In this paper, we study the optimization of joint transmit and receive beamforming design for multiple-input-multiple-output radar systems in the presence of a smart target. The problem is framed as a Stackelberg game, with the radar acting as the leader and the target as the follower. The radar aims to minimize transmit power and interference to a communication base while guaranteeing the desired signal-to-interference-plus-noise ratio (SINR) performance for target tracking. Conversely, the target aims to minimize the radar’s SINR. We derive the best response (BR) strategy of the target and design an iterative algorithm to obtain the radar’s strategy based on the BR. Moreover, we explore the radar’s BR in the absence of the target’s BR. Finally, we provide numerical results to show the effectiveness of the proposed algorithms.