The aim of the present document is to provide a relatively general definition of the notion of game in set-theoretic form, from the vantage viewpoint of structuralistic philosophy of science, in consonance with the state of the art in the foundations of probability theory. I leave out of consideration, however, games of infinite length as well as games with an infinite number of players. More than trying to reach the proof of a particular theorem (like, say, Kuhn's theorem on optimal behavior strategies), the aim of the document is to show the explicit logical structure of the theory. Its unifying power could be tested afterwards in terms of its yielding a criterion to distinguish the most general theorems from those that are relative to specializations of the theory.