PONE-D-22-20446The willingness intensity and co-evolution of decision rationality depending on aspiration enhance cooperation in the spatial public goods gamePLOS ONE

Dear Dr. shounan,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Oct 23 2022 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Xiaojie Chen

Academic Editor

PLOS ONE

Journal Requirements:

1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at 

https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and 

https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf

2. We note that the grant information you provided in the ‘Funding Information’ and ‘Financial Disclosure’ sections do not match. 

When you resubmit, please ensure that you provide the correct grant numbers for the awards you received for your study in the ‘Funding Information’ section.

3. Thank you for stating the following in the Acknowledgments Section of your manuscript: 

"This work was supported by national key research and development plan of China under grants nos. 2019YFB1406500."

We note that you have provided funding information that is not currently declared in your Funding Statement. However, funding information should not appear in the Acknowledgments section or other areas of your manuscript. We will only publish funding information present in the Funding Statement section of the online submission form. 

Please remove any funding-related text from the manuscript and let us know how you would like to update your Funding Statement. Currently, your Funding Statement reads as follows: 

"Unfunded studies

The author(s) received no specific funding for this work."

Please include your amended statements within your cover letter; we will change the online submission form on your behalf.

4. Thank you for stating the following in your Competing Interests section:  

"NO authors have competing interests

Enter: The authors have declared that no competing interests exist."

Please complete your Competing Interests on the online submission form to state any Competing Interests. If you have no competing interests, please state "The authors have declared that no competing interests exist.", as detailed online in our guide for authors at http://journals.plos.org/plosone/s/submit-now 

 This information should be included in your cover letter; we will change the online submission form on your behalf.

5. In your Data Availability statement, you have not specified where the minimal data set underlying the results described in your manuscript can be found. PLOS defines a study's minimal data set as the underlying data used to reach the conclusions drawn in the manuscript and any additional data required to replicate the reported study findings in their entirety. All PLOS journals require that the minimal data set be made fully available. For more information about our data policy, please see http://journals.plos.org/plosone/s/data-availability.

Upon re-submitting your revised manuscript, please upload your study’s minimal underlying data set as either Supporting Information files or to a stable, public repository and include the relevant URLs, DOIs, or accession numbers within your revised cover letter. For a list of acceptable repositories, please see http://journals.plos.org/plosone/s/data-availability#loc-recommended-repositories. Any potentially identifying patient information must be fully anonymized.

Important: If there are ethical or legal restrictions to sharing your data publicly, please explain these restrictions in detail. Please see our guidelines for more information on what we consider unacceptable restrictions to publicly sharing data: http://journals.plos.org/plosone/s/data-availability#loc-unacceptable-data-access-restrictions. Note that it is not acceptable for the authors to be the sole named individuals responsible for ensuring data access.

We will update your Data Availability statement to reflect the information you provide in your cover letter.

6. PLOS requires an ORCID iD for the corresponding author in Editorial Manager on papers submitted after December 6th, 2016. Please ensure that you have an ORCID iD and that it is validated in Editorial Manager. To do this, go to ‘Update my Information’ (in the upper left-hand corner of the main menu), and click on the Fetch/Validate link next to the ORCID field. This will take you to the ORCID site and allow you to create a new iD or authenticate a pre-existing iD in Editorial Manager. Please see the following video for instructions on linking an ORCID iD to your Editorial Manager account: https://www.youtube.com/watch?v=_xcclfuvtxQ.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Yes

Reviewer #3: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: Yes

Reviewer #3: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: No

Reviewer #2: Yes

Reviewer #3: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: In this work, Lu et al. introduced a game mechanism into the spatial public goods game where individuals’ rational emotions change synchronously with their aspiration. Concretely, the satisfaction level of individuals with the current payoffs will affect their rational decision-making level in the next round. They assumed that the intensity of personal subjective willingness to change the status quo is affected by the gap between aspiration and payoff. The greater the gap, the stronger the desire to change. In addition, the role of the strategy-updating rule in the evolution of cooperation has been studied. They found that the heterogeneous strategic update rule would benefit the evolution of cooperation.

While I find the initial idea behind the manuscript very interesting, I do not think that the study is of sufficient quality for publication.

First of all, the setting of the expected payoff of game players is unclear. In equation (2), the authors set that the expected payoffs of game players meet P_iA=A∙ K_i. Why this form? The authors should explain why this linear form is reasonable. Besides, in equation (4), W_i should be changed to w_i.

The second main problem is that the readability of the manuscript is very poor. Almost every page of the manuscript has grammatical problems, which makes reading very difficult.

The level of rationality is an important indicator for the authors to design this study. But I don't seem to see how the average rational level of the whole population will evolve.

Small comments:

In Figure 1 (c), what does data5 mean?

The caption of Figure 2, “The evolution process for A= A=0.3, 0.5, 0.7, 0.7, 0.9, respectively,” “(b) The evolution process for A=0.3, 0.5, 0.7, 0.7, 0.9, respectively, and r=7”. These descriptions do not correspond to those expressed in the Figure 2.

To conclude, I think that the idea behind the manuscript is very interesting and that the authors have made important steps to investigate this idea. However, I advise to rewrite the manuscript more carefully to be ready for publication.

Reviewer #2: This paper has proposed a spatial public goods game model where the individual rational sentiment and the intensity of willingness are changing depended on the difference of aspiration and payoff. The authors consider two types of strategy updating rules, stochastic “win-stay-lose-shift” rule (WSLS) and random imitation rule (IM). Through numerical simulations, they show that high value of enhancement factor is not conducive to cooperation in IM rules. Moreover, for small aspiration level, WSLS is more conducive to promoting cooperation than IM, while the situation is reverse for high payoff aspiration.

The topic of this paper is worth investigation. However, there are still some problems in this paper. These concerns that should be addressed before I can give my final recommendation. My detailed comments are as follows.

1.Eq.(1) can only describe the payoff that individual i obtains from the group centered on himself/herself, the authors need to check whether the results provided in this paper are based on the correct calculation method of accumulating payoff.

2.In the model section, it is mentioned that “when individuals are very dissatisfied with his/her returns, he/she will have a strong desire to change the status quo, and vice versa.”, while it is contrary to Eq.(4). Besides, ‘W_i(t)’ should be revised to ‘omega_i(t)’.

3.Visualization of all figures should be further improved.

4.Many sentences are ill-constructed. I hope that the authors can continue to check grammars, spelling and other problems in the next version of the manuscript.

5.In the introduction section, I suggest authors to mention four related works, i.e., “The role of noise in the spatial public goods game, JSTAT 2016”, “Public cooperation in two-layer networks with asymmetric interaction and learning environments, AMC 2019”, “Heterogeneous investments induced by historical payoffs promote cooperation in spatial public goods games, CSF 2020” and “Evolutionary public goods games on hypergraphs with heterogeneous multiplication factors, Acta Physica Sinica 2022”.

Reviewer #3: Comments on PONE-D-22-20446

Dear authors:

This paper proposes a spatial public goods game mechanism in which individuals' rational sentiment evolves synchronously depending on the difference between aspiration and payoff, and the intensity of their subjective willingness to change the strategies, which are dependent on the gap between aspiration and payoff. In general, this paper is quite interesting and helpful for us to understand the emergence of cooperation in social dilemmas. However, this paper still has some major problems needed to solve before being published in this journal.

1. It is the biggest problem for the authors is to improve their English expression and correct grammar mistakes. Actually, I found a lot of grammar mistakes in the main text, which make your study hard to understand. For example, the sentence, ‘rational sentiment is evolves’ in the Abstract is wrong, and the correct form should be ‘rational sentiment evolves’. I can understand that it is not easy for non-native speakers to write English papers. But to provide readers with a high-quality research, I suggest that the authors should ask native speakers for help to proofread your paper. If the resubmitted paper is still bad-writing, I will reconsider whether this paper is okay to be published on PLOS One.

2. I am confused about the realistic meaning of that the authors combined aspiration with rationality. Could you explain the meaning of the new mechanism you proposed and where it can be applied to solve social dilemma problems in the real world?

3. The mathematical symbols are misleading. For example, W in eq.4 means the willingness, but in eq.6, it represents the probability of updating strategy. The authors should carefully check the main text to avoid similar small mistakes.

4. I doubt the correctness of the simulation results. Because the simulation results in Fig.1 show that the cooperation level is higher as r is lower. This conclusion does not make sense and is contrary to that in obvious studies on the public goods game.

5. In the main text, the authors investigate the cooperation dynamics under WSLS and IM, respectively. But this is not enough to verify the conclusion, namely, ‘The willingness intensity and co-evolution of decision rationality depending on aspiration enhance cooperation in the spatial public goods game’. To provide more persuasive evidence to verify the main conclusion, I suggest the authors introduce a benchmark, which is not influenced by any mechanism. Then, by comparing the cooperation dynamics of the new mechanism proposed with the benchmark, it is easy to verify whether cooperation is promoted by the proposed mechanism.

6. There are some wrong formats of literature in the Reference part, such as [14], [27]. The authors should carefully check and avoid unnecessary errors.

**********

6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

**********

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

PONE-D-22-20446R1The willingness intensity and co-evolution of decision rationality depending on aspiration enhance cooperation in the spatial public goods gamePLOS ONE

Dear Dr. Dai,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Dec 18 2022 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

• A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Xiaojie Chen

Academic Editor

PLOS ONE

Journal Requirements:

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: (No Response)

Reviewer #2: All comments have been addressed

Reviewer #3: All comments have been addressed

********** 

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

********** 

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

********** 

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

********** 

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

********** 

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The authors have substantially revised the manuscript and incorporated my suggestions.

I only have two minor comments.

It is known for the evolutionary game that incentive strategies can significantly affect

the evolution of cooperation (see for example, Chen et al., Journal of the Royal Society Interface 12.102 (2015): 20140935; Physical Review E 92.1 (2015): 012819; Liu and Chen, Applied Mathematics and Computation 425 (2022): 127069;Mathematical Models and Methods in Applied Sciences 29.11 (2019): 2127-2149;Journal of the Royal Society Interface 19.188 (2022): 20210755). It would be very meaningful if the authors add these works.

Characters in the manuscript should be italicized, such as R_i in eq. 5 and eq. 6.

Reviewer #2: The revised manuscript seems enough to persuade me. I would like to recommend it for publication in PLOS ONE.

Reviewer #3: 1. The English expression has been improved, but there are still many grammar mistakes. It is suggested that the author seek professional researchers to modify the grammar.

2. Does A evolve or stay the same during the evolutionary process? And is A heterogeneous among different people? Please elaborate on this question in the revised manuscript.

3. Under the different strategy update rules of WSLS and IM, what new discoveries can be provided by the distribution of strategies, willingness, and rationality on the square lattice? This seems not to be elaborated in the main text.

********** 

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

**********

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

The willingness intensity and co-evolution of decision rationality depending on aspiration enhance cooperation in the spatial public goods game

PONE-D-22-20446R2

Dear Dr. Dai,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Xiaojie Chen

Academic Editor

PLOS ONE

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Review Comments to the Author

Reviewer #1: In their revised version, the authors addressed all points which I raised in a satisfactory manner. As far as I am concerned the paper is worth publishing and is essentially ready to go.

Reviewer #3: (No Response)