The Impact of Fairness on Performance in Congestion Networks

How do incentives that are designed to improve system performance affect fairness among users? Operators of traffic systems are typically concerned with a spectrum of performance metrics including aggregate congestion levels, fairness, and monetary expenditures. In this work, we focus on the design of taxation mechanisms to optimize both aggregate congestion levels as well as fairness, where fairness is defined as a measure of the difference between the quality of service of similar users in the system. Specifically, we derive the explicit trade-off between the performance guarantee and worst-case unfairness when designing a tolling scheme, showing that improved performance guarantees cause increased unfairness. Additionally, we find this relationship in the settings where the toll designer is informed and uninformed on the populations price sensitivities; by comparing the two, one can observe the value of this information when designing fair and good performing tolls.