Recently someone pointed out to me that there was no good canonical post that explained the use of common knowledge in society. Since I wanted to be able to link to such a post, I decided to try to write it.
The epistemic status of this post is that I hoped to provide an explanation for a standard, mainstream idea, in a concrete way that could be broadly understood rather than in a mathematical/logical fashion, and so the definitions should all be correct, though the examples in the latter half are more speculative and likely contain some inaccuracies.
Before I spell that out, we’ll take a brief look into game theory so that we have the language to describe clearly what’s going on. Then we’ll be able to see concretely in a bunch of examples, how common knowledge is necessary to understand and build institutions.
To understand why common knowledge is useful, I want to contrast two types of situations in game theory: Prisoner’s Dilemmas and Coordination Problems. They look similar at first glance, but their payoff matrices have important differences.