Bounding the Inefficiency of Risk-Averse Selfish Routing with Nonadditive CVaR

Abstract

Modern AI-driven systems rely on large populations of autonomous agents that make decentralized routing decisions under uncertainty, where rare but severe tail latency can critically degrade quality of experience, safety, and reliability. To model agents’ aversion to such tail latency, we study nonatomic selfish routing games in which agents minimize the Conditional Value-at-Risk (CVaR) of path latency. CVaR explicitly captures both the likelihood and severity of tail latency, but its inherent nonadditivity across network edges poses a fundamental challenge. We address it by identifying a worst-case dependence structure—tail risk concentration—under which tail latency across network edges is synchronized. We show that CVaR penalizes this dependence structure and becomes additive under worst-case tail dependence, which enables tight inefficiency analysis. To quantify the resulting inefficiency induced by risk-aversion, we adopt the price of risk aversion (PRA), defined as the worst-case ratio between the total system cost at a risk-averse equilibrium and that at a risk-neutral equilibrium. We show that, for arbitrary latency functions and general network topologies, the PRA under CVaR admits a tight upper bound that grows linearly with both the network size and the maximum edge-level upper-tail cost. We further prove that this bound is tight by constructing a family of Braess-type networks that achieve a matching lower bound. These results provide the first tight worst-case inefficiency bound for CVaR-based selfish routing and offer insights into how tail-risk-averse decision making by autonomous agents amplifies congestion externalities in large-scale multi-agent systems.