In this paper, the problem of Stackelberg game-theoretic low probability of intercept (LPI) performance optimization in multistatic radar system is investigated. The goal of the proposed LPI optimization strategy is to minimize the transmitted power of each radar while satisfying a predetermined signal-to-interference-plus-noise ratio (SINR) requirement for target detection. Firstly, a single-leader multi-follower Stackelberg game is adopted to formulate the LPI optimization problem of multistatic radar system. In the considered game model, the hostile intercept receiver plays a role of leader, who decides the prices of power resource first through the maximization of its own utility function. The multiple radars are followers to compete with each other in a non-cooperative game according to the imposed prices from the intercept receiver subsequently. Then, the Nash equilibrium (NE) for the considered game model is derived, and the existence and uniqueness of the NE are analytically proved. Furthermore, a pricing-based distributed iterative power control algorithm is proposed. Finally, some simulation examples are provided to demonstrate that the proposed scheme has remarkable potential to enhance the LPI performance of the multistatic radar system.