 A strategy of player 2 in game \(G(\phi , M, g)\) is a set \(F\) of her strategy functions, one function for each token of \((\vee /\forall y_1 ,\ldots ,\forall y_n)\) and \((\exists x/\forall y_1 ,\ldots ,\forall y_n)\) appearing in \(\phi\). Player 2 is said to follow the strategy \(F\), if for each token of \((\vee /\forall y_1 ,\ldots ,\forall y_n)\) and \((\exists x/\forall y_1 ,\ldots ,\forall y_n)\) for which she must make a move when game \(G(\phi , M, g)\) is played, she makes the move determined by the corresponding strategy function. A winning strategy for player 2 in \(G(\phi , M, g)\) is a strategy \(F\) such that against any sequence of moves by player 1, following strategy \(F\) yields a win for player 2. The notions of strategy and winning strategy can be similarly defined for player  1.[21]