Preserving the availability and integrity of networked computing systems in the face of fast-spreading intrusions requires advances not only in detection algorithms, but also in automated response techniques. In this paper, we propose a new approach to automated response called the Response and Recovery Engine (RRE). Our engine employs a game-theoretic response strategy against adversaries modeled as opponents in a two-player Stackelberg stochastic game. RRE applies attack-response trees to analyze undesired security events and their countermeasures using Boolean logic to combine lower-level attack consequences. In addition, RRE accounts for uncertainties in intrusion detection alert notifications. RRE then chooses optimal response actions by solving a partially observable competitive Markov decision process that is automatically derived from attack-response trees. Experimental results show that RRE, using Snort's alerts, can protect large networks for which attack-response trees have more than 900 nodes.