  We provide an epistemic analysis of arbitrary strategic games based on
possibility correspondences. We first establish a generic result that links
true common beliefs (and, respectively, common knowledge) of players'
rationality defined by means of `monotonic' properties, with the iterated
elimination of strategies that do not satisfy these properties. It allows us to
deduce the customary results concerned with true common beliefs of rationality
and iterated elimination of strictly dominated strategies as simple
corollaries. This approach relies on Tarski's Fixpoint Theorem. We also provide
an axiomatic presentation of this generic result. This allows us to clarify the
proof-theoretic principles assumed in players' reasoning. Finally, we provide
an alternative characterization of the iterated elimination of strategies based
on the concept of a public announcement. It applies to `global properties'.
Both classes of properties include the notions of rationalizability and the
iterated elimination of strictly dominated strategies.
