Within mobility systems, the presence of self-interested users can lead to aggregate routing patterns that are far from the societal optimum which could be achieved by centrally controlling the users' choices. In this paper, we design a fair incentive mechanism to steer the selfish behavior of the users to align with the societally optimal aggregate routing. The proposed mechanism is based on an artificial currency that cannot be traded or bought, but only spent or received when traveling. Specifically, we consider a parallel-arc network with a single origin and destination node within a repeated game setting whereby each user chooses from one of the available arcs to reach their destination on a daily basis. In this framework, taking faster routes comes at a cost, whereas taking slower routes is incentivized by a reward. The users are thus playing against their future selves when choosing their present actions. To capture this complex behavior, we assume the users to be rational and to minimize an urgency-weighted combination of their immediate and future discomfort. To design the optimal pricing, we first derive a closed-form expression for the best individual response strategy. Second, we formulate the pricing design problem for each arc to achieve the societally optimal aggregate flows, and reformulate it so that it can be solved with gradient-free optimization methods. Our numerical simulations show that it is possible to achieve a near-optimal routing whilst significantly reducing the users' perceived discomfort when compared to a centralized optimal but urgency-unaware policy.

翻译：在移动系统中，自利用户的存在可能导致聚合路由模式远离通过集中控制用户选择所能实现的社会最优状态。本文设计了一种公平激励机制，引导用户的利己行为与社会最优聚合路由相一致。所提出的机制基于一种不可交易或购买、仅在出行时消耗或获得的人工货币。具体而言，我们在重复博弈场景中考虑具有单一起点和终点的平行弧网络，每位用户每天从可用弧中选择一条路径抵达目的地。在此框架下，选择快速路径需支付成本，而选择慢速路径则可获得奖励。用户通过当前行动与未来的自己进行博弈。为捕捉这种复杂行为，我们假设用户是理性的，并最小化由紧迫性加权的即时与未来不舒适度之和。为设计最优定价，我们首先推导出最优个体响应策略的闭式表达式；其次，针对每条弧构建定价设计问题以实现社会最优聚合流量，并通过重构使其可利用无梯度优化方法求解。数值模拟表明，与集中式最优但忽略紧迫感知的策略相比，本方法在显著降低用户感知不舒适度的同时，可实现接近最优的路由效果。