  It is well-known that in finite strategic games true common belief (or common
knowledge) of rationality implies that the players will choose only strategies
that survive the iterated elimination of strictly dominated strategies. We
establish a general theorem that deals with monotonic rationality notions and
arbitrary strategic games and allows to strengthen the above result to
arbitrary games, other rationality notions, and transfinite iterations of the
elimination process. We also clarify what conclusions one can draw for the
customary dominance notions that are not monotonic. The main tool is Tarski's
Fixpoint Theorem.
