{"id":2749,"date":"2022-10-11T17:38:29","date_gmt":"2022-10-11T17:38:29","guid":{"rendered":"https:\/\/isipta23.sipta.org\/?page_id=2749"},"modified":"2023-09-04T16:46:13","modified_gmt":"2023-09-04T16:46:13","slug":"michel-grabisch","status":"publish","type":"page","link":"https:\/\/isipta23.sipta.org\/invited-speakers\/michel-grabisch\/","title":{"rendered":"Michel Grabisch"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"2749\" class=\"elementor elementor-2749\" data-elementor-post-type=\"page\">\n\t\t\t\t\t\t\t\t\t<section data-eae-particle=\"{\n  &quot;particles&quot;: {\n    &quot;number&quot;: {\n      &quot;value&quot;: 80,\n      &quot;density&quot;: {\n        &quot;enable&quot;: true,\n        &quot;value_area&quot;: 800\n      }\n    },\n    &quot;color&quot;: {\n      &quot;value&quot;: &quot;#ffffff&quot;\n    },\n    &quot;shape&quot;: {\n      &quot;type&quot;: &quot;circle&quot;,\n      &quot;stroke&quot;: {\n        &quot;width&quot;: 0,\n        &quot;color&quot;: &quot;#000000&quot;\n      },\n      &quot;polygon&quot;: {\n        &quot;nb_sides&quot;: 5\n      },\n      &quot;image&quot;: {\n        &quot;src&quot;: &quot;img\/github.svg&quot;,\n        &quot;width&quot;: 100,\n        &quot;height&quot;: 100\n      }\n    },\n    &quot;opacity&quot;: {\n      &quot;value&quot;: 0.5,\n      &quot;random&quot;: false,\n      &quot;anim&quot;: {\n        &quot;enable&quot;: false,\n        &quot;speed&quot;: 1,\n        &quot;opacity_min&quot;: 0.1,\n        &quot;sync&quot;: false\n      }\n    },\n    &quot;size&quot;: {\n      &quot;value&quot;: 3,\n      &quot;random&quot;: true,\n      &quot;anim&quot;: {\n        &quot;enable&quot;: false,\n        &quot;speed&quot;: 40,\n        &quot;size_min&quot;: 0.1,\n        &quot;sync&quot;: false\n      }\n    },\n    &quot;line_linked&quot;: {\n      &quot;enable&quot;: true,\n      &quot;distance&quot;: 150,\n      &quot;color&quot;: &quot;#ffffff&quot;,\n      &quot;opacity&quot;: 0.4,\n      &quot;width&quot;: 1\n    },\n    &quot;move&quot;: {\n      &quot;enable&quot;: true,\n      &quot;speed&quot;: 6,\n      &quot;direction&quot;: &quot;none&quot;,\n      &quot;random&quot;: false,\n      &quot;straight&quot;: false,\n      &quot;out_mode&quot;: &quot;out&quot;,\n      &quot;bounce&quot;: false,\n      &quot;attract&quot;: {\n        &quot;enable&quot;: false,\n        &quot;rotateX&quot;: 600,\n        &quot;rotateY&quot;: 1200\n      }\n    }\n  },\n  &quot;interactivity&quot;: {\n    &quot;detect_on&quot;: &quot;canvas&quot;,\n    &quot;events&quot;: {\n      &quot;onhover&quot;: {\n        &quot;enable&quot;: true,\n        &quot;mode&quot;: &quot;repulse&quot;\n      },\n      &quot;onclick&quot;: {\n        &quot;enable&quot;: true,\n        &quot;mode&quot;: &quot;push&quot;\n      },\n      &quot;resize&quot;: true\n    },\n    &quot;modes&quot;: {\n      &quot;grab&quot;: {\n        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data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;shape_divider_bottom&quot;:&quot;wave-brush&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t<div class=\"elementor-shape elementor-shape-bottom\" data-negative=\"false\">\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 283.5 27.8\" preserveAspectRatio=\"none\">\n\t<path class=\"elementor-shape-fill\" d=\"M283.5,9.7c0,0-7.3,4.3-14,4.6c-6.8,0.3-12.6,0-20.9-1.5c-11.3-2-33.1-10.1-44.7-5.7\ts-12.1,4.6-18,7.4c-6.6,3.2-20,9.6-36.6,9.3C131.6,23.5,99.5,7.2,86.3,8c-1.4,0.1-6.6,0.8-10.5,2c-3.8,1.2-9.4,3.8-17,4.7\tc-3.2,0.4-8.3,1.1-14.2,0.9c-1.5-0.1-6.3-0.4-12-1.6c-5.7-1.2-11-3.1-15.8-3.7C6.5,9.2,0,10.8,0,10.8V0h283.5V9.7z M260.8,11.3\tc-0.7-1-2-0.4-4.3-0.4c-2.3,0-6.1-1.2-5.8-1.1c0.3,0.1,3.1,1.5,6,1.9C259.7,12.2,261.4,12.3,260.8,11.3z 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d=\"M154.5,26.7c-0.1-0.1-4.6,0.3-7.2,0c-7.3-0.7-17-3.2-16.6-2.9c0.4,0.3,13.7,3.1,17,3.3\tC152.6,27.5,154.6,26.8,154.5,26.7z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M41.9,19.3c0,0,1.2-0.3,2.9-0.1c1.7,0.2,5.8,0.9,8.2,0.7c4.2-0.4,7.4-2.7,7-2.6\tc-0.4,0-4.3,2.2-8.6,1.9c-1.8-0.1-5.1-0.5-6.7-0.4S41.9,19.3,41.9,19.3z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M75.5,12.6c0.2,0.1,2-0.8,4.3-1.1c2.3-0.2,2.1-0.3,2.1-0.5c0-0.1-1.8-0.4-3.4,0\tC76.9,11.5,75.3,12.5,75.5,12.6z\"\/>\n\t<path class=\"elementor-shape-fill\" d=\"M15.6,13.2c0-0.1,4.3,0,6.7,0.5c2.4,0.5,5,1.9,5,2c0,0.1-2.7-0.8-5.1-1.4\tC19.9,13.7,15.7,13.3,15.6,13.2z\"\/>\n<\/svg>\t\t<\/div>\n\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b1b1d02\" data-id=\"b1b1d02\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cd1ef36 elementor-widget elementor-widget-image\" data-id=\"cd1ef36\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.16.0 - 20-09-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" loading=\"lazy\" width=\"1024\" height=\"128\" src=\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white-1024x128.png\" class=\"attachment-large size-large wp-image-546\" alt=\"LogoISIPTA23-long-white\" srcset=\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white-1024x128.png 1024w, https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white-300x38.png 300w, https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white-768x96.png 768w, https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white.png 1284w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-017a3c3 elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"017a3c3\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.16.0 - 20-09-2023 *\/\n.elementor-widget-divider{--divider-border-style:none;--divider-border-width:1px;--divider-color:#0c0d0e;--divider-icon-size:20px;--divider-element-spacing:10px;--divider-pattern-height:24px;--divider-pattern-size:20px;--divider-pattern-url:none;--divider-pattern-repeat:repeat-x}.elementor-widget-divider .elementor-divider{display:flex}.elementor-widget-divider .elementor-divider__text{font-size:15px;line-height:1;max-width:95%}.elementor-widget-divider .elementor-divider__element{margin:0 var(--divider-element-spacing);flex-shrink:0}.elementor-widget-divider .elementor-icon{font-size:var(--divider-icon-size)}.elementor-widget-divider .elementor-divider-separator{display:flex;margin:0;direction:ltr}.elementor-widget-divider--view-line_icon .elementor-divider-separator,.elementor-widget-divider--view-line_text .elementor-divider-separator{align-items:center}.elementor-widget-divider--view-line_icon .elementor-divider-separator:after,.elementor-widget-divider--view-line_icon .elementor-divider-separator:before,.elementor-widget-divider--view-line_text .elementor-divider-separator:after,.elementor-widget-divider--view-line_text .elementor-divider-separator:before{display:block;content:\"\";border-bottom:0;flex-grow:1;border-top:var(--divider-border-width) var(--divider-border-style) var(--divider-color)}.elementor-widget-divider--element-align-left .elementor-divider .elementor-divider-separator>.elementor-divider__svg:first-of-type{flex-grow:0;flex-shrink:100}.elementor-widget-divider--element-align-left .elementor-divider-separator:before{content:none}.elementor-widget-divider--element-align-left .elementor-divider__element{margin-left:0}.elementor-widget-divider--element-align-right .elementor-divider .elementor-divider-separator>.elementor-divider__svg:last-of-type{flex-grow:0;flex-shrink:100}.elementor-widget-divider--element-align-right .elementor-divider-separator:after{content:none}.elementor-widget-divider--element-align-right .elementor-divider__element{margin-right:0}.elementor-widget-divider:not(.elementor-widget-divider--view-line_text):not(.elementor-widget-divider--view-line_icon) .elementor-divider-separator{border-top:var(--divider-border-width) var(--divider-border-style) var(--divider-color)}.elementor-widget-divider--separator-type-pattern{--divider-border-style:none}.elementor-widget-divider--separator-type-pattern.elementor-widget-divider--view-line .elementor-divider-separator,.elementor-widget-divider--separator-type-pattern:not(.elementor-widget-divider--view-line) .elementor-divider-separator:after,.elementor-widget-divider--separator-type-pattern:not(.elementor-widget-divider--view-line) .elementor-divider-separator:before,.elementor-widget-divider--separator-type-pattern:not([class*=elementor-widget-divider--view]) .elementor-divider-separator{width:100%;min-height:var(--divider-pattern-height);-webkit-mask-size:var(--divider-pattern-size) 100%;mask-size:var(--divider-pattern-size) 100%;-webkit-mask-repeat:var(--divider-pattern-repeat);mask-repeat:var(--divider-pattern-repeat);background-color:var(--divider-color);-webkit-mask-image:var(--divider-pattern-url);mask-image:var(--divider-pattern-url)}.elementor-widget-divider--no-spacing{--divider-pattern-size:auto}.elementor-widget-divider--bg-round{--divider-pattern-repeat:round}.rtl .elementor-widget-divider .elementor-divider__text{direction:rtl}.e-con-inner>.elementor-widget-divider,.e-con>.elementor-widget-divider{width:var(--container-widget-width,100%);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9adf215 elementor-widget elementor-widget-heading\" data-id=\"9adf215\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.16.0 - 20-09-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Michel Grabisch<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fac39ee elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fac39ee\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-daa0aae\" data-id=\"daa0aae\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b4d9d71 elementor-widget elementor-widget-text-editor\" data-id=\"b4d9d71\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.16.0 - 20-09-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<a class=\"boton-volver\" href=\"javascript:history.back()\">\u2aa1 Back<\/a>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-99180d5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"99180d5\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1cf27c4\" data-id=\"1cf27c4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-11e022a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"11e022a\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-b727f10\" data-id=\"b727f10\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-dad4d96 elementor-widget elementor-widget-icon-box\" data-id=\"dad4d96\" data-element_type=\"widget\" data-widget_type=\"icon-box.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<link rel=\"stylesheet\" href=\"https:\/\/isipta23.sipta.org\/wp-content\/plugins\/elementor\/assets\/css\/widget-icon-box.min.css\">\t\t<div class=\"elementor-icon-box-wrapper\">\n\t\t\t\t\t\t<div class=\"elementor-icon-box-content\">\n\t\t\t\t<h2 class=\"elementor-icon-box-title\">\n\t\t\t\t\t<a href=\"https:\/\/sites.google.com\/site\/michelgrabisch\/?pli=1\" target=\"_blank\" >\n\t\t\t\t\t\tMichel Grabisch\t\t\t\t\t<\/a>\n\t\t\t\t<\/h2>\n\t\t\t\t\t\t\t\t\t<p class=\"elementor-icon-box-description\">\n\t\t\t\t\t\tUniversit\u00e9 Paris I Panth\u00e9on-Sorbonne\t\t\t\t\t<\/p>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a734043 elementor-widget elementor-widget-image\" data-id=\"a734043\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" loading=\"lazy\" width=\"400\" height=\"448\" src=\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/12\/GRABISCH-Michel.jpg\" class=\"attachment-large size-large wp-image-3263\" alt=\"\" srcset=\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/12\/GRABISCH-Michel.jpg 400w, https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/12\/GRABISCH-Michel-268x300.jpg 268w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<div class=\"elementor-element elementor-element-63d4f60 elementor-widget elementor-widget-heading\" data-id=\"63d4f60\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h1 class=\"elementor-heading-title elementor-size-large\">Balanced Games<\/h1>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fff2981 elementor-widget elementor-widget-heading\" data-id=\"fff2981\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Abstract<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5cd3644 elementor-widget elementor-widget-text-editor\" data-id=\"5cd3644\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Characteristic functions of transferable utility games (abbreviated by &#8220;games&#8221; for simplicity) are set functions defined on a finite set N and vanishing on the empty set. They are of wide use in cooperative game theory, but also in decision theory (capacities are monotone games), combinatorial optimization and discrete mathematics, and are also closely related to imprecise probabilities. Besides, the core of a game is the set of additive games dominating this game and coinciding on N. When the game is a capacity, the core is the set of compatible probability measures. Games with a nonempty core are called balanced.<br aria-hidden=\"true\" \/>\u00a0\u00a0\u00a0 The purpose of the talk is to give a survey on the known properties of balanced games and related notions. First, I will recall the classical Bondareva-Shapley result characterizing balanced games, together with the notion of (minimal) balanced collections. Then, I will address the problem of generating and enumerating minimal balanced collections, and show several applications of minimal balanced collections in cooperative game theory, including core stability, i.e., under which conditions the core of a game is a stable set in the sense of von Neumann and Morgenstern. In the last part, I will study the geometric properties of the set of balanced games, which is a cone, and find its linearity space and extreme rays.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-98da9c6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"98da9c6\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-25 elementor-top-column elementor-element elementor-element-19dc2f1\" data-id=\"19dc2f1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-25 elementor-top-column elementor-element elementor-element-b3ae21b\" data-id=\"b3ae21b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ecc01c5 oew-align-center elementor-widget elementor-widget-oew-button-effects\" data-id=\"ecc01c5\" data-element_type=\"widget\" data-widget_type=\"oew-button-effects.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\r\n\r\n\t\t<div class=\"oew-button oew-btn-effect-30\">\r\n\t\t\t<a href=\"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2023\/07\/grabisch.pdf\" class=\"oew-link\">\r\n\t\t\t\t\r\n\t\t\t\t<span>PRESENTATION<\/span>\r\n\r\n\t\t\t\t\t\t\t<\/a>\r\n\t\t<\/div>\r\n\r\n\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-25 elementor-top-column elementor-element elementor-element-4974f0e\" data-id=\"4974f0e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-db610e8 oew-align-center elementor-widget elementor-widget-oew-button-effects\" data-id=\"db610e8\" data-element_type=\"widget\" data-widget_type=\"oew-button-effects.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\r\n\r\n\t\t<div class=\"oew-button oew-btn-effect-30\">\r\n\t\t\t<a href=\"https:\/\/www.youtube.com\/watch?v=XhS4BdihHIM\" class=\"oew-link\">\r\n\t\t\t\t\r\n\t\t\t\t<span>YOUTUBE LINK<\/span>\r\n\r\n\t\t\t\t\t\t\t<\/a>\r\n\t\t<\/div>\r\n\r\n\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-25 elementor-top-column elementor-element elementor-element-655d12e\" data-id=\"655d12e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-dd2b88d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"dd2b88d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e2b8390\" data-id=\"e2b8390\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e9aa4b4 elementor-widget elementor-widget-text-editor\" data-id=\"e9aa4b4\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<a class=\"boton-volver\" href=\"javascript:history.back()\">\u2aa1 Back<\/a>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fbf1c64 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fbf1c64\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c4790df\" data-id=\"c4790df\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>\u2aa1 Back Michel Grabisch Universit\u00e9 Paris I Panth\u00e9on-Sorbonne Balanced Games Abstract Characteristic functions of transferable utility games (abbreviated by &#8220;games&#8221; for simplicity) are set functions defined on a finite set N and vanishing on the empty set. They are of wide use in cooperative game theory, but also in decision theory (capacities are monotone games), [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":709,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"footnotes":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Michel Grabisch - ISIPTA 2023<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/isipta23.sipta.org\/invited-speakers\/michel-grabisch\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Michel Grabisch - ISIPTA 2023\" \/>\n<meta property=\"og:description\" content=\"\u2aa1 Back Michel Grabisch Universit\u00e9 Paris I Panth\u00e9on-Sorbonne Balanced Games Abstract Characteristic functions of transferable utility games (abbreviated by &#8220;games&#8221; for simplicity) are set functions defined on a finite set N and vanishing on the empty set. 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They are of wide use in cooperative game theory, but also in decision theory (capacities are monotone games), [&hellip;]","og_url":"https:\/\/isipta23.sipta.org\/invited-speakers\/michel-grabisch\/","og_site_name":"ISIPTA 2023","article_modified_time":"2023-09-04T16:46:13+00:00","og_image":[{"url":"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/LogoISIPTA23-long-white-1024x128.png"}],"twitter_card":"summary_large_image","twitter_misc":{"Estimated reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/isipta23.sipta.org\/invited-speakers\/michel-grabisch\/","url":"https:\/\/isipta23.sipta.org\/invited-speakers\/michel-grabisch\/","name":"Michel Grabisch - ISIPTA 2023","isPartOf":{"@id":"https:\/\/isipta23.sipta.org\/#website"},"datePublished":"2022-10-11T17:38:29+00:00","dateModified":"2023-09-04T16:46:13+00:00","breadcrumb":{"@id":"https:\/\/isipta23.sipta.org\/invited-speakers\/michel-grabisch\/#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/isipta23.sipta.org\/invited-speakers\/michel-grabisch\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/isipta23.sipta.org\/invited-speakers\/michel-grabisch\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Portada","item":"https:\/\/isipta23.sipta.org\/"},{"@type":"ListItem","position":2,"name":"Invited Speakers","item":"https:\/\/isipta23.sipta.org\/invited-speakers\/"},{"@type":"ListItem","position":3,"name":"Michel Grabisch"}]},{"@type":"WebSite","@id":"https:\/\/isipta23.sipta.org\/#website","url":"https:\/\/isipta23.sipta.org\/","name":"ISIPTA 2023","description":"The International Symposium on Imprecise Probabilities","publisher":{"@id":"https:\/\/isipta23.sipta.org\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/isipta23.sipta.org\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-GB"},{"@type":"Organization","@id":"https:\/\/isipta23.sipta.org\/#organization","name":"ISIPTA 2023","url":"https:\/\/isipta23.sipta.org\/","logo":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/isipta23.sipta.org\/#\/schema\/logo\/image\/","url":"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/cropped-LogoISIPTA23-white.png","contentUrl":"https:\/\/isipta23.sipta.org\/wp-content\/uploads\/2022\/08\/cropped-LogoISIPTA23-white.png","width":500,"height":500,"caption":"ISIPTA 2023"},"image":{"@id":"https:\/\/isipta23.sipta.org\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/pages\/2749"}],"collection":[{"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/comments?post=2749"}],"version-history":[{"count":81,"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/pages\/2749\/revisions"}],"predecessor-version":[{"id":7147,"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/pages\/2749\/revisions\/7147"}],"up":[{"embeddable":true,"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/pages\/709"}],"wp:attachment":[{"href":"https:\/\/isipta23.sipta.org\/wp-json\/wp\/v2\/media?parent=2749"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}