  We introduce a new game-theoretic semantics (GTS) for the modal mu-calculus.
Our so-called bounded GTS replaces parity games with alternative evaluation
games where only finite paths arise; infinite paths are not needed even when
the considered transition system is infinite. The novel games offer alternative
approaches to various constructions in the framework of the mu-calculus. For
example, they have already been successfully used as a basis for an approach
leading to a natural formula size game for the logic. While our main focus is
introducing the new GTS, we also consider some applications to demonstrate its
uses. For example, we consider a natural model transformation procedure that
reduces model checking games to checking a single, fixed formula in the
constructed models, and we also use the GTS to identify new alternative
variants of the mu-calculus with PTime model checking.
