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

The Role of Monotonicity in the Epistemic Analysis of Strategic Games