  We introduce versions of game-theoretic semantics (GTS) for Alternating-Time
Temporal Logic (ATL). In GTS, truth is defined in terms of existence of a
winning strategy in a semantic evaluation game, and thus the game-theoretic
perspective appears in the framework of ATL on two semantic levels: on the
object level in the standard semantics of the strategic operators, and on the
meta-level where game-theoretic logical semantics is applied to ATL. We unify
these two perspectives into semantic evaluation games specially designed for
ATL. The game-theoretic perspective enables us to identify new variants of the
semantics of ATL based on limiting the time resources available to the verifier
and falsifier in the semantic evaluation game. We introduce and analyse an
unbounded and (ordinal) bounded GTS and prove these to be equivalent to the
standard (Tarski-style) compositional semantics. We show that in these both
versions of GTS, truth of ATL formulae can always be determined in finite time,
i.e., without constructing infinite paths. We also introduce a non-equivalent
finitely bounded semantics and argue that it is natural from both logical and
game-theoretic perspectives.
