Given a state \(w\in W\), the cell \(\Pi_i(w)\) is called agent \(i\)’s information set. Following standard terminology, if \(\Pi_i(w)\subseteq E\), we say the agent \(i\) knows the event \(E\) at state \(w\). Given an event \(E\), the event that agent \(i\) knows \(E\) is denoted \(K_i(E)\). Formally, we define for each agent \(i\) a knowledge function assigning to every event \(E\) the event that the agent \(i\) knows \(E\):