2019/09/09 by Ashish Cherukuri, Cherukuri, Ashish
Economics, Econometrics and Finance · #Climate Change Policy and Economics #Economic theories and models #FOS: Electrical engineering #FOS: Mathematics #Game Theory and Voting Systems #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1909.03783
openalex publication_date 2019/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper focuses on the class of routing games that have uncertain costs.\nAssuming that agents are risk-averse and select paths with minimum conditional\nvalue-at-risk (CVaR) associated to them, we define the notion of CVaR-based\nWardrop equilibrium (CWE). We focus on computing this equilibrium under the\ncondition that the distribution of the uncertainty is unknown and a set of\nindependent and identically distributed samples is available. To this end, we\ndefine the sample average approximation scheme where CWE is estimated with\nsolutions of a variational inequality problem involving sample average\napproximations of the CVaR. We establish two properties for this scheme. First,\nunder continuity of costs and boundedness of uncertainty, we prove asymptotic\nconsistency, establishing almost sure convergence of approximate equilibria to\nCWE as the sample size grows. Second, under the additional assumption of\nLipschitz cost, we prove exponential convergence where the probability of the\ndistance between an approximate solution and the CWE being smaller than any\nconstant approaches unity exponentially fast. Simulation example validates our\ntheoretical findings.\n