With the emergence of physical layer security, there has been an increasing interest toward its framework comprising a wiretap channel with a transmitter, a receiver, and an eavesdropper. In this paper, the eavesdropper operates in a full-duplex mode so as to reduce the secrecy rate of the transmitter-receiver pair through simultaneous wiretapping and jamming. On the other hand, the transmitter-receiver pair aims to increase its achievable secrecy rate. To examine the power decision processes between the transmitter and the eavesdropper, a two-player noncooperative game is proposed. We first provide sufficient conditions for the existence of the pure-strategy Nash equilibrium (NE), and then derive the closed-form NEs for two special cases, i.e., the eavesdropper close to and far away from the receiver. For discrete approximation of the game, we utilize a fictitious play-based algorithm to achieve the mixed-strategy NE. Based on the equilibrium, a switch policy is provided for the eavesdropper to determine its optimal mode between the full-duplex and half-duplex, depending on the self-interference and location. Numerical results show that this switch policy improves the monitoring performance in terms of utility, which is the linear combination of the secrecy rate and the power consumption.