Computing Optimal Tolls in Routing Games without Knowing the Latency Functions

TL;DR

This paper investigates whether optimal tolls in nonatomic routing games can be computed without explicit knowledge of latency functions, demonstrating impossibility with limited information and proposing a solution with additional total latency data.

Contribution

It introduces a model where tolls are computed via an oracle, showing that with only flow responses it is impossible, but with total latency feedback, optimal tolls can be efficiently determined.

Findings

Impossible to compute optimal tolls with only equilibrium flow responses.

Adding total latency feedback enables polynomial-time computation of optimal tolls.

Abstract

We consider the following question: in a nonatomic routing game, can the tolls that induce the minimum latency flow be computed without knowing the latency functions? Since the latency functions are unknown, we assume we are given an oracle that has access to the underlying routing game. A query to the oracle consists of tolls on edges, and the response is the resulting equilibrium flow. We show that in this model, it is impossible to obtain optimal tolls. However, if we augment the oracle so that it returns the total latency of the equilibrium flow induced by the tolls in addition to the flow itself, then the required tolls can be computed with a polynomial number of queries.