature review and discuss research in jump bidding and English auctions where bidders can revise their reserve price during the course of the auction

Author Response

Dear reviewer,

Thanks for your comments that helped me improve the paper.

Let me point out to you the changes introduced following your comments.

I like this paper. It does exactly what it claims it does: provide a simple yet important example of how reserve price can increase competition when most existing literature claims otherwise. It does not go beyond it and did not try to include any comparative analysis or make any predictions, and it is a good thing: the main contribution of the paper is pointing out (with numerical example) that existing view of the effect of the reserve price on the competition may not be correct all the time. 

Thanks for the nice words, I am glad you liked the original submission.

The only suggestion I have is to expand the literature review and discuss research in jump bidding and English auctions where bidders can revise their reserve price during the course of the auction

Thanks for this suggestion. I have now expanded considerably the introduction/literature review. Before I had 12 references, now 26. That includes more references on jump bidding as you suggested. 

Notice that I have also edited the text of the first proposition and added further comments in the second part of page 4 to explain more clearly why it cannot be strictly profitable for more than one entrant to enter. Finally, I have expanded the conclusions to put this contribution more into perspective and to point out how new research should focus more into less canonical settings like this paper and those cited through the introduction do.

I hope you will find that the revised version improved compared to the original submission.

Thanks again, and I look forward to any further comments you might have.

Best wishes.

Round 2

Reviewer 1 Report

Good paper, can be published in the present form.

Author Response

Dear reviewer,

Many thanks once again for your comments, and for your positive feedback.

Best wishes.

Reviewer 2 Report

Even though the appearance of the manuscript has been improved, there are still issues that need to be worked on (and which I drew attention to for the first time).

“The abstract seems too swift” - the author or authors (?) added 1 sentence.

“I recommend that equations, mathematical formulas should be numbered (1), (2) ... etc. in the order of their appearance” – row 220

JEL classification to Games journal ?

Author Response

Dear reviewer,

Many thanks for your additional feedback. I hope you will find my corrections satisfactory.

“The abstract seems too swift” - the author or authors (?) added 1 sentence.

I have written a new abstract. It is longer and it provides more information on existing, and how they differ from mine. I hope it goes in the direction you had in mind. Thanks for encouraging me to revise it.

“I recommend that equations, mathematical formulas should be numbered (1), (2) ... etc. in the order of their appearance” – row 220

I have now eliminated the equation of row 220, as well as the one after. Instead, I refer to the same equation that is already present (and numbered) in the main proposition. This way I avoid a perhaps non necessary repetition. Thanks for pointing this out. 

JEL classification to Games journal ?

 I saw them in another paper published in the Games  journal, so I thought it was ok to add them (and the option was on the template).  However, I have now deleted them.

Thanks again, and my best regards.

Reviewer 3 Report

In fact, in this latest version the manuscript has improved substantially. Not as much as we would like, but enough to deserve publication in "Games".
Just one more request: At the end of the Introduction, refer to the organization of the article.

Author Response

In fact, in this latest version the manuscript has improved substantially. Not as much as we would like, but enough to deserve publication in "Games".
Just one more request: At the end of the Introduction, refer to the organization of the article.

Dear reviewer,

Thanks again for your comments. I am happy that the revision when in the right direction, although not all the way. I tried to do my best, given the quite limited time to submit a new version.

Thanks also for your last suggestion. I have now incorporated a paragraph at the end of the introduction that describes the content of the sections that follow.

My best regards.