Modern cyberattacks such as advanced persistent threats have become sophisticated. Hackers can stay undetected for an extended time and defenders do not have sufficient countermeasures to prevent advanced cyberattacks. Reflecting on this phenomenon, we propose a game-theoretic model to analyze strategic decisions made by a hacker and a defender in equilibrium. In our game model, the hacker launches stealthy cyberattacks for a long time and the defender decides when to disable a suspicious user based on noisy observations of the user’s activities. Damages caused by the hacker can be enormous if the defender does not immediately ban a suspicious user under certain circumstances, which can explain the emerging sophisticated cyberattacks with detrimental consequences. Our model also predicts that the hacker may opt to be behavioral to avoid worst cases. This is because behavioral cyberattacks are less threatening and the defender decides not to immediately block a suspicious user to reduce cost of false detection.