Scaling Marginal Cost Tolling to Address Heterogeneity under Imperfect Information in Routing Games

Andries Rosseau, Paolo Turrini, Marjon Blondeel, Ann Nowe

Keywords: Congestion, Routing, Price of Anarchy, Multi-Agent, Learning, Mechanism, Marginal Cost, Heterogeneous

TL;DR: We introduce 𝜇-MCT, a practical and scalable tolling strategy designed for routing games with users that have unknown heterogeneous preferences.

Abstract: In routing games, agents select routes in a network in order to minimize their individual latency. Resulting Nash equilibria are known generally not to minimize the total latency across the system, which often requires further coordination. A well-known method that addresses the inefficiency caused by self-interested decision making is marginal cost tolling (MCT). Under the traditional assumption of homogeneous agents that trade off time (latency) and money (tolls) equally, marginal cost tolling induces optimal behavior and minimizes total latency. However, how should agents be tolled when their preferences are heterogeneous? We introduce $\mu$-MCT, a tolling mechanism that scales marginal cost tolls for routing networks with unknown heterogeneous preferences. In contrast to previous work on heterogeneous routing games, $\mu$-MCT does not assume knowledge of the agents' preferences, thereby respecting privacy concerns, nor does it require knowledge of the network structure. Moreover, an equal amount is tolled to agents that travel the same route, which addresses fairness concerns as well. $\mu$-MCT only has a single parameter, $\mu$, which scales marginal cost tolls and creates a spectrum of tolling mechanisms. We show the properties of $\mu$-MCT for several heterogeneous populations in a set of benchmark networks with high inefficiency. Our results indicate that $\mu$-MCT can considerably improve total latency for a broad range of $\mu$ values (and even for surprisingly small tolls). We further ask what $\mu$ value should be chosen when optimization is limited and discuss sample-efficient gradient-free learning. $\mu$-MCT is easy to compute, requiring only a derivative of the latency, and can be an elegant tolling mechanism for routing networks when working under imperfect information.

Type Of Paper: Full paper (max page 8)

Anonymous Submission: Anonymized submission.

Submission Number: 29