In adversarial scenarios, it is crucial to timely monitor what tactical messages that opponent transmitters are sending to intended receiver(s), and disrupt the transmissions immediately if in need. The issue becomes more challenging in face of an intelligent transmitter. To address the above-stated issue, a full-duplex (FD) technique is utilized to enable simultaneous jamming and eavesdropping (SJE) at a friendly jammer node. In particular, the "Two Birds with One Stone" strategy is utilized at the jammer node to realize effective rate degradation and information eavesdropping. A confrontation game between an intelligence-empowered FD jammer and its opponent is investigated. Specifically, to capture their adversarial relationship in an environment with incomplete information, a power-domain Bayesian-Stackelberg game is proposed. The existence of a Stackelberg equilibrium (SE) power solution is proved. The semi-closed-form solutions of SE are derived, which are proved to be asymptotically optimal (have a gap of less than 1% with the exact utility), and improves the jammer node 10% utility compared with the Nash equilibrium. Additionally, the SJE strategy outperforms the half-duplex (HD) and other benchmark schemes.