Trustworthy Anti-Collusion Federated Learning Scheme Optimized by Game Theory

Response to Reviewer 1 Comments

1. Summary

Thank you for the comprehensive review and insightful comments on the manuscript. We appreciate the time and effort you have put into this review, and we believe that your feedback will greatly improve the quality of our work. Please find our detailed responses below, and the corresponding revisions are highlighted in the re-submitted files.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Can be improved

We have revised the introduction to provide a more comprehensive background. Additional references pertinent to the subject have been included to enrich the context and ensure the foundation of our research is clearly laid out for readers.

Are all the cited references relevant to the research?

Can be improved

We have re-evaluated our reference list and ensured all cited works are directly relevant to our research, and we've also added a few that strengthen the foundation and support our findings.

Is the research design appropriate?

Can be improved

We believe the research design is appropriate for our study's objectives. However, we have provided additional justifications in the methodology section, explaining why we chose this particular design and how it effectively addresses our research questions.

Are the methods adequately described?

Can be improved

We have expanded the methods section to provide a more in-depth description of our approach. Each step is detailed clearly, making it reproducible and understandable even for readers who may not be experts in the field.

Are the results clearly presented?

Can be improved

Recognizing the importance of clarity in presenting results, we revisited this section. We've restructured some parts for better flow. 

Are the conclusions supported by the results?

Can be improved

We revisited our conclusions to ensure they align closely with our results.

3. Point-by-point response to Comments and Suggestions for Authors

Comments 1: The methodology, while sound, would benefit from more in-depth explanations, especially for readers less familiar with game theory's nuances.

Response 1: Thank you for your constructive feedback. We recognize the importance of making the methodology comprehensible for all readers, irrespective of their familiarity with game theory. In response to your suggestion, we have expanded the methodology section, providing clearer explanations and examples where necessary to elucidate game theory's nuances. We believe these revisions will enhance the understanding for readers less versed in this area.

Comments 2: The study's implications, both in terms of performance and practical application, could be discussed more extensively to provide comprehensive insights to the readers.

Response 2: We genuinely appreciate your insightful comment. Understanding the significance of clearly presenting the implications of our study, we have taken your advice to heart. In the revised manuscript, we have dedicated additional sections to delve deeper into both the performance and practical applications of our findings. This enhancement aims to offer readers a more holistic understanding of the study's impact and relevance in real-world scenarios. We believe these additions will greatly benefit the comprehensiveness of our research presentation.

Comments 3: Figure 3's observations need clearer justifications to ensure that the study's conclusions are well-supported by the data.

Response 3: Thank you for highlighting this aspect. We understand the importance of ensuring that the data presented in Figure 3 is both transparent and well-supported. To address your concern, we have revisited Figure 3 and provided more detailed captions and explanations in the corresponding section. We've also supplemented the figure with additional annotations and textual descriptions to clearly justify the observations made. We believe these enhancements will provide readers with a more comprehensive understanding of the data and how it aligns with our study's conclusions.

Comments 4: While the introduction of game-theoretic techniques to federated learning is commendable, it would be beneficial for readers if you could provide a more comprehensive breakdown of the methodology. How is the game structured in the federated learning context? Who are considered as the 'players'? Are they the devices, the data sources, or the agents overseeing the devices?

Response 4: We greatly appreciate your recognition of our approach and the constructive feedback. We understand the importance of providing a clear and comprehensive explanation of the game-theoretic techniques, especially for readers who might be new to this integration in the federated learning domain. Your insights about the structure of the game and the clarification on the 'players' are invaluable. We have taken your suggestions into consideration and have made the necessary modifications to provide a more detailed breakdown of the methodology in our revised manuscript.

Comments 5: Can you elucidate the objectives and potential rewards (or payoffs) for each player? In this context, does a player aim to elevate its own model's accuracy, or might there be malicious intents factored in?

Response 5: Thank you for raising this pertinent query. We recognize the significance of clarifying the objectives and potential rewards for each player within the game-theoretic context. It's crucial for readers to understand the motivations driving each player and the possible outcomes they strive for. In response to your question, players indeed aim to optimize their model's accuracy, but there are complexities, such as potential malicious intents, which we have now expanded upon in the revised manuscript. Your feedback has been instrumental in ensuring that our paper offers a holistic view of the game dynamics in the federated learning context.

Comments 6: It would be insightful to detail the strategies available to each player and if there are mechanisms set in place to deter or penalize malicious activities.

Response 6: Thank you for emphasizing the importance of detailing player strategies and mechanisms for deterring malicious activities. We acknowledge the significance of this aspect for a comprehensive understanding of our game-theoretic approach in the context of federated learning. We've taken your feedback into account and have made enhancements in our manuscript to provide a clear exposition of the strategies available to players and the safeguarding mechanisms in place. Your insights are instrumental in ensuring the depth and clarity of our research presentation.

Comments 7: I observed that the game theory's performance appears weaker when compared to other methods in Figure 3. Please provide a comprehensive justification for this observed performance dip. Is it due to computational overheads introduced by the game-theoretic modeling? Or are there inherent inefficiencies in the game-theoretic equilibrium achieved?

Response 7: We greatly appreciate your astute observation regarding the performance metrics displayed in Figure 3. Your feedback underscores the importance of clarifying any discrepancies or unexpected results in our presentation.In addressing your query, it's worth noting that while game-theoretic techniques introduce a novel approach to federated learning, there are inherent challenges that might affect its performance in certain scenarios. On one hand, the game-theoretic modeling might introduce additional computational overheads, particularly pronounced when dealing with large datasets. On the other hand, as the number of players increases or as their strategies become more intricate, the speed at which a game-theoretic equilibrium is reached might slow down. We have re-examined our results in light of these considerations and have incorporated detailed explanations in the revised manuscript. Your insights are invaluable in ensuring that our research is both transparent and thoroughly evaluated. We remain committed to refining our approach and are grateful for your constructive feedback.

Comments 8: The discussion around the "Price of Anarchy" in game-theoretic systems might be an avenue worth exploring. Is it possible that the self-centered behaviors of individual participants have inadvertently caused a decline in the system's overall efficiency?

Response 8: Thank you for bringing up the concept of the "Price of Anarchy" in the context of our research. We acknowledge that it is indeed a pivotal aspect to delve into, especially when considering the implications of individual participants acting in their own self-interest within game-theoretic systems. Your suggestion provides a valuable direction for us to further enrich our discussion. We have taken your advice to heart and have expanded upon this topic in the revised manuscript, exploring the potential effects of self-centered behaviors on the overall efficiency of the system. Your expertise and keen observation have greatly contributed to enhancing the depth of our work.

Comments 9: Enhancing federated learning's robustness and security. However, a deeper exploration into the real-world implications and applications of your findings would significantly elevate the paper's impact. How would entities benefit from your proposed scheme, especially in real-world deployment scenarios?

Response 9: We genuinely appreciate your feedback emphasizing the practical implications and applications of our work. We recognize that while our research contributes to the theoretical foundation, it's crucial to bridge the gap between theory and real-world applicability to truly resonate with a broader audience. Your suggestion to delve deeper into how entities might benefit from our proposed scheme in real-world scenarios is indeed valuable. We have expanded upon this in the revised manuscript, outlining potential benefits and considerations for real-world deployments. Your insights are instrumental in ensuring our research not only advances academic knowledge but also offers tangible value to practical implementations.

4. Response to Comments on the Quality of English Language

Point 1: OK

Response 1: We are pleased to hear that the quality of English language in our manuscript meets the standards. We have endeavored to maintain clarity and coherence throughout the paper. Thank you for acknowledging this aspect.  

5. Additional clarifications

None at this moment. We believe we have addressed all the concerns and comments raised by the reviewers.

Response to Reviewer 2 Comments

1. Summary

Thank you for the comprehensive review and insightful comments on the manuscript. We appreciate the time and effort you have put into this review, and we believe that your feedback will greatly improve the quality of our work. Please find our detailed responses below, and the corresponding revisions are highlighted in the re-submitted files.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Can be improved

We have revised the introduction to provide a more comprehensive background. Additional references pertinent to the subject have been included to enrich the context and ensure the foundation of our research is clearly laid out for readers.

Are all the cited references relevant to the research?

Can be improved

We have re-evaluated our reference list and ensured all cited works are directly relevant to our research, and we've also added a few that strengthen the foundation and support our findings.

Is the research design appropriate?

Can be improved

We believe the research design is appropriate for our study's objectives. However, we have provided additional justifications in the methodology section, explaining why we chose this particular design and how it effectively addresses our research questions.

Are the methods adequately described?

Can be improved

We have expanded the methods section to provide a more in-depth description of our approach. Each step is detailed clearly, making it reproducible and understandable even for readers who may not be experts in the field.

Are the results clearly presented?

Can be improved

Recognizing the importance of clarity in presenting results, we revisited this section. We've restructured some parts for better flow. 

Are the conclusions supported by the results?

Can be improved

We revisited our conclusions to ensure they align closely with our results.

3. Point-by-point response to Comments and Suggestions for Authors

Comments 1: What motivated your research in the context of federated learning, and what are the key challenges you aimed to address?

Response 1: Thank you for posing this fundamental question. The motivation for our research stemmed from the growing importance of federated learning in preserving data privacy, especially in scenarios where data cannot be centrally aggregated. We observed that while federated learning provides robustness against certain challenges, there are still inherent issues, particularly in the realm of strategic behavior of participants and potential inefficiencies. Our primary goal was to address these challenges by incorporating game-theoretic approaches, aiming to enhance both the efficiency and fairness of federated learning systems. Your query has prompted us to reflect further on our motivations, and we have now added a more comprehensive explanation in the introduction of our revised manuscript.

Comments 2:  Can you explain the significance of ensuring data privacy and security in federated learning?

Response 2: We appreciate your inquiry into the significance of data privacy and security in the context of federated learning. Ensuring data privacy in federated learning is of paramount importance, especially given the distributed nature of the framework where raw data remains localized. Federated learning is often adopted in scenarios where data privacy regulations or concerns prohibit central data aggregation. By maintaining data at the source, we can mitigate potential breaches or misuse. Moreover, as devices collaborate to build a global model, ensuring the security of this process prevents adversarial attacks and ensures the model's integrity and accuracy. Your question underscores the foundational principles of federated learning, and we have made sure to emphasize and further elaborate on this significance in the revised manuscript.

Comments 3: How does your proposed scheme leverage game-theoretic techniques to enhance the security of federated learning?

Response 3: Thank you for your insightful question, which gets to the heart of our research's contribution. Our proposed scheme integrates game-theoretic techniques to model the interactions between participating devices in a federated learning system. By considering each device as a player in the game, we analyze their potential strategies, focusing on both cooperative and adversarial behaviors.In our approach, game-theoretic modeling provides a framework to understand the incentives and potential payoffs for each player. This allows us to identify and mitigate possible malicious strategies, ensuring that participating devices collaborate effectively without compromising the system's security. Furthermore, by analyzing the equilibrium states of the game, we can design mechanisms that deter malicious activities and promote behaviors that benefit the overall federated learning process.

To illustrate, in the "Methods" section of our manuscript, we detailed how the Nash Equilibrium can be used to predict the strategies of rational players, thereby allowing the system to anticipate and counteract adversarial actions.We believe that by intertwining federated learning with game-theoretic principles, we can create a more resilient and secure system. We have expanded on this explanation in our revised manuscript to provide a clearer picture of our methodology and its significance.

Comments 4:  What are the main advantages of using game theory in this context?

Response 4: We truly value your inquiry into the core advantages of employing game theory within our federated learning context. Game theory offers a robust framework to model and analyze the interactions among multiple participants, each with their own objectives.

Strategic Behavior Modeling: Game theory allows us to comprehensively model the strategic behaviors of participants. As we discussed in the "Methods" section of our paper, by considering each device or agent in federated learning as a 'player', we can anticipate their potential strategies, both cooperative and adversarial.

Incentive Alignment: With game-theoretic insights, we can design mechanisms that align individual incentives with the global objective. This ensures that even if individual devices act selfishly, the overall system still converges to an efficient and fair solution.

Your question has prompted us to reflect deeper on the strengths of our approach. We have incorporated a more detailed discussion on these advantages in the revised manuscript to ensure readers grasp the full breadth of the benefits offered by our game-theoretic approach in federated learning.

Comments 5: Could you elaborate on the anti-collusion mechanisms employed in your scheme to prevent malicious actors?

Response 5: We appreciate your inquiry into the anti-collusion mechanisms within our proposed scheme. Addressing collusion and malicious actors is indeed a crucial aspect of ensuring the robustness of our federated learning system.

In our research, we employed game-theoretic principles to design mechanisms that deter collusion. Specifically, by modeling the interactions among devices as a game, we can analyze the potential payoffs for different strategies, including those that involve collusion. This allows us to:

Identify Potential Collusive Behaviors: Through game-theoretic analysis, as detailed in the "Methods" section, we can predict scenarios where devices might find it beneficial to collude, thereby preemptively addressing such situations.

Incentive Design: By appropriately designing the reward and penalty structure, we can ensure that it is not in the best interest of the devices to collude. This means that even if devices act selfishly, they find non-collusive strategies to be more rewarding.

Monitoring and Detection: Our scheme incorporates monitoring mechanisms to detect anomalies in the contributions of devices. Such anomalies could be indicative of collusive behaviors, and once detected, corrective actions can be taken.

Diverse Participation Encouragement: By promoting diverse participation in the federated learning process, we reduce the chances of a single malicious group dominating the learning process.

Comments 6: What strategies or incentives are introduced through game theory to discourage collusion among participants?

Response 6: Thank you for highlighting this crucial aspect of our study. The prevention of collusion among participants is of paramount importance, and game theory offers us tools to design mechanisms that can actively discourage such behaviors.

Dynamic Payoff Structures: As we elaborated in the "Methods" section, our game-theoretic approach allows us to design dynamic payoff structures. By tailoring the rewards and penalties based on participants' behaviors, we can ensure that colluding provides a lesser payoff than honest participation.

Punishment Mechanisms: Game theory introduces the concept of punitive strategies, where malicious or colluding actors face consequences that deter them from such behaviors. For instance, a device found to be colluding might receive reduced rewards or even be temporarily excluded from the learning process.

Reputation Systems: Drawing inspiration from game-theoretic models, we've incorporated a reputation system where devices build trust over time through honest participation. Colluding devices risk damaging their reputation, which in turn affects their future interactions and potential payoffs.

Your question has reinforced the importance of explicitly discussing the anti-collusion strategies we've implemented. In the revised manuscript, we've enriched our discussion on this topic, detailing how game theory has guided our design choices to effectively discourage collusion among participants.

Comments 7: How do rational trust models and functional encryption contribute to the overall trustworthiness of your federated learning scheme?

Response 7: We truly appreciate your query, which touches upon two integral components of our federated learning scheme: rational trust models and functional encryption.

Rational Trust Models: Within our federated learning framework, the rational trust model acts as a foundational layer to assess and predict the behavior of participating devices. As delineated in the "Methods" section, by assuming devices are rational players, we anticipate their strategies and actions based on the perceived benefits. This model allows us to design incentive mechanisms that steer participants towards cooperative behaviors, thereby enhancing the overall trustworthiness of the system.

Functional Encryption: Functional encryption is a crucial pillar in preserving data privacy while allowing specific computations on encrypted data. As discussed in the "Security Measures" subsection, our use of functional encryption ensures that while individual data points remain encrypted and private, the global model can still be updated and refined. This not only preserves the privacy of individual participants but also engenders trust in the system, as devices are assured that their data won't be exposed or misused.

Together, the rational trust model and functional encryption bolster the robustness and security of our federated learning scheme. The former provides a framework to predict and manage participant behaviors, while the latter ensures data confidentiality without compromising the learning process. Your question has shed light on the need for a clearer exposition of these aspects. In our revised manuscript, we've taken care to elaborate on the synergistic roles of rational trust models and functional encryption in enhancing the trustworthiness of our scheme.

Comments 8: Can you provide examples of scenarios where these trust models are particularly beneficial?

Response 8: Certainly, and we appreciate your interest in delving deeper into the practical applications of our trust models. The rational trust model, embedded in our federated learning framework, offers significant advantages in various scenarios:

Heterogeneous Devices Participation: In federated learning environments where devices of varying computational capacities participate, some might be incentivized to free-ride, leveraging the computations of others without contributing meaningfully. The trust model can predict such behaviors, allowing the system to introduce incentives that encourage active and genuine participation.

Data Privacy Concerns: In sectors like healthcare or finance, where data is sensitive, devices might be hesitant to share data due to privacy concerns. The trust model, combined with our encryption mechanisms, ensures these devices that their data remains confidential, fostering more active participation.

Your question has made us realize the importance of illustrating the practical benefits of our trust model through tangible scenarios.

Comments 9: What role do smart contracts play in your scheme, and how do they enhance security and transparency?

Response 9: Thank you for drawing attention to the role of smart contracts within our federated learning framework. Smart contracts are indeed a pivotal component of our scheme, ensuring both operational efficiency and security.

Transparent Operations: Every operation executed by the smart contract is recorded on the blockchain, ensuring complete transparency. This immutable record ensures that participants can verify actions, fostering trust in the system.

Security Enhancements: Smart contracts, by their very nature, are tamper-proof. Once deployed, their logic cannot be altered, ensuring consistent behavior. This prevents malicious actors from modifying contract logic to their advantage.

Incentive Mechanisms: Our federated learning scheme, as described in the "Reward Distribution" subsection, employs smart contracts to manage rewards and penalties. By automating this process, we ensure timely and fair distribution based on participants' contributions, discouraging malicious or lazy behavior.

Your inquiry has emphasized the importance of articulating the multifaceted role of smart contracts in our scheme. In the revised manuscript, we've dedicated a more comprehensive section to elucidate how smart contracts intertwine with our game-theoretic approach to enhance both security and transparency in the federated learning process.

Comments 10: Are there specific use cases or interactions where smart contracts are crucial?

Response 10: Thank you for this pertinent question, emphasizing the practical significance of smart contracts within our federated learning framework.Indeed, there are several use cases and interactions in our scheme where the role of smart contracts is not just beneficial but crucial:

Data Verification: In federated learning systems, ensuring the authenticity and integrity of data shared by devices is paramount. Smart contracts can automate the verification process, checking the data against predefined criteria before it's accepted into the system, as discussed in the "Data Integrity" subsection.

Reward Distribution: As highlighted in the "Reward Distribution" subsection, the fair and transparent allocation of rewards based on contributions is managed by smart contracts. This not only ensures objective reward distribution but also significantly reduces disputes.

Penalty Enforcement: In scenarios where devices act maliciously or do not adhere to the system's guidelines, smart contracts can automatically impose penalties, thus ensuring compliance and deterring malevolent behaviors.

Your question underscores the multifaceted role of smart contracts in our scheme. We've taken your feedback into account and enhanced our discussion in the manuscript, providing more detailed examples of scenarios where smart contracts play an indispensable role in the federated learning process.

Comments 11: Author can read the following papers to increase the technical strength of the paper: InFeMo: flexible big data management through a federated cloud system,  Gradient Boosting for Health IoT Federated Learning.

Response 11: We are sincerely grateful for your recommendation to delve into the mentioned papers. These references indeed seem pivotal to enhancing the technical depth of our work.Upon your suggestion, we reviewed "InFeMo: flexible big data management through a federated cloud system" and found valuable insights on optimizing data management in a federated system. Your guidance has undeniably strengthened the technical rigor of our paper. We've duly cited these references in our revised manuscript and expanded our discussions based on the insights gleaned from them.

Comments 12: You mentioned empirical evaluations using MNIST, CIFAR-10, and Fashion MNIST datasets. What were the key findings or insights from these evaluations?

Response 12: We appreciate your keen interest in the empirical evaluations conducted in our study. Indeed, using the MNIST, CIFAR-10, and Fashion MNIST datasets was instrumental in validating the effectiveness of our proposed scheme. Performance Metrics: As detailed in the "Experimental Results" section, our federated learning approach, when combined with game-theoretic strategies, consistently yielded superior accuracy rates across all three datasets compared to traditional federated learning methods. Our scheme demonstrated faster convergence rates, especially evident in the MNIST evaluations. This implies that devices can achieve optimal learning with fewer rounds of communication, thus saving on computational resources and time. Your question has prompted us to reflect on the clarity and comprehensiveness of our results presentation. In the revised manuscript, we have endeavored to present the findings from these evaluations in a more structured manner, ensuring readers can easily discern the key insights and benefits of our approach.

Comments 13: How did data distribution, particularly IID and Non-IID setups, impact the performance of your scheme?

Response 13: We value your attention to this significant aspect of our study. Indeed, data distribution is a crucial factor that can greatly influence the performance of federated learning systems.In our research, as discussed in the "Data Distribution Impact" subsection:

IID Setup: Under the IID scenario, where each device's local dataset is a representative sample of the global dataset, our federated learning approach exhibited consistent and robust performance. The game-theoretic strategies ensured that even in such ideal conditions, devices were incentivized to actively and honestly participate, leading to fast convergence and high accuracy.

Non-IID Setup: In the more challenging Non-IID setting, where local data might be skewed or not representative of the global distribution, our scheme demonstrated its resilience. The game-theoretic principles, combined with the rational trust models, helped in mitigating the challenges of data heterogeneity. While there was an expected dip in performance compared to the IID setup, our method still outperformed traditional federated learning approaches in this scenario.

The impact of data distribution on our scheme underscores the flexibility and robustness of our approach. It's designed to handle both ideal (IID) and real-world, more complex (Non-IID) data distributions effectively.Your inquiry has prompted us to re-evaluate the clarity with which we've presented these findings. In the revised manuscript, we've expanded our discussion on the effects of data distribution, ensuring that the distinctions between IID and Non-IID setups and their implications on our scheme are clearly articulated.

4. Response to Comments on the Quality of English Language

Point 1: Moderate editing of English language required

Response 1: We genuinely appreciate your feedback regarding the language quality of our manuscript. We recognize the importance of clear and precise communication in presenting our research. To address this, we have undertaken a thorough review of the paper and sought the assistance of a professional teacher to refine the language and ensure it meets the standards of the journal. We believe that the revised manuscript now offers improved readability and clarity. Once again, thank you for highlighting this aspect, and we apologize for any inconvenience caused in the initial submission.

5. Additional clarifications

None at this moment. We believe we have addressed all the concerns and comments raised by the reviewers.

Response to Reviewer 3 Comments

1. Summary

Thank you for the comprehensive review and insightful comments on the manuscript. We appreciate the time and effort you have put into this review, and we believe that your feedback will greatly improve the quality of our work. Please find our detailed responses below, and the corresponding revisions are highlighted in the re-submitted files.

2. Questions for General Evaluation

Reviewer’s Evaluation

Response and Revisions

Does the introduction provide sufficient background and include all relevant references?

Yes

We appreciate the positive feedback on our introduction. We will continue to ensure that the background and references provide a solid foundation for our research.

Are all the cited references relevant to the research?

Can be improved

We have re-evaluated our reference list and ensured all cited works are directly relevant to our research, and we've also added a few that strengthen the foundation and support our findings.

Is the research design appropriate?

Can be improved

We believe the research design is appropriate for our study's objectives. However, we have provided additional justifications in the methodology section, explaining why we chose this particular design and how it effectively addresses our research questions.

Are the methods adequately described?

Yes

Thank you for acknowledging the clarity in our methods description. We will maintain this level of detail and clarity in the revised manuscript and any subsequent works.

Are the results clearly presented?

Yes

We're pleased to know our presentation of results met your expectations. We'll strive to maintain this clarity in future iterations and other sections of the paper.

Are the conclusions supported by the results?

Yes

Thank you for recognizing the alignment between our conclusions and results. We believe it's crucial to derive conclusions directly from empirical evidence and are glad to see this aspect of our paper was well-received.

3. Point-by-point response to Comments and Suggestions for Authors

Comments 1: While I appreciate the authors’ utilization of game theoretic components in their research on federated learning, I found their choice of ‘Nash Equilibrium’ and their expectation of it noteworthy. It is well known that Nash Equilibrium represents a stable state in a game. But it does not inherently guarantee that the outcome of a game is globally optimal or the best possible outcome for all parties involved. On page 7, lines 274 to 281, the authors describe how the asymmetric information of rational participants and their choices of honest strategies will lead to ‘optimal model update parameters.’ However, what is described in lines 278 to 281 guarantees a stable state rather than an optimal solution. I think the manuscript would benefit from an extra statement from the authors that justifies their choice of Nash Equilibrium in light of the above explanation.

Response 1:

Thank you for taking the time to review our manuscript, "Trustworthy Anti-collusion Federated Learning Scheme Optimized by Game Theory". We are gratified to note that you recognize the potential and innovations in our research, and we highly appreciate your constructive feedback, which we believe will help improve the quality and clarity of our work.Specific Comments:

Reviewer Comment: While I appreciate the authors’ utilization of game theoretic components in their research on federated learning, I found their choice of ‘Nash Equilibrium’ and their expectation of it noteworthy.

Response: We acknowledge your observation regarding the application of the Nash Equilibrium in our research. Indeed, our choice was based on the premise that in federated learning scenarios, ensuring stability and predictability is crucial, especially when multiple rational actors are involved.

Reviewer Comment: It is well known that Nash Equilibrium represents a stable state in a game but does not inherently guarantee that the outcome of a game is globally optimal or the best possible outcome for all parties involved.

Response: You're absolutely right. Nash Equilibrium ensures that no player has a unilateral incentive to deviate from their strategy, assuming other players' strategies remain unchanged. However, this does not always equate to a global optimum. In our context, while we aim for a globally optimal outcome, achieving stability in participants' strategies is a priority, given the potential adversarial nature of some participants.

Reviewer Comment: On page 7, lines 274 to 281, the authors describe how the asymmetric information of rational participants and their choices of honest strategies will lead to ‘optimal model update parameters.’ However, what is described guarantees a stable state rather than an optimal solution.

Response: We sincerely thank you for pointing this out. We realize that our wording may have implied a global optimality, whereas our intention was to express the achievement of a stable state that benefits the system as a whole. In light of your feedback, we have revised the stated section to better articulate our intent and clarify the distinction between stability and global optimality. We've also expanded upon the implications of achieving a Nash Equilibrium in the context of federated learning in our paper.

Reviewer Comment: I think the manuscript would benefit from an extra statement from the authors that justifies their choice of Nash Equilibrium in light of the above explanation.

Response: We completely agree. To this end, we have added a dedicated subsection within the "Methods" section titled "Rationale for Nash Equilibrium in Federated Learning". In this subsection, we delve deeper into why Nash Equilibrium is a suitable choice for our model, given the challenges and dynamics of federated learning systems.

Thank you once again for your insightful comments and recommendations. They have been instrumental in refining our manuscript. We believe that the revisions have addressed your concerns, and we are hopeful that our work now stands improved in its clarity and comprehensiveness.

4. Response to Comments on the Quality of English Language

Point 1: English language fine. No issues detected

Response 1: We greatly appreciate your positive feedback regarding the quality of the English language used in our manuscript. We have made efforts to ensure clarity and coherence in our writing, and we're glad to know it met the standards. Thank you for acknowledging it.

5. Additional clarifications

None at this moment. We believe we have addressed all the concerns and comments raised by the reviewers.