{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,24]],"date-time":"2026-10-24T14:50:13Z","timestamp":1792853413011,"version":"4.5.0"},"reference-count":31,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,29]],"date-time":"2024-01-29T00:00:00Z","timestamp":1706486400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["ZR2023QF044"],"award-info":[{"award-number":["ZR2023QF044"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>False data injection attacks are executed in the electricity markets of smart grid systems for financial benefits. The attackers can maximize their profits through modifying the estimated transmission power and changing the prices of market electricity. As a response, defenders need to minimize expected load losses and generator trips through load and power generation adjustments. The selection of strategies of the attacking and defending sides turns out to be a symmetric game process. This article proposes a hybrid game theory method for analyzing the attack\u2013defense confrontation: firstly, a micro-grid-based power market model considering false data injection attacks is established using the Nash equilibrium method; secondly, the attack\u2013defense game function is constructed and solved via the Stackelberg equilibrium algorithm. The Markov game algorithm and distributed learning algorithm are used to update equilibrium function; finally, a dynamic game behavior model of the two players is constructed through simulating the attack\u2013defense probability. The evolutionary game method is used to select the optimal defense strategy for dynamic probability changes. Modified IEEE standard bus systems are illustrated to certify the effectiveness of the proposed model.<\/jats:p>","DOI":"10.3390\/sym16020156","type":"journal-article","created":{"date-parts":[[2024,1,29]],"date-time":"2024-01-29T08:11:27Z","timestamp":1706515887000},"page":"156","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Attack\u2013Defense Confrontation Analysis and Optimal Defense Strategy Selection Using Hybrid Game Theoretic Methods"],"prefix":"10.3390","volume":"16","author":[{"given":"Bao","family":"Jin","sequence":"first","affiliation":[{"name":"Institute of Engineering, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaodong","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Taishan University, Tai\u2019an 271000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dongmei","family":"Yuan","sequence":"additional","affiliation":[{"name":"College of Electric Engineering, Nanjing Xiaozhuang University, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5060","DOI":"10.1109\/TSG.2021.3095896","article-title":"On the Use of Common Information Model for Smart Grid Applications\u2014A Conceptual Approach","volume":"12","author":"Shahid","year":"2021","journal-title":"IEEE Trans. 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