Cooperative driving is crucial for improving traffic efficiency and safety for connected and automated vehicles (CAVs), especially in traffic bottlenecks. However, most of the state-of-the-art cooperative driving strategies neglect the issue of fairness. Fairness is essential to properly allocate road resources and improve the travel experience. In this paper, we focus on the fairness concerns in the on-ramp cooperative driving problem. First, we note that enhancing traffic efficiency usually leads to unfairness, but we propose solutions to balance both aspects. Using the fundamental relation in traffic flow theory, we illustrate the existence of the trade-off at congested on-ramps. We then make some modifications to the cooperative driving strategies to incorporate fairness considerations. Simulation results show that the modified strategies achieve trade-offs in agreement with the theoretical one, laying the foundation for implementing the trade-off in real-world scenarios. These findings are enlightening for the increasing research on fairness issues in cooperative driving, and contribute to the optimization of traffic management strategies.INDEX TERMS Connected and automated vehicles (CAVs), cooperative driving, on-ramp scenario, fairness and efficiency.