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We define players\u2019 utilities taking into account a multilayer structure of the network by specifying different ways of accounting players\u2019 costs. Using two approaches, we obtain stability conditions for special multilplex structures including all-layer complete, all-layer star with unique or different centers, and all-layer unique networks.<\/jats:p>","DOI":"10.1093\/comnet\/cnae040","type":"journal-article","created":{"date-parts":[[2024,10,21]],"date-time":"2024-10-21T17:57:47Z","timestamp":1729533467000},"source":"Crossref","is-referenced-by-count":0,"title":["Stable multiplex networks: definitions and characterizations"],"prefix":"10.1093","volume":"12","author":[{"given":"Ziyu","family":"Ma","sequence":"first","affiliation":[{"name":"Saint Petersburg State University, Faculty of Applied Mathematics and Control Processes , Universitetskaya nab., 7-9 , Saint Petersburg, 199034, Russia"}]},{"ORCID":"http:\/\/orcid.org\/0000-0003-3976-7180","authenticated-orcid":false,"given":"Elena","family":"Parilina","sequence":"additional","affiliation":[{"name":"Saint Petersburg State University, Faculty of Applied Mathematics and Control Processes , Universitetskaya nab., 7-9 , Saint Petersburg, 199034, Russia"}]}],"member":"286","published-online":{"date-parts":[[2024,10,21]]},"reference":[{"key":"2024102117574325400_cnae040-B1","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1093\/comnet\/cnu016","article-title":"Multilayer networks","volume":"2","author":"Kivel\u00e4","year":"2014","journal-title":"J Complex Netw"},{"key":"2024102117574325400_cnae040-B2","first-page":"141","author":"Li","year":"2012"},{"key":"2024102117574325400_cnae040-B3","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.1145\/2020408.2020594","volume-title":"Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining","author":"Ng","year":"2011"},{"key":"2024102117574325400_cnae040-B4","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.apm.2017.07.012","article-title":"A new centrality measure of nodes in multilayer networks under the framework of tensor computation","volume":"54","author":"Wang","year":"2018","journal-title":"Appl Math Modell"},{"key":"2024102117574325400_cnae040-B5","doi-asserted-by":"crossref","first-page":"853","DOI":"10.1137\/17M1137668","article-title":"Node and layer Eigenvector centralities for multiplex networks","volume":"78","author":"Tudisco","year":"2018","journal-title":"SIAM J Appl Math"},{"key":"2024102117574325400_cnae040-B6","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/978-3-319-92255-3","volume-title":"Multiplex Networks: Basic Formalism and Structural Properties. 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