We sincerely thank the reviewer for efforts and the useful suggestions. We have prioritized and organized the reviewer’s comments, and our responses are as follows:

S1. It is suggested to include evaluations on larger-scale scenarios.

R1. Thank you for the suggestion. We have supplemented Appendix A.2 with results for settings with 6 and 9 agents. In addition, we also add an experiment with 24 agents, presented below. The results indicate that as the number of agents increases, our method maintains its advantage.

S2. Another suggestion is to include a visualization section in Section 5.

R2. Thank you for the suggestion. Our goal is to address the performance degradation that arises when deploying models in lossy communication scenarios, thus robustness is the core metric we intend to highlight. We believe that a tabular format can more clearly convey the robustness achieved under various lossy communication scenarios. Nevertheless, we will adopt your suggestion. We have generated training curves and a bar chart comparing the final rewards based on the log data. These figures will be presented in the revised appendix.

S3. It is recommended to remove the related work mentioning the issue of limited communication bandwidth.

R3. Thank you for the suggestion. We will remove in the revised version.

S4. The authors are advised to conduct a thorough review for minor issues, such as missing symbols in Equation (2)(6).

R4. Thank you for the suggestion. We will carefully ensure equation consistency in the revised version.

We sincerely thank the reviewer for the time and efforts. Below please find the responses to some specific comments.

Q1. Can the proposed method still work well in cooperative scenarios where the agent can defect for self-interest?

A1. Our proposed method does not specifically address this issue. Our approach targets the alleviate the degradation of MARL performance under lossy communication, whereas cooperative scenarios in which agents may defect for self-interest—often termed social dilemmas—require dedicated methods (e.g., incorporating social preferences), which is out of our scope. We are happy to investigate the influence of lossy communication in such scenarios as future work

Q2. It seems one key related paper on limited bandwidth with information bottleneck is missing: "Wang et al. 2020. Learning Efficient Multi-agent Communication: An Information Bottleneck Approach."

A2. Thank you very much for the reminder. We will add the relevant work in the revised version.

W1. It is not clear the scalability capacity of the proposed method in multi-agent scenarios where the number of agents is huge.

R1. Thank you for pointing out this. We have supplemented Appendix A.2 with results for settings with 6 and 9 agents. In addition, for verity the scalability capacity, we also add an experiment with 24 agents, presented below. The results indicate that as the number of agents increases, our method maintains its advantage.

Thanks for the responses.

We sincerely thank the reviewer for the time and efforts. Below please find the responses to some specific comments.

Q1. Is the binary communication prior overly simplified?

A1. Thank you for pointing out this. We would like to clarify this assumption in two points. First, it aligns well with real-world scenarios that the communication could be broken occasionally, e.g., For example, during network transmission, data are segmented into individual packets. Packet loss occurs when one or more packets are lost in transit and fail to reach the destination, yielding an inherently binary outcome—either the packet arrives or it does not. Likewise, in underwater communication among UUVs, once the distance exceeds a certain threshold, message transmission is naturally dropped, producing the same binary-like outcome. Second, this binary-like abstraction of realistic communication scenarios poses a significant challenge to conventional communication-based MARL. As shown in Table 1, their performance degrades markedly as the proportion of lost messages increases. Moreover, the binary-like abstraction is also partially employed in the validation of the MAIC method.

Q2. Why is MADDPG used as the base algorithm?

A2. Thank you for your concern. We choose MADDPG as the base algorithm for two reasons. First, it embodies both the AC architecture and CTED framework, making it representative of many MARL methods. Second, MADDPG integrates naturally with communication mechanisms without requiring additional modifications, enabling ablation studies to cleanly verify the effectiveness of each module in our approach. By contrast, in standard MAPPO the actor network employs an RNN; when combined with a communication mechanism, this typically could necessitate designing new neural network components, making it difficult to disentangle whether performance changes arise from the neural network architecture or from our algorithmic modules. While our method is orthogonal to existing MARL approaches in principle. We will include more results on the backbone of other MARL algorithms, such as MAPPO in our revised version.

Q3. What is the training overhead of Du-MIE?

A3. We report the training time for each algorithm over 10 runs, with 4 million steps per run. All runs were conducted on the same server equipped with an NVIDIA A5000 GPU.

It is noted that the Du-MIE module doesn’t induce heavy workload of training resources, considering the advantages contributed to the final performance.

W1. Limited Related Work and Baseline Coverage.

R1. Thank you for your comment. We have investigated the degradation of MARL performance under lossy communication. However, there are quite few works in this domain. Approaches that assume noisy (rather than lossy) communication differ from our problem formulation: Approaches with noisy communication assume that noise can be modeled and noisy messages can be repaired, while we assume that messages are directly lost and messages are unusable. Thus, approaches with noisy communication not suitable as baselines.

W2. Lack of Experimental Detail and Visualization.

R2. Thank you for your comment. For training our algorithm, we used random seed 1(no average over at least 5 seeds), which yielded the best performance. During evaluation, we did not fix the random seed. Moreover, our goal is to address the performance degradation that arises when deploying models in lossy communication scenarios, and robustness is the core metric we intend to highlight. We believe that, instead of presenting numerous training curves for different tasks, a tabular format can more clearly convey the robustness achieved under various lossy communication scenarios. Nevertheless, we will adopt your suggestion. We have compiled the training curves and will present them in the appendix.

W3. Inconsistent Mathematical Notation.

R3. Thank you for the comment. We will carefully ensure notation consistency in the final version.

We sincerely thank the reviewer for the time and efforts. Below please find the responses to some specific comments.

Q1. During practical implementation, how is the agent-pair-specific state component sij distilled from the global state s? Specifically, what key information dimensions does sij encompass?

A1. Thank you for your concern. In MPE, the environment state is formed by concatenating the local observations of all agents. Simply splitting this vector yields the entries relevant to agents i and j, notably their respective spatial positions and velocities.

Q2. Would significant imbalance in the ratio between lossless and lossy messages lead to substantial performance degradation?

A2. Thank you for your concern. It indeed leads to degraded performance, as demonstrated by our experiments. We configured two lossy communication scenarios, MBC and DBC, correspondingly set two parameters—loss probability and distance threshold—that govern the ratio between lossless and lossy messages. We further stratified the severity of communication loss into three levels: high, medium, and low. As shown in Table 1, FC-MADDPG with full communication performs worse when the proportion of lossy messages exceeds that of lossless messages, whereas the no-communication MADDPG deteriorates when the proportion of lossy messages is lower than that of lossless messages due to interference from redundant messages. We attribute the performance degraded mainly to the mismatch between the message distributions at training and testing. Specifically, FC-MADDPG is trained under full communication yet evaluated under lossy communication, while MADDPG is trained without communication but tested in the same lossy communication. We will add the analysis in the revised version.

W1. Inadequate baseline comparison.

R1. Thank you for the comment. We have conducted new experiments to compare with the baselines the reviewer suggested. However, we want to clarify that NDQ is incompatible since it addresses limited communication bandwidth and cannot be applied to lossy communication settings. MAIC is designed for discrete action spaces, accordingly, we discretized the MPE setting and have

Experimental results indicate that MAIC performs worse than our proposed method under these lossy-communication scenarios.

W2. Limited test scenarios.

R2. Thank you for the comment. We add an experiment on a cooperative–competitive scenario (simple_adversary), and the results show that our proposed method likewise exhibits a performance advantage.

W3 (original Q2). Oversimplified test conditions

R3. Thank you for pointing out this. We would like to clarify this assumption in two points. First, this test conditions pose a significant challenge to conventional communication-based MARL. As shown in Table 1, their performance degrades markedly as the proportion of lost messages increases. Moreover, the test conditions (binary-like) is also partially employed in the validation of the MAIC method. Second, it aligns well with real-world scenarios that the communication could be broken occasionally, e.g., For example, during network transmission, data are segmented into individual packets. Packet loss occurs when one or more packets are lost in transit and fail to reach the destination, yielding an inherently binary outcome—either the packet arrives or it does not. Likewise, in underwater communication among UUVs, once the distance exceeds a certain threshold, message transmission is naturally dropped, producing the same binary-like outcome.

W4. It should be noted that the methodology substantially inherits PMIC's foundational framework, and this design choice has, to some extent, constrained the innovative demonstration of this research.

R4. Thank you for the comment. We believe that the novelty of our method is by no means limited to this single aspect. We are the first to formalize lossy communication and to propose an innovative communication-constrained prior model. Leveraging a Dual-MIE scheme, we simultaneously (1) mitigate the adverse effects of lossy messages and (2) amplify the beneficial influence of lossless messages. Both the modeling framework and the solution procedure make a substantial contribution to MARL with lossy communication research and facilitate the rapid transfer of MARL techniques to real-world applications.

Moreover, our work is not a mere duplication of PMIC. Two clarifications are in order:

(1) Problem scope. We address robust policy learning under lossy communication, whereas PMIC focuses on solving overgeneralization issues in MASs.

(2) Methodological framework. Although both approaches employ JSD and CLUB as MIE, their roles differ markedly: we measure the MI between messages and individual behaviors to control the influence of communication on policy training, while PMIC uses it to distinguish the optimal trajectories and sub-optimal ones. Consequently, our method does not require the additional dual buffer used in PMIC.