 A state in a type structure is a tuple \((\sigma, t)\) where \(\sigma\) is a strategy profile and \(t\) is “type profile”, a tuple of types, one for each player. Let \(B_i(E) = \{(\sigma_{-j}, t_{-j}) : t_i \text{ believes that } E \}\) be the event (for \(j\)) that \(i\) believes that \(E\). Then agent \(j\) believes that \(i\) believes that \(E\) when \(\lambda_j(t_j)(B_i(E)) = 1\). We can continue in this manner computing any (finite) level of such higher-order information.