Robust Solutions to Least-Squares Problems with Uncertain Data
SIAM Journal on Matrix Analysis and Applications
Mathematics of Operations Research
Robust Truss Topology Design via Semidefinite Programming
SIAM Journal on Optimization
Robust portfolio selection problems
Mathematics of Operations Research
Mathematical Programming: Series A and B
A survey on networking games in telecommunications
Computers and Operations Research
Wardrop Equilibria with Risk-Averse Users
Transportation Science
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Agents competing in a network game typically prefer the least expensive route to their destinations. However, identifying such a route can be difficult when faced with uncertain cost estimates. We introduce a novel solution concept called robust Wardrop equilibria (RWE) that takes into account these uncertainties. Our approach, which generalizes the traditional Wardrop equilibrium, considers that each agent uses distribution-free robust optimization to take the uncertainty into account. By presenting a nonlinear complementary problem that captures this user behavior, we show that RWE always exist and provide an efficient algorithm based on column generation to compute them. In addition, we present computational results that indicate that RWE are more stable than their nominal counterparts because they reduce the regret experienced by agents.