{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T11:03:33Z","timestamp":1762081413782,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T00:00:00Z","timestamp":1672185600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["72001209","72231011","71971213","72071206","2020RC4046","2022JJ20047"],"award-info":[{"award-number":["72001209","72231011","71971213","72071206","2020RC4046","2022JJ20047"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012269","name":"Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province","doi-asserted-by":"publisher","award":["72001209","72231011","71971213","72071206","2020RC4046","2022JJ20047"],"award-info":[{"award-number":["72001209","72231011","71971213","72071206","2020RC4046","2022JJ20047"]}],"id":[{"id":"10.13039\/501100012269","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science Foundation for Outstanding Youth Scholars of Hunan Province","award":["72001209","72231011","71971213","72071206","2020RC4046","2022JJ20047"],"award-info":[{"award-number":["72001209","72231011","71971213","72071206","2020RC4046","2022JJ20047"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Today, people rely heavily on infrastructure networks. Attacks on infrastructure networks can lead to significant property damage and production stagnation. The game theory provides a suitable theoretical framework for solving the problem of infrastructure protection. Existing models consider only the beneficial effects that the defender obtains from information gaps. If the attacker\u2019s countermeasures are ignored, the defender will become passive. Herein, we consider that a proficient attacker with a probability in the game can fill information gaps in the network. First, we introduce the link-hiding rule and the information dilemma. Second, based on the Bayesian static game model, we establish an attack\u2013defense game model with multiple types of attackers. In the game model, we consider resource-consistent and different types of distributions of the attacker. Then, we introduce the solution method of our model by combining the Harsanyi transformation and the bi-matrix game. Finally, we conduct experiments using a scale-free network. The result shows that the defender can be benefited by hiding some links when facing a normal attacker or by estimating the distribution of the attacker correctly. The defender will experience a loss if it ignores the proficient attacker or misestimates the distribution.<\/jats:p>","DOI":"10.3390\/e25010057","type":"journal-article","created":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T02:56:50Z","timestamp":1672282610000},"page":"57","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Attack\u2013Defense Game Model with Multi-Type Attackers Considering Information Dilemma"],"prefix":"10.3390","volume":"25","author":[{"given":"Gaoxin","family":"Qi","sequence":"first","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Jichao","family":"Li","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Chi","family":"Xu","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Gang","family":"Chen","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}]},{"given":"Kewei","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, Changsha 410073, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1016\/j.jlp.2016.07.010","article-title":"Using game theory to optimize allocation of defensive resources to protect multiple chemical facilities in a city against terrorist attacks","volume":"43","author":"Feng","year":"2016","journal-title":"J. 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