{"id":1157,"date":"2020-05-21T20:14:09","date_gmt":"2020-05-21T18:14:09","guid":{"rendered":"http:\/\/www.filosofia.unimi.it\/~hosni\/?p=1157"},"modified":"2020-05-21T20:21:59","modified_gmt":"2020-05-21T18:21:59","slug":"possibilistic-randomisation-in-strategic-form-games","status":"publish","type":"post","link":"https:\/\/sites.unimi.it\/hosni\/2020\/05\/possibilistic-randomisation-in-strategic-form-games\/","title":{"rendered":"Possibilistic randomisation in strategic-form games"},"content":{"rendered":"<blockquote><p><a href=\"https:\/\/i0.wp.com\/sites.unimi.it\/hosni\/wp-content\/uploads\/2020\/05\/IJAR.jpg?ssl=1\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"1158\" data-permalink=\"https:\/\/sites.unimi.it\/hosni\/2020\/05\/possibilistic-randomisation-in-strategic-form-games\/ijar\/\" data-orig-file=\"https:\/\/i0.wp.com\/sites.unimi.it\/hosni\/wp-content\/uploads\/2020\/05\/IJAR.jpg?fit=563%2C768&amp;ssl=1\" data-orig-size=\"563,768\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"IJAR\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/i0.wp.com\/sites.unimi.it\/hosni\/wp-content\/uploads\/2020\/05\/IJAR.jpg?fit=220%2C300&amp;ssl=1\" data-large-file=\"https:\/\/i0.wp.com\/sites.unimi.it\/hosni\/wp-content\/uploads\/2020\/05\/IJAR.jpg?fit=563%2C768&amp;ssl=1\" class=\"size-medium wp-image-1158 alignright\" src=\"https:\/\/i0.wp.com\/sites.unimi.it\/hosni\/wp-content\/uploads\/2020\/05\/IJAR.jpg?resize=220%2C300&#038;ssl=1\" alt=\"\" width=\"220\" height=\"300\" srcset=\"https:\/\/i0.wp.com\/sites.unimi.it\/hosni\/wp-content\/uploads\/2020\/05\/IJAR.jpg?resize=220%2C300&amp;ssl=1 220w, https:\/\/i0.wp.com\/sites.unimi.it\/hosni\/wp-content\/uploads\/2020\/05\/IJAR.jpg?w=563&amp;ssl=1 563w\" sizes=\"(max-width: 220px) 100vw, 220px\" data-recalc-dims=\"1\" \/><\/a>Since the seminal work of John Nash, convex combinations of actions are known to guarantee the existence of equilibria in strategic-form games. This paper introduces an alternative notion of randomisation among actions \u2013\u00a0<em>possibilistic randomisation<\/em>\u00a0\u2013 and investigates the mathematical consequences of doing so. The framework of possibility theory gives rise to two distinct notions of equilibria both of which are characterised in our main results: a qualitative one based on the Sugeno integral and a quantitative one based on the Choquet integral. Then the two notions of equilibrium are compared against a coordination game with payoff-distinguishable equilibria known as the Weak-link game.<\/p>\n<p>KEYWORDS:\u00a0Possibilistic randomisation; Mixed strategies; Possibilistic expected utility; Nash equilibria; Weak-link game; Selection of multiple equilibria<\/p><\/blockquote>\n<p>Hosni, H and E. Marchioni.\u00a0(2019). \u201c<em>Possibilistic randomisation in strategic-form games<\/em>\u201d <strong><i>Internatonal Journal of Approximate Reasoning,<\/i><\/strong>\u00a0114, 204-225.\u00a0<a href=\"https:\/\/doi.org\/10.1016\/j.ijar.2019.08.008\">\u00a0https:\/\/doi.org\/10.1016\/j.ijar.2019.08.008<\/a><\/p>\n<p><a href=\"https:\/\/sites.unimi.it\/hosni\/wp-content\/uploads\/2020\/05\/revision-possibilistic-equilibria-journal-FINAL.pdf\">Preprint<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Since the seminal work of John Nash, convex combinations of actions are known to guarantee the existence of equilibria in strategic-form games. This paper introduces an alternative notion of randomisation among actions \u2013\u00a0possibilistic randomisation\u00a0\u2013 and investigates the mathematical consequences of doing so. The framework of possibility theory gives rise to two distinct notions of equilibria&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[26,5],"tags":[],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7c8zZ-iF","_links":{"self":[{"href":"https:\/\/sites.unimi.it\/hosni\/wp-json\/wp\/v2\/posts\/1157"}],"collection":[{"href":"https:\/\/sites.unimi.it\/hosni\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.unimi.it\/hosni\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.unimi.it\/hosni\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.unimi.it\/hosni\/wp-json\/wp\/v2\/comments?post=1157"}],"version-history":[{"count":3,"href":"https:\/\/sites.unimi.it\/hosni\/wp-json\/wp\/v2\/posts\/1157\/revisions"}],"predecessor-version":[{"id":1162,"href":"https:\/\/sites.unimi.it\/hosni\/wp-json\/wp\/v2\/posts\/1157\/revisions\/1162"}],"wp:attachment":[{"href":"https:\/\/sites.unimi.it\/hosni\/wp-json\/wp\/v2\/media?parent=1157"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.unimi.it\/hosni\/wp-json\/wp\/v2\/categories?post=1157"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.unimi.it\/hosni\/wp-json\/wp\/v2\/tags?post=1157"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}