50 years of “Agreeing to Disagree”

Herakles Polemarchakis
Warwick University, Economics, UK
 

Half a century after its publication, 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. This result builds on a conceptual innovation that is as powerful as elegant: identifying what is commonly known between the participants in an exchange with the meet—the finest common coarsening—of the information partitions.

The agreement result and the formal language for modeling knowledge and beliefs introduced by Aumann have inspired research in multiple directions, such as:

• dynamic foundations of the Agreement Theorem through Bayesian dialogues and applications to betting and trading scenarios;

• generalizations and extensions of the formal framework, such as moving from finite partitions to σ-algebras and from knowledge of events to knowledge of random variables;

• axiomatizations of knowledge and belief in terms of modal knowledge operators;

• relaxations of common knowledge through notions of “almost” common knowledge and common belief;

• applications to distributed computing systems and classical agreement problems in computer science, such as “coordinated attack” and simultaneous Byzantine agreement;

• relaxations of the common prior hypothesis addressing the robustness of the Agreement Theorem.

With this special issue, we mark the fiftieth anniversary of the publication of “Agreeing to Disagree.” We aim in particular to highlight the productivity of the theory for stimulating new research and providing insights into contemporary problems.

Besides original contributions to any of the research programs mentioned above, we invite:

• critical methodological or historical assessments of the Agreement Theorem, or more generally, the concept of common knowledge and models of interactive knowledge and belief revision;

• comparisons to similar accounts in other fields, such as philosophy and linguistics;

• novel applications of the Agreement Theorem to problems in economics, computer science, political science, philosophy, linguistics, sociology, psychology, or any other field.

Submissions: Through editorial system of Games and Economic Behavior by mentioning “Special Issue ‘50 Years of Agreeing to Disagree’” in the cover letter.

Due date: December 30, 2026.