{"id":949,"date":"2025-04-30T20:58:05","date_gmt":"2025-04-30T20:58:05","guid":{"rendered":"https:\/\/www.ccor.hu\/?p=949"},"modified":"2025-04-30T20:58:06","modified_gmt":"2025-04-30T20:58:06","slug":"corvinus-game-theory-seminar-43","status":"publish","type":"post","link":"http:\/\/www.ccor.hu\/?p=949","title":{"rendered":"Corvinus Game Theory Seminar"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\"><strong>May 15 (10:00-11:00) room C.510<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><strong><strong><strong>Zs\u00f3fia Dornai<\/strong> <\/strong><\/strong><\/strong>(HUN-REN Centre for Economic and Regional Studies, Institute of Economics, Game Theory\u00a0Research Group)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>TU-games with utility functions: dually u-essential coalitions and other characterization sets for the u-prenucleolus<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The u-prenucleolus is a generalization of the prenucleolus using utility functions. The u-prenucleolus can also be considered as a generalization of the per-capita prenucleolus. Generalizations of some important theorems about the prenucleolus to the u-prenucleolus stand, such as Kohlberg\u2019s theorem, the theorem of Katsev and Yanovskaya about a sufficient and necessary condition on the unicity of the u-prenucleolus and a generalization of Huberman\u2019s theorem, which claims that the u-essential coalitions characterize the u-prenucleolus of u-balanced games. Considering the dual of the game, we define the u-anti-prenucleolus, and show that the u-anti-essential coalitions characterize it,\u00a0if the game is u-balanced. Using these results, we get that in the primal game the dually u-essential coalitions \u2013 which generalize the dually essential coalitions defined by Solymosi and Sziklai &#8211; characterize the u-prenucleolus of u-balanced games. In addition, we show, that in case of games where the u-least-core is a proper subset of the u-core the intersection of u-essential and dually u-essential coalitions also characterize the u-prenucleolus. To prove this latter theorem, we also give a generalization of a theorem by Granot, Granot and Zhu about a sufficient condition of a set of coalitions characterizing the u-prenucleolus, which also extends this result to games with restricted cooperation. <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The talk is based on joint work with Mikl\u00f3s Pint\u00e9r.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>May 15 (10:00-11:00) room C.510 Zs\u00f3fia Dornai (HUN-REN Centre for Economic and Regional Studies, Institute of Economics, Game Theory\u00a0Research Group) TU-games with utility functions: dually u-essential coalitions and other characterization sets for the u-prenucleolus The u-prenucleolus is a generalization of <span class=\"readmore\"><a href=\"http:\/\/www.ccor.hu\/?p=949\">Continue Reading &#8230;<\/a><\/span><\/p>\n","protected":false},"author":6,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-949","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/www.ccor.hu\/index.php?rest_route=\/wp\/v2\/posts\/949","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.ccor.hu\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.ccor.hu\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.ccor.hu\/index.php?rest_route=\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"http:\/\/www.ccor.hu\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=949"}],"version-history":[{"count":1,"href":"http:\/\/www.ccor.hu\/index.php?rest_route=\/wp\/v2\/posts\/949\/revisions"}],"predecessor-version":[{"id":950,"href":"http:\/\/www.ccor.hu\/index.php?rest_route=\/wp\/v2\/posts\/949\/revisions\/950"}],"wp:attachment":[{"href":"http:\/\/www.ccor.hu\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=949"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.ccor.hu\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=949"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.ccor.hu\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=949"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}