Abstract. Probabilistic model checking for stochastic games enables formal verification of systems where competing or collaborating entities operate in a stochastic environment. While good progress has been made in the area, existing approaches focus on zero-sum goals and cannot reason about distinct entities collaborating whilst working to different objectives. In this paper, we propose probabilistic model checking techniques for concurrent stochastic games based on Nash equilibria. We extend the temporal logic rPATL (probabilistic alternating-time temporal logic with rewards) for reasoning about players with distinct quantitative goals which relate to either the probability of an event occurring or a reward measure. We present algorithms to synthesise strategies that are subgame perfect social welfare optimal Nash equilibria, i.e., where there is no incentive for any players to unilaterally change their strategy in any state of the game, whilst the combined probabilities or rewards are maximised. We implement our techniques in an extension of the PRISM-games tool and demonstrate their application to several case studies, including network protocols and robot navigation.