This paper explores ways of expanding the logical and linguistic theory kno
wn as game-theoretic semantics (GTS) to cover some new linguistic categorie
s and expressions. I will show the applicability and relevance of GTS to a
cross-sample of linguistic categories, ranging from polarity items (many of
which are lexical), the morpheme even, and adverbs of quantification, to t
he realm of generalised quantifiers. I will also suggest how eventualities
can be dealt with in a game-theoretic way. I argue that in each of the case
s, GTS provides a theoretically motivated methodological foundation in its
treatment of these constructions, and its potentials are evident in many ot
her linguistic categories as well, seen from the cross-categorial phenomeno
n of informational independence, which in this paper is illustrated in term
s of eventualities.