Common knowledge

In the previous step we asked what would happen if Anna and Ben had inaccurate beliefs about each other’s knowledge.

We analysed the situation presented in the table below.

We assumed that:

• Ben knows what Anna’s preferences are
• Anna knows what Ben’s preferences are
• Ben believes (inaccurately) that Anna thinks he does not want to clean no matter the situation
• Anna believes (inaccurately) that Ben thinks she does not want to clean no matter the situation

As a result of the inaccurate beliefs neither Ben nor Anna clean the kitchen. Ben believes that Anna thinks that he does not want to clean. He knows that thinking that she prefers to clean. As a result Ben believes that Anna will clean and in this situation he prefers not to clean. The same reasoning applies to Anna. No player is cleaning and both are surprised that the other person does not clean.

Below we present a table where the outcome of the inaccurate beliefs is hatched. Look at the hatched arrows. They indicate that this outcome is not a good solution to the presented problem for anybody. The green hatched arrow says that given Ben’s choice Anna would rather clean. The blue hatched arrow says that given Anna’s choice Ben would rather clean.

Why is nobody happy? Because having inaccurate beliefs about each other’s knowledge they are solving a different problem from the one they are actually facing. While false beliefs are sometimes an issue in real life we do not want to start with situations this complex. We want to start by having Anna and Ben understand the problem as it really is. Common knowledge is an assumption that guarantees just that.

Common knowledge

Common knowledge is a type of knowledge that is shared in a group, when each member of the group knows some fact, and knows that all the members of the group know this fact, and knows that all the members of the group know that all the members of the group know this fact and so on ad infinitum. It might seem complex at the first sight but it is actually really easy to achieve.

For example, say there is some misdoing in a company and every employee knows about this, but each thinks they are the only person who unearthed the truth. One day in a meeting of all employees one person stands up and says out loud “There is some misdoing in this company”. This is how the misdoing becomes common knowledge. Not only everybody knows there is a misdoing. They also know that everybody knows that there is a misdoing, they know that everybody knows that everybody knows that there is a misdoing, and so on.

Meeting by Christina via unsplash

In the example with Anna and Ben the fact that everybody is aware of are the preferences of both players. We start by assuming that both Anna and Ben know them. This is equivalent to saying that each of them knows how the flow diagram for their game looks like. For the preferences to become common knowledge Anna and Ben could be shown the flow diagram in each other’s presence. When they see each other seeing the diagram they will understand instantly that they both get the same picture of the situation. This will enable them to stop guessing what the other person knows.

The concept of common knowledge is fundamental to many social problems. If you want to learn more on the topic there is a great entry in the Stanford Encyclopaedia of Philosophy that you might explore.