50 Years of Aumann’s Agreement Theorem
One of the most popular posts in this blog’s history was Common Knowledge and Aumann’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’m proud to say, is that (according to Steven Pinker) it helped to inspire Steve’s excellent recent popular book, which you should read, entitled What Everyone Knows That Everyone Knows…: Common Knowledge and the Mysteries of Money, Power, and Everyday Life.
Two weeks ago, I was privileged to attend a workshop in Paris on “50 Years of Agreeing to Disagree,” where (among other things) I got to meet the 96-year-old Economics Nobel Laureate Robert Aumann for the first time.
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 The Complexity of Agreement, with New Directions and Applications (link goes to my PowerPoint slides).
Aran Nayebi has graciously posted on YouTube some partial video from the meeting, including his talk, brief snippets from my talk, and Aumann’s own remarks:
Meanwhile, here were the Aumannian insights that I remembered to write down:
AUDIENCE QUESTION: What questions did people ask you after you published your famous agreement theorem in 1976?
AUMANN: I don’t remember what happened yesterday, let alone 1976.
Also:
ME: I thought you might enjoy knowing that I just came here from a meeting of rationalists…
AUMANN: A meeting of who?
ME: Rationalists, they call themselves, at a beautiful venue called Lighthaven in Berkeley, and that they named the main building there “Aumann Hall” in your honor.
AUMANN: OK, so I’ve made it then.
One reccent result announced at the workshop, for those who care, is that the proof of Aumann’s Theorem has now been formalized in Lean, by Scott Kominers at Harvard and a group from the startup company Axiom Math.
Thanks so much to Christina Katt-Pawlowitsch, Ziv Hellman, and others for organizing the workshop and for including me in it.
Happy to field questions in the comments, although if someone wants to call me an idiot like usual, we’ll just need to agree to disagree!