The mutual dependence between autonomous vehicles and human drivers is an open problem for the safety and feasibility of autonomous driving. This paper introduces a game-theoretic trajectory planner and decision-maker for mixed-traffic environments. Our solution accounts for interaction withthe surrounding vehicles while making decisions, and uses a clothoid interpolation method to generate human-like trajectories. The Particle Swarm Optimizer (PSO) used here bridges the decision-making and the trajectory generating processes for a joined execution. We chose an unsignalized intersection crossing scenarios to demonstrate the feasibility of our method. Testing results show that our approach reduces the dimension of the search space for the trajectory optimization problem and enforces geometric constraints on path curvature