We study automated intrusion response and formulate the interaction between an attacker and a defender as an optimal stopping game where attack and defense strategies evolve through reinforcement learning and self-play. The game-theoretic modeling enables us to find defender strategies that are effective against a dynamic attacker, i.e., an attacker that adapts its strategy in response to the defender strategy. Further, the optimal stopping formulation allows us to prove that best response strategies have threshold properties. To obtain near-optimal defender strategies, we develop Threshold Fictitious Self-Play (T-FP), a fictitious self-play algorithm that learns Nash equilibria through stochastic approximation. We show that T-FP outperforms a state-of-the-art algorithm for our use case. The experimental part of this investigation includes two systems: a simulation system where defender strategies are incrementally learned and an emulation system where statistics are collected that drive simulation runs and where learned strategies are evaluated. We argue that this approach can produce effective defender strategies for a practical IT infrastructure.