 The arguments of \(f\) are the elements \(a_1 ,\ldots ,a_m\) that player 1 has chosen so as to interpret the quantifiers \(\forall z_1 ,\ldots ,\forall z_m\). The value \(f(a_1 ,\ldots ,a_m)\) is the left or the right disjunct when the token is a disjunction; and an element of the domain when the token is an existential quantifier. 