{"id":9875,"date":"2026-06-28T09:56:56","date_gmt":"2026-06-28T14:56:56","guid":{"rendered":"https:\/\/scottaaronson.blog\/?p=9875"},"modified":"2026-06-29T11:04:15","modified_gmt":"2026-06-29T16:04:15","slug":"50-years-of-aumanns-agreement-theorem","status":"publish","type":"post","link":"https:\/\/scottaaronson.blog\/?p=9875","title":{"rendered":"50 Years of Aumann&#8217;s Agreement Theorem"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">One of the most popular posts in this blog&#8217;s history was <a href=\"https:\/\/scottaaronson.blog\/?p=2410\">Common Knowledge and Aumann&#8217;s Agreement Theorem<\/a>, based on a lecture that I gave to high-school students 11 years ago.  One of the impacts of that post, I&#8217;m proud to say, is that (according to Steven Pinker) it helped to inspire Steve&#8217;s excellent recent popular book, which you should read, entitled <a href=\"https:\/\/www.amazon.com\/When-Everyone-Knows-That-Knowledge\/dp\/1668011573\"><em>What Everyone Knows That Everyone Knows&#8230;: Common Knowledge and the Mysteries of Money, Power, and Everyday Life<\/em><\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Two weeks ago, I was privileged to attend a workshop in Paris on &#8220;50 Years of Agreeing to Disagree,&#8221; where (among other things) I got to meet the 96-year-old Economics Nobel Laureate <a href=\"https:\/\/en.wikipedia.org\/wiki\/Robert_Aumann\">Robert Aumann<\/a> for the first time.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/scottaaronson.blog\/wp-content\/uploads\/2026\/06\/aumann.jpeg\"><img loading=\"lazy\" decoding=\"async\" width=\"768\" height=\"1024\" src=\"https:\/\/scottaaronson.blog\/wp-content\/uploads\/2026\/06\/aumann-768x1024.jpeg\" alt=\"\" class=\"wp-image-9876\" srcset=\"https:\/\/scottaaronson.blog\/wp-content\/uploads\/2026\/06\/aumann-768x1025.jpeg 768w, https:\/\/scottaaronson.blog\/wp-content\/uploads\/2026\/06\/aumann-225x300.jpeg 225w, https:\/\/scottaaronson.blog\/wp-content\/uploads\/2026\/06\/aumann.jpeg 1024w\" sizes=\"auto, (max-width: 768px) 100vw, 768px\" \/><\/a><figcaption class=\"wp-element-caption\">Me and my friend <a href=\"https:\/\/anayebi.github.io\/\">Aran Nayebi<\/a> (CS professor at CMU) with Robert Aumann<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">I got to catch up there with Steven Pinker as well, who gave a phenomenal talk on the psychology of common knowledge.  My own talk was entitled <a href=\"https:\/\/www.scottaaronson.com\/talks\/agree-paris.pptx\">The Complexity of Agreement, with New Directions and Applications<\/a> (link goes to my PowerPoint slides).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aran Nayebi has graciously <a href=\"https:\/\/www.youtube.com\/watch?v=WD_OQbNzml4\">posted on YouTube<\/a> some partial video from the meeting, including his talk, brief snippets from my talk, and Aumann&#8217;s own remarks:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<span class=\"embed-youtube\" style=\"text-align:center; display: block;\"><iframe loading=\"lazy\" class=\"youtube-player\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/WD_OQbNzml4?version=3&#038;rel=1&#038;showsearch=0&#038;showinfo=1&#038;iv_load_policy=1&#038;fs=1&#038;hl=en-US&#038;autohide=2&#038;wmode=transparent\" allowfullscreen=\"true\" style=\"border:0;\" sandbox=\"allow-scripts allow-same-origin allow-popups allow-presentation allow-popups-to-escape-sandbox\"><\/iframe><\/span>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Meanwhile, here were the Aumannian insights that I remembered to write down:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">AUDIENCE QUESTION: What questions did people ask you after you published your famous agreement theorem in 1976?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">AUMANN: I don\u2019t remember what happened yesterday, let alone 1976.<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">Also:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\">ME: I thought you might enjoy knowing that I just came here from a meeting of rationalists\u2026<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">AUMANN: A meeting of who?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">ME: Rationalists, they call themselves, at a beautiful venue called Lighthaven in Berkeley, and that they named the main building there <a href=\"https:\/\/www.tagvenue.com\/us\/rooms\/berkeley\/107899\/lighthaven\/aumann-hall\">\u201cAumann Hall\u201d<\/a> in your honor.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">AUMANN: OK, so I\u2019ve made it then.<\/p>\n<\/blockquote>\n\n\n\n<p class=\"wp-block-paragraph\">One recent result announced at the workshop, for those who care, is that the proof of Aumann&#8217;s Theorem has now been <a href=\"https:\/\/papers.ssrn.com\/sol3\/papers.cfm?abstract_id=6837298\">formalized in Lean<\/a>, by Scott Kominers at Harvard and a group from the startup company Axiom Math.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thanks so much to Christina Katt-Pawlowitsch, Ziv Hellman, and others for organizing the workshop and for including me in it.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Happy to field questions in the comments, although if someone wants to call me an idiot like usual, we&#8217;ll just need to agree to disagree!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>One of the most popular posts in this blog&#8217;s history was Common Knowledge and Aumann&#8217;s Agreement Theorem, based on a lecture that I gave to high-school students 11 years ago. One of the impacts of that post, I&#8217;m proud to say, is that (according to Steven Pinker) it helped to inspire Steve&#8217;s excellent recent popular [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_seo_schema_type":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"{title}\n\n{excerpt}\n\n{url}","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[10,5],"tags":[],"class_list":["post-9875","post","type-post","status-publish","format-standard","hentry","category-adventures-in-meatspace","category-complexity"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/9875","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9875"}],"version-history":[{"count":4,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/9875\/revisions"}],"predecessor-version":[{"id":9893,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/9875\/revisions\/9893"}],"wp:attachment":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9875"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9875"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9875"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}