Scanning large amounts of bandwidth for anomalous signals is a fundamental tool to building secure spectrum sharing system. When designing a bandwidth scanning algorithm, the system engineer faces several problems: which band to scan, how long to scan the band, and how to detect whether a malicious adversary is present. It is often not possible to conclusively detect an adversary's presence during a single scan, and therefore the anomaly detection procedure needs to run continuously. For a spectrum scanning system that runs continuously, it is possible to tune the algorithm to better detect the presence of a malicious threat by adapting one's belief as to whether the adversary is present, particularly if the previous scanning attempt failed to detect an adversary in the previous time slot. In this paper, by means of a game theoretical model, we demonstrate some approaches to solve these scanning problems. The equilibrium strategies in the suggested models are obtained explicitly, and thereby allows for interesting properties associated with the problems and related scanning algorithms to be established.