The parameter \(X\) in the above definitions is intended to represent the set of strategy profiles that the player \(i\) take to be “live possibilities”. Each state in an epistemic (-plausibility) model is associated with a such a set of strategy profiles. Given a possible world \(w\) in a game model, let \(S_{-i}(w)\) denote the set of states that player \(i\) “thinks” are possible. The precise definition depends on the type of game model: