The advent of autonomous vehicles heralds a new era in traffic management, presenting unprecedented opportunities and complex challenges. This paper aims to develop automated negotiation mechanisms for autonomous vehicles that navigate intersections without traditional traffic signals. We introduce a goal-oriented negotiation protocol grounded in the utilization of curvilinear coordinates. This approach is complemented by introducing a decision-making algorithm and a counteroffer algorithm for vehicles, both of which play pivotal roles in the negotiation protocol. Moreover, we provide evidence of the protocol’s convergence and elucidate the time complexity of the underlying algorithm. We validate our algorithms with experiments using the AIM4 simulator, showcasing significant improvements in travel times compared to conventional traffic light systems and first-come-first-served methods. The results underscore our protocol’s potential to reduce average travel time, enhancing overall traffic flow efficiency.