  Various extensions of the temporal logic ATL have recently been introduced to
express rich properties of multi-agent systems. Among these, ATLsc extends ATL
with strategy contexts, while Strategy Logic has first-order quantification
over strategies. There is a price to pay for the rich expressiveness of these
logics: model-checking is non-elementary, and satisfiability is undecidable.
  We prove in this paper that satisfiability is decidable in several special
cases. The most important one is when restricting to turn-based games. We prove
that decidability also holds for concurrent games if the number of moves
available to the agents is bounded. Finally, we prove that restricting strategy
quantification to memoryless strategies brings back undecidability.
