Negotiations among drivers and pedestrians are common on roads, but it is still challenging for a self-driving vehicle to negotiate for its right of way with other human road users, especially pedestrians. Currently, the self-driving vehicles are programmed for conservative behavior, yielding to approaching pedestrians. Consequently, the future urban traffic will slow down significantly. In this paper, a conceptual model of vehicle-pedestrian negotiation is proposed. This model allows individual decision making of multiple vehicles and pedestrians, extending a prior negotiation model for a single vehicle and a single pedestrian. The possible negotiation opportunities for vehicles are modeled considering different risk-taking behaviors of pedestrians. Simulation results show an overall improvement in the waiting time of vehicles and thus in the intersection throughput, compared to conservative vehicle behavior. The simulation results show also that the benefit of reduced waiting times for vehicles comes at the cost of some waiting time for pedestrians. However, the observed pedestrian waiting times in this model are not more than the generally accepted waiting times reported in empirical studies.