{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:12:10Z","timestamp":1760148730220,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T00:00:00Z","timestamp":1684972800000},"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":["71961003","12061020","[2017] 7223","(2019) 49"],"award-info":[{"award-number":["71961003","12061020","[2017] 7223","(2019) 49"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Qian Ke He LH","award":["71961003","12061020","[2017] 7223","(2019) 49"],"award-info":[{"award-number":["71961003","12061020","[2017] 7223","(2019) 49"]}]},{"name":"Talent Introduction Foundation of Guizhou University","award":["71961003","12061020","[2017] 7223","(2019) 49"],"award-info":[{"award-number":["71961003","12061020","[2017] 7223","(2019) 49"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we propose a characteristic function of the maxmax defensive-equilibrium representation that maps every TU-game with strategies to a TU-game. This characteristic function is given by a two-step procedure in which each of any two complementary coalitions successively selects the equilibrium in a way that maximizes its utility. We then investigate the properties of this characteristic function and present the relations of the cores under three characteristic functions. Finally, as applications of our findings, we provide a firm production advertising game, a supply chain network game, a cost game with strategies, and a Cournot game.<\/jats:p>","DOI":"10.3390\/axioms12060521","type":"journal-article","created":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T02:05:44Z","timestamp":1685066744000},"page":"521","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Characteristic Function of Maxmax Defensive-Equilibrium Representation for TU-Games with Strategies"],"prefix":"10.3390","volume":"12","author":[{"given":"Chenwei","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8724-6449","authenticated-orcid":false,"given":"Shuwen","family":"Xiang","sequence":"additional","affiliation":[{"name":"College of Mathematical and Information Science, Guiyang University, Guiyang 550005, China"},{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}]},{"given":"Yanlong","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,25]]},"reference":[{"key":"ref_1","unstructured":"von Neumann, J., and Morgenstern, O. 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