Epistemic models represent the informational context of a given game in terms of possible configurations of states of the game and the hard information that the agents have about them. The function \(\sigma\) assigns to each possible world a unique state of the game in which every ground fact is either true or false. If \(\sigma(w) = \sigma(w')\) then the two worlds \(w,w'\) will agree on all the ground facts (i.e., what actions the players will choose) but, crucially, the agents may have different information in them. So, elements of \(W\) are richer, than the elements of \(S\) (more on this below).