  We present a general way of defining various reduction games on \omega\ which
"represent" corresponding topologically defined classes of functions. In
particular, we will show how to construct games for piecewise defined
functions, for functions which are pointwise limit of certain sequences of
functions and for \Gamma-measurable functions. These games turn out to be
useful as a combinatorial tool for the study of general reducibilities for
subsets of the Baire space [10].
