 As in the case of first-order logic and independence-friendly logic, in the imperfect-information game for dependence logic the positions of the game are pairs \((\theta, s)\), where \(\theta\) is an instance of a subformula of \(\phi\) (that is, multiple occurrences of the same expression as a subformula of \(\phi\) are to be considered separately) and \(s\) is a variable assignment over the model  \(M\).[1]  The initial position is \((\phi, \emptyset)\), where \(\emptyset\) is the empty assignment; and a non-deterministic strategy \(\sigma_0\) for Player \(0\) selects, for every disjunction and existential quantification, one or more successors of the current position according to the following rules: