we need to represent the players’ knowledge in a possibility structure where the \(K_i\) operators do not necessarily satisfy negative introspection. A possibility structure is a tuple \(\langle W, \{P_i\}_{i\in\A}, \sigma\rangle\) where \(P_i:W\rightarrow \pow(W)\). The only difference with an epistemic model is that the \(P_i(w)\) do not necessarily form a partition of \(W\). We do not go into details here—see Halpern (1999) for a complete discussion of possibility structures and how they relate to epistemic models. The knowledge operator is defined as it is for epistemic models: for each event \(E\), \(K_i(E)=\{w \mid P_i(w)\subseteq E\}\). However, S. Modica and A. Rustichini (1994, 1999) argue that even the more general possibility structures cannot be used to describe a player’s unawareness.