When people choose routes minimizing their individual delay, the aggregate congestion can be much higher compared to that experienced by a centrally-imposed routing. Yet centralized routing is incompatible with the presence of self-interested users. How can we reconcile the two? In this paper we address this question within a repeated game framework and propose a fair incentive mechanism based on artificial currencies that routes selfish users in a system-optimal fashion, while accounting for their temporal preferences. We instantiate the framework in a parallel-network whereby users commute repeatedly (e.g., daily) from a common start node to the end node. Thereafter, we focus on the specific two-arcs case whereby, based on an artificial currency, the users are charged when traveling on the first, fast arc, whilst they are rewarded when traveling on the second, slower arc. We assume the users to be rational and model their choices through a game where each user aims at minimizing a combination of today’s discomfort, weighted by their urgency, and the average discomfort encountered for the rest of the period (e.g., a week). We show that, if prices of artificial currencies are judiciously chosen, the routing pattern converges to a system-optimal solution, while accommodating the users’ urgency. We complement our study through numerical simulations. Our results show that it is possible to achieve a system-optimal solution whilst significantly reducing the users’ perceived discomfort when compared to a centralized optimal but urgency-unaware policy.

当人们选择最小化个人延迟的路线时，与集中施加的路线相比，总体拥堵可能要高得多。然而，集中式路由与自利用户的存在不相容。我们如何调和两者？在本文中，我们在一个重复的博弈中解决了这个问题框架并提出了一种基于人工货币的公平激励机制，该机制以系统优化的方式路由自私的用户，同时考虑到他们的时间偏好。我们在一个并行网络中实例化了框架，由此用户从一个共同的开始节点到结束节点重复（例如，每天）通勤。此后，我们专注于特定的双弧案例，其中，基于人工货币，用户在第一个较快的弧上行驶时收取费用，而在第二个较慢的弧上行驶时获得奖励。我们假设用户是理性的，并通过游戏模拟他们的选择，其中每个用户的目标是最小化今天的不适（由他们的紧迫性加权）和剩余时间段（例如，一周）遇到的平均不适。我们表明，如果明智地选择人工货币的价格，路由模式将收敛到系统最优解决方案，同时满足用户的紧迫性。我们通过数值模拟来补充我们的研究。我们的结果表明，与集中式最优但不知道紧急情况的策略相比，有可能实现系统最优解决方案，同时显着减少用户的不适感。