  Definition 2.7 (Qualitative Type Space)  A Qualitative type space for a (nonempty) set of states of nature \(S\) and agents \(\Agt\) is a tuple \(\langle \{T_i\}_{i\in\A}, \{\lambda_i\}_{i\in\Agt},S\rangle\) where for each \(i\in\Agt\), \(T_i\) is a nonempty set and