Universal Method of Searching for Equilibria and Stochastic Equilibria in Transportation Networks

A universal method of searching for usual and stochastic equilibria in congestion population games is proposed. The Beckmann and stable dynamics models of an equilibrium flow distribution over paths are considered. A search for Nash(–Wardrop) stochastic equilibria leads to entropy-regularized convex...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2019, Vol.59 (1), p.19-33
Main Authors: Baimurzina, D. R., Gasnikov, A. V., Gasnikova, E. V., Dvurechensky, P. E., Ershov, E. I., Kubentaeva, M. B., Lagunovskaya, A. A.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Convexity
Economic models
Equilibrium
Equilibrium flow
Flow distribution
Game theory
Mathematics
Mathematics and Statistics
Optimization
Searching
Smoothness
Transportation
Transportation networks
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Summary:A universal method of searching for usual and stochastic equilibria in congestion population games is proposed. The Beckmann and stable dynamics models of an equilibrium flow distribution over paths are considered. A search for Nash(–Wardrop) stochastic equilibria leads to entropy-regularized convex optimization problems. Efficient solutions of such problems, more exactly, of their duals are sought by applying a recently proposed universal primal-dual gradient method, which is optimally and adaptively tuned to the smoothness of the problem under study.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542519010020