Common Knowledge in Game Theory

When something is known to all and everybody knows that it is known to all, everybody knows that everybody knows that it is known to all and so on ad infinitum, this thing is said to be common knowledge. Aumann [1976] was the first to provide a formal characterization of the notion of common knowledge in his celebrated article "Agreeing to Disagree." This formalism has raised a number of exciting questions. Can commonly known individual differences in actions or beliefs be explained by asymmetric information? Do players need some sort of common knowledge to coordinate on some action profile? Can a group of individuals achieve common knowledge by communicating with each other? The purpose of this article is to review the work that has attempted to answer these questions.