Path deviations outperform approximate stability in heterogeneous congestion games

TL;DR

This paper analyzes how path deviations affect the efficiency of equilibrium flows in heterogeneous congestion games, showing that deviations are less detrimental than approximate stability, with tight bounds established for various scenarios.

Contribution

It introduces a detailed analysis of path deviations in heterogeneous congestion games, providing tight bounds on inefficiency and highlighting differences from approximate stability.

Findings

Path deviations are less harmful than approximate stability in heterogeneous populations.

Tight bounds on inefficiency are derived for various types of congestion games.

A tight bound on the Price of Risk-Aversion for matroid congestion games is established.

Abstract

We consider non-atomic network congestion games with heterogeneous players where the latencies of the paths are subject to some bounded deviations. This model encompasses several well-studied extensions of the classical Wardrop model which incorporate, for example, risk-aversion, altruism or travel time delays. Our main goal is to analyze the worst-case deterioration in social cost of a perturbed Nash flow (i.e., for the perturbed latencies) with respect to an original Nash flow. We show that for homogeneous players perturbed Nash flows coincide with approximate Nash flows and derive tight bounds on their inefficiency. In contrast, we show that for heterogeneous populations this equivalence does not hold. We derive tight bounds on the inefficiency of both perturbed and approximate Nash flows for arbitrary player sensitivity distributions. Intuitively, our results suggest that the negative impact of path deviations (e.g., caused by risk-averse behavior or latency perturbations) is less severe than approximate stability (e.g., caused by limited responsiveness or bounded rationality). We also obtain a tight bound on the inefficiency of perturbed Nash flows for matroid congestion games and homogeneous populations if the path deviations can be decomposed into edge deviations. In particular, this provides a tight bound on the Price of Risk-Aversion for matroid congestion games.