PCSY-D-23-00002

Emergence of economic and social disparities by gift interaction networks

PLOS Complex Systems

Dear Dr. Kaneko,

Thank you for submitting your manuscript to PLOS Complex Systems. After careful consideration, we feel that it has merit but does not fully meet PLOS Complex Systems'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 within 60 days Mar 24 2024 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 complexsystems@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcsy/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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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.

We look forward to receiving your revised manuscript.

Kind regards,

Marian-Gabriel Hancean, Ph.D.

Academic Editor

PLOS Complex Systems

Journal Requirements:

Additional Editor Comments (if provided):

The referees have raised a number of concerns relating to your model and results, which we ask you address. There were also a number of points requiring some additional clarifications. Please, pay careful attention to each of the comments made by the reviewers. This way we can avoid future rounds of clarifications and revisions, moving swiftly to a decision.

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Does this manuscript meet PLOS Complex Systems’s publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

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

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. 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

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

PLOS Complex Systems 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: Yes

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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: The authors have studied social evolution based on gift interactions. They propose that the model has four phases: band, tribe, chiefdom, and kingdom, depending on the economic and social disparities. The interest rate and the frequency of gifts are identified as key parameters for the transition among the four phases.

While it is unlikely that any kingdom has ever been established solely by gift donations in history, this theory is falsifiable and can contribute to the scientific community. I recommend this article for publication in PLOS Complex Systems.

Reviewer #2: In this article the authors propose a model for the evolution of social organization dependent on fluctuations of economic and social disparities. These disparities are modelled through the frequency of reciprocation - and its associated interest rate (r) -, and frequency of gift giving (l). The combination of these variables throughout the steps of a simulation creates distributions of wealth scores and in-degree scores translated as social reputation. While the authors acknowledge that this model can serve as possible explanation only for pre-modern communities, there are some points which need to be addressed to better understand the merits and limits of their model, given that the inferences raised have implications for social theories of reciprocity and gift exchange.

First of all, the proposed model needs clarification:

a) It is not clear what are wealth values (w_i) assigned to nodes in the first step of the simulations. Does each node start with the same or different wealth values?

b) At page 3/15 (lines 89 and 90) the authors state “l gives an expected number of steps each individual experiences before dying, which we term the frequency of gifts in a lifetime”. How is this expected value, l, assigned to nodes?

c) At page 3/15 (lines 88 and 89), the authors state that when “Individuals die with a probability of 1/l and are replaced by a new individual with w_i = 1/l and q_(i*) = q_(*i) = 1”. This means that at some step n in the system is introduced an actor with the same characteristics as an actor present in the first step of the simulation. What are the implications of this introduction of a new node at some step n? Are these new nodes in a disadvantage of accumulating wealth and reputation compared to nodes present from the first step?

d) Why the model does not or cannot take into account the dissolution of a tie between i and j or the refusal of a tie which creates the risk of over-indebtedness?

Second, the only qualitative relationship created between nodes is based on previous exchanges. The authors acknowledge that including kinship in the model is “too complicated to quantitatively analyze the transitions in social organizations or socioeconomic disparities”, but they should explain why. Also, the non-inclusion of different kinds of ties and the relations they imply should be expanded upon in the discussion section. For example, Haas and Deseran (1981) state that a quick return of the gift can indicate a lack of interest in the continuation of the relationship if there is no emotional connection between the social actors. Yet, from the model proposed by the authors, fast reciprocation (gift giving and repayment) in fewer steps is desirable. Sherry (1983) also mentions that gift exchange and its implications – types of gifts, type of reciprocity, the value of gifts – are dependent on the status and role relations between two persons.

Building on the previous point, the third remark is that the model takes into account only two basic scenarios between the two nodes i and j: “reciprocation” and “subordination”. The instances of subordination are when we don’t have a “proper reciprocity” between i and j that results in “equal social ties” (page 4, lines 112-114). As such, the social reputation of a node grows along its in-degree score - “[…] if i’s gift is so large that it takes j several steps to complete the reciprocation, q_ij increases by 1 and, q_ji by more. If j is in debt, j’s constant production 1/l will be paid to i, and i’s reputation increases by 1/l in each step. Hence, individuals elevate their status by the amount of the credits they earn” (page 4, lines 116-119). From certain points of view, it makes sense, since social reputation is in relation with other nodes as well, not just dyadic. Yet, since “gift” can mean anything, it begs the question: why is this always a situation of “positive” reputation? (since ‘subordination’ of i to j only increases j’s reputation). This is true only in a culture where is mandatory to receive and repay gifts independent of the relations between the actors. Lemmergaard and Muhr (2011) mention that we can have situations when a person refuses to enter an exchange relations if he or she feels that they can’t honor (reciprocate equally or more). In the same spirit, Gouldner (1960) states that the norm of reciprocity exists in a larger moral code of interactions which adjusts or penalizes situations of over-indebtedness / over-benefiting.

Fourth, the phases are modelled with different, but with constant interest rates (r) and gift frequencies (l) inside each phase. However, we can have different rates and gift frequencies inside each phase, depending on the type and strength of social ties between actors. These implications and limits of the proposed model should be expanded upon in the Discussion section of the manuscript.

As a corollary of the aforementioned remarks, the authors should clearly state what model of reciprocity and gift exchange they refer to. In the manuscript, they talk about gift exchange in general, as a process with economic and social consequences, yet it is clear that there are some theoretical preferences on how gift exchange is viewed. For example, Belk and Coon (1993) distinguish between the economic and social model of gift exchange, where the former is built on “balanced or negative reciprocity” and the latter is built on “generalized reciprocity”. The model proposed by the authors of the manuscript are compatible with the model of “balanced or negative reciprocity”, where the moments between gift giving and reciprocations are rather short and lack of repayment might end up in debt. Such assumptions and their implications on the theoretical model and the statistical model built upon it should be discussed. Also, the authors are invited to explore the possibility that not including other qualitative features in their models (e.g.., status / role relations between i and j, emotional closeness, kinship, the possibility to refuse or dissolve a tie, etc.) is what gives rise to the “kingdom phase” (a reverting to exponential distribution from power-law) where “dragon-kings” appear as a result of over-indebtedness / over-benefiting because nodes cannot refuse or dissolve ties.

All in all, the article presents an interesting take on how social reputation is formed and how inequalities arise through the mechanism of gift-exchange and is a step forward in the understanding of how complex systems arise from rules of networked interactions.

References:

Belk, R. W., & Coon, G. S. (1993). Gift giving as agapic love: An alternative to the exchange paradigm based on dating experiences. Journal of Consumer Research, 20(3), 393–417.

Gouldner, A. W. (1960). The norm of reciprocity: A preliminary statement. American Sociological Review, 161–178.

Haas, D. F., & Deseran, F. A. (1981). Trust and symbolic exchange. Social Psychology Quarterly, 3–13.

Lemmergaard, J., & Muhr, S. L. (2011). Regarding gifts—On Christmas gift exchange and asymmetrical business relations. Organization, 18(6), 763–777.

Sherry Jr, J. F. (1983). Gift giving in anthropological perspective. Journal of Consumer Research, 10(2), 157–168.

Reviewer #3: This study presents an intriguing exploration of social organization evolution through gift exchanges. The authors introduce a model illustrating four phases - "band," "tribe," "monarch," and "kingdom" - differentiated by wealth disparity and social reputation. A mean-field analysis is provided to interpret the model's outcomes.

While the study offers an innovative approach, potentially contributing significantly to social evolution theory, I have concerns regarding the model's justification and the clarity of its definition. My comments will focus on these aspects, as the results and analysis are challenging to fully assess due to existing ambiguities.

## Concerns about Model Justification

1. Reciprocity Assumption in Gift Exchanges: The model's premise that gifts must be reciprocated with a greater value seems at odds with the general understanding of gift-giving, which is usually to please others and enhance one's reputation. In this model, the donor unilaterally decides on the recipient, obligating them to a greater debt without refusal options. This resembles enforced debt more than gift exchange. Clarification or justification for this assumption is necessary.

2. Total Wealth Transfer by Donors: The assumption that a donor gives away all their wealth to one recipient is unrealistic. Though the authors argue this only alters the timescale, strategic considerations like saving a portion of wealth or diversifying gifts among multiple recipients are ignored. These scenarios, which are more reflective of real-world dynamics, could significantly impact the model's outcomes. Thus, a more robust justification is needed for the current assumption.

3. Reinforcement of Link Weight w_{ij}: It is unclear why the link weight increases whenever wealth is transferred from one player to another. Typically, reinforcement in behavioral models occurs when an action yields a benefit. However, when a player pays a debt, they do not receive an immediate benefit, yet they are more likely to choose the same recipient in the future. This assumption warrants further explanation.

4. Incremental Link Weight Regardless of Gift Size: The model's approach of increasing link weight by a fixed amount, irrespective of the gift's size, seems oversimplified. A larger gift could logically lead to a greater increase in link weight. Additionally, the form of giving could influence the link weight. Justification for the current approach is needed.

5. Definition of Reputation Score: The manuscript defines reputation based on the in-strength of a node, which is inconsistent with the stated premise that gifts bring honor to the donor. (In line 23, the authors state "gifts bring goods to the recipient and honor to the donor," on which I agree with the authors.) A more intuitive approach might be to define reputation based on out-strength, where a player's reputation grows with their generosity.

## Ambiguities in Model Definition

The model's definition contains several ambiguities. Based on my understanding and the source code, the model operates in three stages per time step: 1) wealth transfer to chosen recipients, 2) wealth increment by 1/l for each player, and 3) debt repayment. Clarifications are needed on the following points:

1. Debt Repayment Dynamics: How are multiple debts handled? Are all debts settled in one round if possible, or does the player address debts to individual creditors sequentially? The method of selecting a creditor in such cases is unclear.

2. Partial Debt Repayments: In c

PCSY-D-23-00002R1

Emergence of economic and social disparities through competitive gift-giving

PLOS Complex Systems

Dear Dr. Kaneko,

Thank you again for submitting your manuscript to PLOS Complex Systems. As discussed, we are sending a Minor Revision to allow you to address the remaining review comments.

Please submit your revised manuscript within 30 days Jun 15 2024 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 complexsystems@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcsy/ 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 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.

We look forward to receiving your revised manuscript.

Kind regards,

Luca Pappalardo

Section Editor

PLOS Complex Systems

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.

Additional Editor Comments (if provided):

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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: All comments have been addressed

Reviewer #2: All comments have been addressed

Reviewer #3: (No Response)

Reviewer #4: All comments have been addressed

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2. Does this manuscript meet PLOS Complex Systems's publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

Reviewer #4: Yes

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

Reviewer #1: N/A

Reviewer #2: Yes

Reviewer #3: Yes

Reviewer #4: Yes

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4. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. 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

Reviewer #4: Yes

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

PLOS Complex Systems 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: Yes

Reviewer #4: Yes

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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: (No Response)

Reviewer #2: I have reviewed the modifications made by the authors to the received comments. The authors have implemented all the necessary changes with regard to my observations. More so, I appreciate that they made adjustments to the title and throughout the manuscript, and centred the subject of their research on “competitive gift-giving”.

Therefore, I recommend the publication of their study inside the PLOS Complex Systems journal.

Reviewer #3: The authors have made efforts to address the concerns highlighted by the reviewers. Despite acknowledging their efforts, I find that the revisions partially address the issues, leaving significant concerns regarding the model's definition and justification unresolved. In this review, I will concentrate on these remaining issues related to model justification.

> 1. Reciprocity Assumption in Gift Exchanges:

The authors clarified their focus on competitive gift-giving in traditional societies, emphasizing obliged reciprocation. The manuscript now clearly states the authors' interest in obliged gift-giving.

> 2. Total Wealth Transfer by Donors:

>>> As we have explained, the strategy to save a proportion of wealth alters the parameter value of r (but not timescale). Because smaller r leads to smaller disparities, our model indicates that such a strategy leads to different types of social organizations. Additionally, distributing gifts among multiple recipients can also be analyzed as a parameter change.

The authors' explanation that saving a portion of wealth affects the parameter value of r is convincing. However, the rationale behind how the parameters l and r scale with the distribution of wealth among k recipients is still unclear. The donor should obtain $rw_i$ after the reciprocations from all these recipients are complete, which means the interest rate remains $r$.

Let us consider the extreme case to elucidate the issue. If the donors distribute their wealth to all other players equally, inequality would not happen. So how the donor distributes their wealth should impact the model outcome.

> 3. Reinforcement of Link Weight wij:

>>> We have clarified in lines 71–78 that our goal is to examine the social consequences of competitive gift-giving by assuming the norm to obligate reciprocation and strengthen social relationships based on interactions.

The clarification provided in lines 71–78 does not adequately address my question regarding the assumption that link weight increases are independent of the forms of wealth transfer (donation, reciprocation, or repaying debts).

> 4. Incremental Link Weight Regardless of Gift Size:

>>> The current model is designed to measure how large the gift is in terms of the recipient’s wealth. Indeed, in the competitive gift-giving, such a too late reciprocation leads to greater social indebtedness.

The explanation is only partially convincing. It remains unclear why a player with higher social indebtedness (due to late reciprocation) is more likely to receive gifts in subsequent rounds.

> 5. Definition of Reputation Score:

>>> Thank you for your suggestion. We have updated our model interpretations to define reputation based on out-strength (lines 120–135).

This is the most puzzling answer in the letter.

- In line 131, "However, if i's gift is so large that it takes j several steps to complete the reciprocation, $q_{ji}$ increases by 1 (because the reciprocation is counted as 1), and q_{ij} increases by the number of steps needed for reciprocation."

- I don't get why $q_{ij}$ increases. Isn't it $q_{ji}$?

- In line 133, "If j is in debt, j's constant production 1/l will be paid to i, and i's reputation will increase by 1/l with each step."

- Is it i's reputation? It seems to me that j's reputation has increased.

It seems to me that the wealth and the social status are anti-correlated. In this model, the more you repay your debt and the poorer you are, the higher social status you get, which does not sound like a reasonable assumption to me.

Given these unresolved issues, I am unable to recommend the publication of this manuscript, despite recognizing the novelty and potential impact of the approach. I encourage the authors to further refine the model and address these concerns in their future study.

Reviewer #4: The paper has been carefully revised, and all concerns have been addressed. Thus, I would recommend its acceptance.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

Reviewer #4: No

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Emergence of economic and social disparities through competitive gift-giving

PCSY-D-23-00002R2

Dear Prof. Kaneko,

We are pleased to inform you that your manuscript 'Emergence of economic and social disparities through competitive gift-giving' has been re-accepted for publication in PLOS Complex Systems. 

I consider that the questions and concerns raised by the reviewers and editors during the revision rounds were properly addressed. Therefore, I keep my initial decision to "Accept" and recommend this contribution to the PLOS Complex Systems journal.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow-up email from a member of our team. 

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

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Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Complex Systems.

Best regards,

Marian-Gabriel Hancean, Ph.D.

Academic Editor

PLOS Complex Systems

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