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When people choose routes minimizing their individual delay, the aggregatecongestion can be much higher compared to that experienced by acentrally-imposed routing. Yet centralized routing is incompatible with thepresence of self-interested agents. How can we reconcile the two? In this paperwe address this question within a repeated game framework and propose a fairincentive mechanism based on artificial currencies that routes selfish agentsin a system-optimal fashion, while accounting for their temporal preferences.We instantiate the framework in a parallel-network whereby agents commuterepeatedly (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 artificialcurrency, the agents are charged when traveling on the first, fast arc, whilstthey are rewarded when traveling on the second, slower arc. We assume theagents to be rational and model their choices through a game where each agentaims at minimizing a combination of today's discomfort, weighted by theirurgency, and the average discomfort encountered for the rest of the period(e.g., a week). We show that, if prices of artificial currencies arejudiciously chosen, the routing pattern converges to a system-optimal solution,while accommodating the agents' urgency. We complement our study throughnumerical simulations. Our results show that it is possible to achieve asystem-optimal solution whilst reducing the agents' perceived discomfort by14-20% when compared to a centralized optimal but urgency-unaware policy.

Urgency-aware Optimal Routing in Repeated Games through Artificial Currencies