Speaker: Eric Pacuit (University of Maryland)
Date and time: Thursday, September 4th 2025, 16:30-18:00
Venue: online
Title: Agreement Under Common p-Belief: Beyond Partitions and Probabilities.
Abstract. Aumann’s famous Agreeing to Disagree Theorem states that if a group of agents share a common prior, update their beliefs by Bayesian conditioning based on private information (represented by partitions), and have common knowledge of their posterior beliefs regarding some event, these posteriors must be identical. There is an elegant generalization of this theorem by Monderer and Samet (1989), later refined by Neeman (1996): if a group of agents share a common prior, update their beliefs using Bayesian conditioning on private information (represented by partitions), and have common p-belief of their posteriors, these posteriors must be close (i.e., they cannot differ by more than 1-p). Here, common p-belief generalizes the concept of common knowledge to probabilistic beliefs. This talk will discuss recent work that generalizes the Monderer-Samet-Neeman theorem in two directions. The first generalization drops the partitionality assumption, allowing for non-partitional representation of information. The second generalization goes beyond probabilistic models of beliefs to consider more general models of beliefs, such as Dempster-Shafer belief functions.
This is joint work with Leo Yang.