A (global) state, or possible world is a tuple \((t_1,t_2,\ldots,t_n,s)\) where \(t_i\in T_i\) for each \(i=1,\ldots,n\) and \(s\in S\). If \(S=\bigtimes S_i\) is the set of strategy profiles for some game, then we write a possible world as: \((t_1,s_1,t_2,s_2,\ldots,t_n,s_n)\) where \(s_i\in S_i\) for each \(i=1,\ldots,n\).