The Game Description Language (GDL) is a special purpose declarative language for defining games. GDL is used in the AAAI General Game Playing Competition, which tests the ability of computer programs to play games in general, rather than just the ability to play a specific game. Participants in the competition are provided with a previously unknown game specified in GDL, and are required to dynamically and autonomously determine how best to play this game. Recently, there has been much interest in the use of strategic cooperation logics for reasoning about game-like scenarios—the Alternating-time Temporal Logic (ATL) of Alur, Henzinger, and Kupferman is perhaps the best known example. Such logics are specifically intended to support reasoning about game-theoretic properties of multi-agent systems. In short, the aim of this article is to make a concrete link between ATL and GDL, with the ultimate goal of using ATL to reason about GDL-specified games. We make the following contributions. First, we demonstrate that GDL can be understood as a specification language for ATL models, and prove that the problem of interpreting ATL formulae over propositional GDL descriptions is EXPTIME-complete. Second, we use ATL to characterize a class of ‘fair playability’ conditions, which might or might not hold of various games.