We study selfish routing games where users can choose between regular and priority service for each network edge on their chosen path. Priority users pay an additional fee, but in turn they may travel the edge prior to non-priority users, hence experiencing potentially less congestion. For this model, we establish existence of equilibria for linear latency functions and prove uniqueness of edge latencies, despite potentially different strategic choices in equilibrium. Our main contribution demonstrates that marginal cost pricing achieves system optimality: When priority fees equal marginal externality costs, the equilibrium flow coincides with the socially optimal flow, hence the price of anarchy equals $1$. This voluntary priority mechanism therefore provides an incentive-compatible alternative to mandatory congestion pricing, whilst achieving the same result. We also discuss the limitations of a uniform pricing scheme for the priority option.

翻译：本文研究自私路由博弈，其中用户可在其选定路径的每条网络边选择常规服务或优先服务。优先用户需支付额外费用，但可优先于非优先用户通行该边，从而可能经历更低的拥堵。针对该模型，我们在线性延迟函数条件下证明了均衡的存在性，并证明了尽管均衡中可能存在不同的策略选择，边延迟具有唯一性。我们的主要贡献在于证明边际成本定价能够实现系统最优：当优先费用等于边际外部性成本时，均衡流与社会最优流重合，因此无政府价格等于$1$。这种自愿优先机制为强制拥堵定价提供了具有激励相容性的替代方案，同时能达到相同效果。我们还讨论了优先选项统一定价方案的局限性。