The interaction between vehicles or with human agents is a fundamental problem for planning and control. Game theory is the most useful tool for making decisions in such situations. In this project, a motion planning algorithm based on game theory is presented. First, candidate paths are generated for ego car and opponent using a conformal lattice planner, and then the utility of each path is calculated for ego and opponent, and a path is selected using Nash equilibrium. Finally, using two longitudinal and lateral PID controllers, the car is controlled in the selected path. We defined a race between two vehicles in the CARLA simulator, the results of which indicate the proper performance of the motion planner.