4th Paris Workshop

on Game Theory and Language

Half a Century of “Agreeing to Disagree”

June 11-12, 2026

Half a century after its publication, Robert Aumann’s Agreement Theorem (“Agreeing to Disagree”, The Annals of Statistics, 1976) has not ceased to intrigue and inspire.

The Agreement Theorem states that if two individuals assign the same prior probability over the set of possible states of the world and if — thanks to the common knowledge of their information partitions — the posterior probabilities they attribute to an event are common knowledge, then these posterior probabilities must be identical.

Aumann’s result builds on a conceptual innovation that is as powerful as elegant: identifying what is commonly known between the participants of an exchange with the meet — the finest common coarsening — of the information partitions.

The agreement result and the formal language of modeling knowledge and beliefs introduced by Aumann have generated research in multiple directions:

• dynamic foundations in the form of Bayesian dialogues and applications of these to betting and trading scenarios (Bacharach 1979, Geanakoplos and Polemarchakis 1982, Milgrom and Stokey 1982, Sebenius and Geanakoplos 1983),
• generalizations of the result moving from partitions to σ-algebras and from knowledge of an event to knowledge of random variables (for instance, Nielsen 1984)
• notions of “almost” common knowledge (Halpern 1986, Rubinstein 1989, Halpern and Moses 1990, Fagin et al. 1995) and approximate common knowledge in the form of common belief (Geanakoplos 1994, Morris 1999, Monderer and Samet 1989),
• relaxations of the common prior hypothesis (Di Tillio, Lehrer, and Samet 2022, Gizatulina and Hellman 2019, Hellman and Pintér 2022).

With this workshop, we honor the fiftieth anniversary of the publication of “Agreeing to Disagree.”

More information and program on the Workshop’s website.