Common Knowledge in Interaction Structures

TL;DR

This paper explores how common knowledge in communication networks affects group reasoning, focusing on hypergraph structures and conditions for distributing common knowledge over disjunctions, with implications for understanding communication limitations.

Contribution

It introduces two variants of a framework for analyzing knowledge in communication groups, clarifies epistemic issues, and extends classic results on the impossibility of common knowledge without simultaneous events.

Findings

Common knowledge's dependence on hypergraph structure.

Conditions under which common knowledge distributes over disjunction.

Classic result that common knowledge requires a simultaneous event.

Abstract

We consider two simple variants of a framework for reasoning about knowledge amongst communicating groups of players. Our goal is to clarify the resulting epistemic issues. In particular, we investigate what is the impact of common knowledge of the underlying hypergraph connecting the players, and under what conditions common knowledge distributes over disjunction. We also obtain two versions of the classic result that common knowledge cannot be achieved in the absence of a simultaneous event (here a message sent to the whole group).