Reactive jamming, which performs jamming attacks on condition of detecting the legitimate transmissions, is widely considered as one of the most serious security challenges in wireless communications. In this paper, we tackle the reactive jamming issue from a novel yet realistic perspective -the jammer may not always be able to accurately detect the legitimate transmissions, which in turn, can be exploited by the legitimate user to enhance security. In accordance with the detection-then-jamming characteristic of reactive jamming, we formulate the transmitting-jamming problem within a Stackelberg game framework, where the legitimate user takes action first, followed by the reactive jammer. To optimize its own utility, the legitimate user needs to determine the transmission strategy by elaborately achieving the tradeoff between the signalto-interference-plus-noise ratio (SINR) and the probability to be accurately detected and thus jammed by its adversary. The investigation on Stackelberg equilibrium provides the solution to the game model. Furthermore, we consider the more practical situation that the legitimate user has only incomplete knowledge regarding its adversary and analyze the corresponding impact on the game and equilibrium. Simulation results demonstrate significant performance superiority in terms of secure legitimate transmissions compared with the classical approach.