{"title":"On the symmetry relation between different characteristic functions for additively separable cooperative games","authors":"E. Gromova, K. Savin","doi":"10.3934/jdg.2022017","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>We analyze 4 characteristic functions <inline-formula><tex-math id=\"M1\">\\begin{document}$ V^\\alpha $\\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M2\">\\begin{document}$ V^\\delta $\\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M3\">\\begin{document}$ V^\\zeta $\\end{document}</tex-math></inline-formula>, and <inline-formula><tex-math id=\"M4\">\\begin{document}$ V^\\eta $\\end{document}</tex-math></inline-formula>, and give a necessary condition for these functions to satisfy the relation <inline-formula><tex-math id=\"M5\">\\begin{document}$ V^\\alpha - V^\\delta = V^\\zeta - V^\\eta $\\end{document}</tex-math></inline-formula> for all coalitions <inline-formula><tex-math id=\"M6\">\\begin{document}$ S $\\end{document}</tex-math></inline-formula>. To do so, we define and formally analyze the class of additively separable games. It is shown that many important types of games, both static and dynamic, belong to this class.</p>","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"10 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamics and Games","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/jdg.2022017","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
We analyze 4 characteristic functions \begin{document}$ V^\alpha $\end{document}, \begin{document}$ V^\delta $\end{document}, \begin{document}$ V^\zeta $\end{document}, and \begin{document}$ V^\eta $\end{document}, and give a necessary condition for these functions to satisfy the relation \begin{document}$ V^\alpha - V^\delta = V^\zeta - V^\eta $\end{document} for all coalitions \begin{document}$ S $\end{document}. To do so, we define and formally analyze the class of additively separable games. It is shown that many important types of games, both static and dynamic, belong to this class.
We analyze 4 characteristic functions \begin{document}$ V^\alpha $\end{document}, \begin{document}$ V^\delta $\end{document}, \begin{document}$ V^\zeta $\end{document}, and \begin{document}$ V^\eta $\end{document}, and give a necessary condition for these functions to satisfy the relation \begin{document}$ V^\alpha - V^\delta = V^\zeta - V^\eta $\end{document} for all coalitions \begin{document}$ S $\end{document}. To do so, we define and formally analyze the class of additively separable games. It is shown that many important types of games, both static and dynamic, belong to this class.
期刊介绍:
The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.