Game-Theoretic Power Control Modeling for Interference Management in 5G Networks—A System Dynamics Approach

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Vague and Potentially Incompatible is the How of Integration.

The main novelty, which is a combination of game theory and System Dynamics (SD) is not explained mechanically. Game theory tends to search and SD models of feedback, which are time-varying. The paper fails to specify how an equilibrium in a game theoretic model is determined or implemented in a continuous and feedback-controlled VENSIM model.

 

Reduced and possibly unrealistic Power Control Algorithms.

The power control algorithms as proposed in SD model are too simple and might not be representative of the complexity of a game as per the game theory. In the noncooperative model, a simple SINR low-power up logic (Eq. 20, 21), that is typical of control-theoretic strategies, is used, rather than a strategic game in which players expect their competitors to respond.

 

Absence of a Framework for Comparing Performance.

There is a lack of a well-defined quantitative framework, as the article establishes two cases and two strategies (cooperative vs. noncooperative). It cannot be determined whether the suggested practices are working because there are no established measures or a benchmark.

 

The Assumptions of the models may not be true in the Real 5G Deployments.

Several major assumptions restrict the relevance of the findings in practice. The theoretical simplifications of the full buffer traffic model and the fixed association of users do not the bursty and mobile characteristics of actual 5G traffic and user movement.

The Model is not Verifiable Because Critical Figures are missing.

There are numerous mentions of visual models (Causal Loop Diagrams, Stock-and-Flow diagrams) that are crucial to the comprehension of the proposed SD framework, but these visuals are not presented in the excerpt.

Author Response

Thank you very much for taking the time to review this manuscript. The authors sincerely thank you for the insightful comments and constructive suggestions. Your thoughtful feedback has been invaluable in strengthening the analysis and improving the clarity of the manuscript. We have carefully addressed all points raised in the revised version. We have attached a pdf file for your attention.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

It is a Good paper to be considered to publish, but need to check some issues.

Add quantitative performance results (e.g., “the cooperative model improved SINR by X% and spectral efficiency by Y% compared to the noncooperative case”).
Replace vague phrasing (“models are verified to establish a basis…”) with explicit methods or metrics used for verification.
Avoid redundancy (lines 30–45 and 52–61 repeat similar ideas about interference management and SD modeling).
Include a comparative summary table (e.g., Table 1) summarizing prior studies, their approaches, methods, and limitations.
Add recent references (2022–2025), especially works on AI-enhanced power control, multi-agent reinforcement learning, or distributed optimization in 5G.
Figures 1–3 are clear, but captions should be more descriptive. 
Equations (1)–(3) should include units and reference the specific path loss model section of 3GPP TR 38.901 (e.g., Urban Macro NLOS).
Clarify the physical meaning of constants such as 128.1 and 37.6 (path loss parameters).
Use flow diagrams to contrast cooperative vs. noncooperative interactions.
Explicitly explain how utilities and costs are computed in VENSIM.
Clarify the convergence criteria for Nash Equilibrium (e.g., tolerance level for ΔU < 10⁻³).
Clarify how feedback loops influence interference levels over time (e.g., does interference at t affect power control decisions at t+1?).
Include quantitative comparisons (tables/plots) between cooperative and noncooperative models for variables.
Discuss the computational complexity or simulation time trade-offs.
Provide practical implications: How might network operators implement such strategies in real 5G NR deployments?
Define all acronyms at first use.
Some sections switch between “chapter” and “paper”—use one term consistently (“paper”).

Author Response

Thank you very much for taking the time to review this manuscript. The authors sincerely thank you for the insightful comments and constructive suggestions. Your thoughtful feedback has been invaluable in strengthening the analysis and improving the clarity of the manuscript.

Please find the detailed responses in the attached PDF file and the corresponding revisions/corrections highlighted (in green) in the re-submitted files.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The article belongs to two larger domains: game theory and system dynamics modelling in 5G networks. Specifically, the authors are tackling a research problem of developing power control models for mitigating high inter-cell interference between macro users and femto users in heterogeneous 5G networks. A hybrid approach is used that combines game-theoretic strategies (cooperative and noncooperative) with system dynamics modelling (using a system dynamics simulation tool VENSIM). From presentational and grammatical points of view, the article is fine (i.e., no major errors or typos were observed).

Main things to improve upon:

• The second section, called »2. Objectives« is quite short. I think it can be integrated into the introduction.
• Sensitivity analysis could also include other parameters (e.g., power adjustment factor) to evaluate the robustness of the model under varying network conditions (e.g., dynamic user behaviour).
• “A full buffer traffic model is assumed for both the MUE and FUE.” – Maybe add a short explanation of how this differs from the real-world 5G network scenario (i.e., where users join, leave, are idle, …, this can have an impact on Signal-to-Interference-plus-Noise Ratio (SINR)). In short, because this variability can impact SINR it should be acknowledged as a limitation.
• You have mentioned scalability concerns of cooperative strategies (e.g., signaling overhead): “the simulations reveal that cooperative mode requires approximately 40-50% more signaling overhead compared to noncooperative operation”. It would be good to quantitatively analyze scalability in terms of latency impact or feasibility in ultra-dense deployments (e.g., what happens with 100+ femtocells).

Possible text enhancements and improvements:

• “Other solution concepts, such as correlated equilibrium [35] and dominant-strategy equilibrium [36], can also be used.” – It would be useful to provide additional information on how these two options are different from the Nash equilibrium (i.e., what would be the advantage?).
• The theoretical part is quite lengthy and very descriptive, which I don’t see as a problem per se. Meaning, sometimes a reader is better off if everything necessary to understand the experiment is gathered in one place. Especially with a good referencing provided, like in this article. However, it could certainly be a bit shorter in some sections (e.g., game theory is explained at various points) [this note is just for consideration]. 

Minor errors:

• (line 266) “is given as follows:The path”, (line 440) “(17).The Nash“, (line 1330) “Shannon-Hartley theorem( 𝑆𝑆𝑆 ” - A space is missing.
• “[50], [51] is adopted.” – No comma between the references.

Overall, it is an interesting article combining game theory and system dynamics modelling in the problem domain of interference management among macro and femto users in 5G networks. I am recommending minor revisions.

Author Response

Thank you very much for taking the time to review this manuscript. The authors sincerely thank you for the insightful comments and constructive suggestions. Your thoughtful feedback has been invaluable in strengthening the analysis and improving the clarity of the manuscript.

Please find the detailed responses in the attached PDF file and the corresponding revisions/corrections highlighted (in red) in the re-submitted files.

Author Response File: Author Response.pdf