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We consider non-atomic network congestion games with heterogeneous playerswhere the latencies of the paths are subject to some bounded deviations. Thismodel encompasses several well-studied extensions of the classical Wardropmodel which incorporate, for example, risk-aversion, altruism or travel timedelays. Our main goal is to analyze the worst-case deterioration in social costof a perturbed Nash flow (i.e., for the perturbed latencies) with respect to anoriginal Nash flow. We show that for homogeneous players perturbed Nash flowscoincide with approximate Nash flows and derive tight bounds on theirinefficiency. In contrast, we show that for heterogeneous populations thisequivalence does not hold. We derive tight bounds on the inefficiency of bothperturbed and approximate Nash flows for arbitrary player sensitivitydistributions. Intuitively, our results suggest that the negative impact ofpath deviations (e.g., caused by risk-averse behavior or latency perturbations)is less severe than approximate stability (e.g., caused by limitedresponsiveness or bounded rationality). We also obtain a tight bound on theinefficiency of perturbed Nash flows for matroid congestion games andhomogeneous populations if the path deviations can be decomposed into edgedeviations. In particular, this provides a tight bound on the Price ofRisk-Aversion for matroid congestion games.

Path deviations outperform approximate stability in heterogeneous congestion games