Parked vehicle assisted edge computing is a paradigm to employ parked vehicles for processing workloads in vehicular networks. They collaborate with edge servers for joint task execution within task deadline and parking durations. We study task assignment problem with Stackelberg game, where the overall cost of a task publisher in terms of monetary cost and subjective dissatisfaction caused by un-offloaded workloads is minimized. To reach Stackelberg equilibrium, a dedicated algorithm is performed among players in a distributed manner for privacy preservation. Numerical results indicate that the cost is decreased about 25% in our scheme compared to that in existing work.