Invariant Price of Anarchy: a Metric for Welfarist Traffic Control

TL;DR

This paper introduces the Invariant Price of Anarchy, a new metric for evaluating traffic system efficiency that remains consistent despite arbitrary transformations of agents' cost functions, ensuring more robust policy guidance.

Contribution

It defines the Invariant PoA using social choice theory, providing an axiomatic foundation for efficiency metrics that are unaffected by cost rescaling or translation.

Findings

The Invariant PoA remains stable under cost transformations.

Different tolling strategies can appear equally efficient under traditional PoA but differ under Invariant PoA.

Explicit axiomatic foundations improve robustness of efficiency evaluations.

Abstract

The Price of Anarchy (PoA) is a standard metric for quantifying inefficiency in socio-technical systems, widely used to guide policies like traffic tolling. Conventional PoA analysis relies on exact numerical costs. However, in many settings, costs represent agents' preferences and may be defined only up to possibly arbitrary scaling and shifting, representing informational and modeling ambiguities. We observe that while such transformations preserve equilibrium and optimal outcomes, they change the PoA value. To resolve this issue, we rely on results from Social Choice Theory and define the Invariant PoA. By connecting admissible transformations to degrees of comparability of agents' costs, we derive the specific social welfare functions which ensure that efficiency evaluations do not depend on arbitrary rescalings or translations of individual costs. Case studies on a toy example and the Zurich network demonstrate that identical tolling strategies can lead to substantially different efficiency estimates depending on the assumed comparability. Our framework thus demonstrates that explicit axiomatic foundations are necessary in order to define efficiency metrics and to appropriately guide policy in large-scale infrastructure design robustly and effectively.