Invariant Price of Anarchy: a Metric for Welfarist Traffic Control

2025-12-05

AI Summary

Traditional Price of Anarchy (PoA) relies on precise cost values, yet in socio-technical systems (e.g., traffic control), costs often merely represent agents’ ordinal preferences—rendering their scale and zero point arbitrary. Consequently, PoA is not invariant under affine cost transformations, undermining its robustness. Method: We introduce Invariant PoA, the first efficiency metric for mechanisms grounded in social choice theory, axiomatically defined to be fully invariant under affine cost transformations. Leveraging a comparability-ranking framework, we characterize the class of social welfare functions satisfying this invariance and prove their uniqueness. Results: Empirical evaluation on real-world networks—including Zurich’s traffic system—demonstrates that conventional PoA exhibits estimation errors up to several-fold across different cost representations, whereas Invariant PoA yields consistent, robust welfare assessments. This provides a theoretically sound and practically applicable efficiency benchmark for policy design.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

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.

Problem

• Defines Invariant PoA to handle cost scaling and shifting ambiguities.
• Ensures efficiency metrics are independent of arbitrary cost transformations.
• Demonstrates need for axiomatic foundations in policy guidance.

Innovation

• Defines Invariant Price of Anarchy metric
• Connects cost transformations to social welfare functions
• Ensures efficiency evaluations independent of arbitrary rescaling