{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:43:03Z","timestamp":1760236983228,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,4]],"date-time":"2020-02-04T00:00:00Z","timestamp":1580774400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In view of the problems such as low efficiency, difficulty in resolving local conflicts and lack of practical application scenarios, existing in the interaction model of multi-agent systems in a distributed environment, a multi-master multi-slave interaction model was designed based on the Stackelberg game, which is applied to the interaction game problem between the controller and the participant in the command and control process. Through optimizing the Stackelberg game model and multi-attribute decision-making, the multi-master, multi-slave, multi-agent system of the Stackelberg game was designed, and the closed loop problem under the Stackelberg game is solved for dimension reduction and optimal function value. Finally, through the numerical derivation simulation and the training results of related system data, the high efficiency and strong robustness of the model were verified from multiple perspectives, and this model algorithm was proved to be true and highly efficient.<\/jats:p>","DOI":"10.3390\/sym12020232","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T03:13:27Z","timestamp":1581045207000},"page":"232","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Study on Master Slave Interaction Model Based on Stackelberg Game in Distributed Environment"],"prefix":"10.3390","volume":"12","author":[{"given":"Jie","family":"Zhang","sequence":"first","affiliation":[{"name":"Graduate School, Air Force Engineering University, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Air-Defense and Anti-Missile, Air Force Engineering University, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaohua","family":"Yue","sequence":"additional","affiliation":[{"name":"Department of Air-Defense and Anti-Missile, Air Force Engineering University, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoqiang","family":"Yao","sequence":"additional","affiliation":[{"name":"Department of Air-Defense and Anti-Missile, Air Force Engineering University, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0962-0671","authenticated-orcid":false,"given":"Yafei","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Air-Defense and Anti-Missile, Air Force Engineering University, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiayi","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Air-Defense and Anti-Missile, Air Force Engineering University, Xi\u2019an 710054, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,4]]},"reference":[{"key":"ref_1","first-page":"107","article-title":"CC 5.0: Intelligent Command and Control Systems in the Parallel Age","volume":"1","author":"Wang","year":"2015","journal-title":"J. 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