We develop a game theoretic model predictive controller (GTMPC) to deal with the mandatory lane change (MLC) problem for a subject vehicle (SV) in presence of multiple surrounding vehicles (SRV). The GTMPC uses game theory as a high-level controller, which regards at most three SRVs as the game theoretic candidate vehicles (GCV), with each playing a game with SV. The payoff of GCV is defined as the acceleration utility plus a convex combination of the space utility and safety utility, whose weights are associated with GCV's aggressiveness. Model predictive control (MPC) is utilized as a metric for SV's payoff in the game as well as a low-level controller that is responsible for both SV's longitudinal positioning and lane decision. GTMPC uses fuzzy Markov chain to generate the prediction of GCV's future motion, which is utilized in both defining GCV's payoffs over the prediction horizon in the game and as the reference of the MPC. Simulation showed the GTMPC was able to intelligently drive SV into the selected gap and accomplish the MLC in a dynamic situation without knowing the exact model of SRVs.