In this paper, we propose a novel behavior planner that combines game theory with search-based planning for automated lane merging. Specifically, inspired by human drivers, we model the interaction between vehicles as a gap selection process. To overcome the challenge of multi-modal behavior exhibited by the surrounding vehicles, we formulate the trajectory selection as a matrix game and compute an equilibrium. Next, we validate our proposed planner in the high-fidelity simulator CARLA and demonstrate its effectiveness in handling interactions in dense traffic scenarios.