{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T22:54:19Z","timestamp":1777589659910,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,8,23]],"date-time":"2025-08-23T00:00:00Z","timestamp":1755907200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Construction of Material Lifecycle Data Resource Node","award":["2024ZD0607600"],"award-info":[{"award-number":["2024ZD0607600"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the face of increasingly severe cybersecurity threats, incomplete information and environmental dynamics have become central challenges in network attack\u2013defense scenarios. In real-world network environments, defenders often find it difficult to fully perceive attack behaviors and network states, leading to a high degree of uncertainty in the system. Traditional approaches are inadequate in dealing with the diversification of attack strategies and the dynamic evolution of network structures, making it difficult to achieve highly adaptive defense strategies and efficient multi-agent coordination. To address these challenges, this paper proposes a multi-agent network defense approach based on joint game modeling, termed JG-Defense (Joint Game-based Defense), which aims to enhance the efficiency and robustness of defense decision-making in environments characterized by incomplete information. The method integrates Bayesian game theory, graph neural networks, and a proximal policy optimization framework, and it introduces two core mechanisms. First, a Dynamic Communication Graph Neural Network (DCGNN) is used to model the dynamic network structure, improving the perception of topological changes and attack evolution trends. A multi-agent communication mechanism is incorporated within the DCGNN to enable the sharing of local observations and strategy coordination, thereby enhancing global consistency. Second, a joint game loss function is constructed to embed the game equilibrium objective into the reinforcement learning process, optimizing both the rationality and long-term benefit of agent strategies. Experimental results demonstrate that JG-Defense outperforms the Cybermonic model by 15.83% in overall defense performance. Furthermore, under the traditional PPO loss function, the DCGNN model improves defense performance by 11.81% compared to the Cybermonic model. These results verify that the proposed integrated approach achieves superior global strategy coordination in dynamic attack\u2013defense scenarios with incomplete information.<\/jats:p>","DOI":"10.3390\/e27090892","type":"journal-article","created":{"date-parts":[[2025,8,25]],"date-time":"2025-08-25T00:10:36Z","timestamp":1756080636000},"page":"892","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Research on Joint Game-Theoretic Modeling of Network Attack and Defense Under Incomplete Information"],"prefix":"10.3390","volume":"27","author":[{"given":"Yifan","family":"Wang","sequence":"first","affiliation":[{"name":"Software College, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0666-4102","authenticated-orcid":false,"given":"Xiaojian","family":"Liu","sequence":"additional","affiliation":[{"name":"Software College, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuejun","family":"Yu","sequence":"additional","affiliation":[{"name":"Software College, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"64465","DOI":"10.1109\/ACCESS.2022.3183103","article-title":"Topological Graph Convolutional Network Based on Complex Network Characteristics","volume":"10","author":"Gao","year":"2022","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1186\/s41239-023-00389-3","article-title":"Extracting topological features to identify at-risk students using machine learning and graph convolutional network models","volume":"20","author":"Albreiki","year":"2023","journal-title":"Int. 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