Public Information Generators: Common Knowledge and Information Loops

Abstract

We analyze incomplete-information games where an oracle publicly shares information with privately informed players. One oracle dominates another if, for every experiment of the latter, it can choose an experiment that supports, in every game, every equilibrium outcome distribution induced by the other. We fully characterize equivalence (mutual dominance) and identify the information-loop obstruction governing one-sided dominance, obtaining necessity in general and sufficiency under separated-loop structures. The analysis highlights the role of common-knowledge components and develops a theory of information loops, thereby extending the seminal work of Blackwell (1951) to strategic environments and Aumann (1976)'s theory of common knowledge.