Abstract

Aumann’s agreeing to disagree theorem is a central theorem of game theory. This result says that if two agents have a common prior, then they cannot agree (have common knowledge of their posteriors) to disagree (while these posteriors are not identical). This thesis looks at the agreeing to disagree theorem from the perspective of probabilistic dynamic epistemic logic. The first goal of the thesis is to establish a new connection between game theory and epistemic logic. We prove (local model-based versions and global frame-based versions of) several semantic agreement theorems, and show that these are natural formalizations of Aumann’s original result. We also provide axiomatizations of (dynamic) agreement logics, in which the first of these agreement theorems can be derived syntactically. The second goal is the further technical development of probabilistic dynamic epistemic logic. We mention three examples. First, to model the experiment dynamics, we enrich the probabilistic Kripke models with ‘experiment relations’, thus establishing a link with the dynamic epistemic logic of questions. Second,

Citations