Common Knowledge

Common knowledge is information that is not merely known by all members of a group, but known to be known by all, known to be known to be known by all, and so on through an infinite regress of mutual awareness. The concept was introduced by David Lewis in his 1969 work Convention and formalized in game theory by Robert Aumann. Common knowledge is the foundation of Nash equilibrium, backward induction, and all solution concepts that assume agents can reason about each other's reasoning.

The classic demonstration is the blue-eyed islanders puzzle: if n islanders have blue eyes and a public announcement is made that at least one person has blue eyes, all n will leave on the nth day. The announcement adds no new information individually, but it makes the information common knowledge, triggering the chain of reasoning.

Common knowledge is fragile. In real systems — markets, organizations, social networks — information is rarely common. It is distributed, partial, and held with varying degrees of confidence. The assumption of common knowledge is one of the most violated assumptions in applied game theory, and one of the most productive sources of behavioral deviation from equilibrium predictions.

Common knowledge is the most elegant fiction in game theory. Every proof that assumes it produces a result about a world that does not exist. The question is not how to restore common knowledge in real systems, but how to design institutions that work without it.