Stochastic game logic (SGL) is a new temporal logic that combines features of alternating temporal logic (to formalize the individual views and cooperation and reaction facilities of agents in a multiplayer game), probabilistic computation tree logic and extended temporal logic (to reason about qualitative and quantitative, linear or branching time winning objectives). The paper presents the syntax and semantics of SGL and discusses its model checking problem. The model checking problem of SGL turns out to be undecidable when the strategies are history-dependent. We show PSPACE completeness for memoryless deterministic strategies and the EXPSPACE upper bound for memoryless randomized strategies. For the qualitative fragment of SGL we show PSPACE completeness for memoryless strategies.