This paper studies the problem of robust Stackelberg game-based low probability of intercept (LPI) performance optimization for multistatic radar system. Recognizing that the precise knowledge of path propagation loss coefficients is not exactly known, these parameters are assumed to lie in uncertainty sets bounded by known upper and lower bounds. The strategy aims to minimize the worst-case radiated power of multistatic radar by optimizing power allocation with uncertain path propagation loss coefficients, subject to a desired signal-to-interference-plus-noise ratio (SINR) requirement for target detection and several resource constraints. We formulate this optimization process as a robust hierarchical Stackelberg game, where the fusion center of the multistatic radar acts as a leader, and the multiple radars play the role of followers. The robust Nash bargaining solution (RNBS) solution for the formulated game is derived. Then, the existence and uniqueness of the RNBS are strictly proved. Moreover, a distributed iterative approach is developed to solve the resulting problem. Finally, simulation results demonstrate the effectiveness of the proposed strategy.