In this article, we develop a game theoretic model predictive controller (GTMPC) with aggressiveness estimation to deal with the mandatory lane change (MLC) problem in presence of several surrounding vehicles. GTMPC is responsible for driving a subject vehicle (SV) to a desired longitudinal position and executing lane-changing at the optimal moment. Specifically, GTMPC constantly establishes and solves Stackelberg games corresponding to multiple game candidate vehicles (GCV) within the game scope when SV is able to interact with GCVs by signaling a lane change intention through turn signal. GTMPC first selects one target vehicle (TV) within multiple GCVs based on the Stackelberg equilibrium, followed by estimating TV's aggressiveness based on the interaction between SV and TV, then completes the maneuver through MPC. GTMPC performance is compared with level-k game theoretic controller. Human-in-the-Loop results showed that GTMPC is capable to safely complete the MLC by properly assessing the aggressiveness of surrounding vehicles, driven either by intelligent driver model or human drivers.