On stability of users equilibria in heterogeneous routing games

On stability of users equilibria in heterogeneous routing games

The asymptotic behaviour of deterministic logit dynamics in heterogeneous routing games is analyzed. It is proved that in directed multigraphs with parallel routes, and in series composition of such multigraphs, the dynamics admits a globally asymptotically stable fixed point. Moreover, the unique f...

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Bibliographic Details
Main Authors: Cianfanelli, Leonardo, Como, Giacomo
Format: Journal Article
Language:English
Published: 04-12-2019
Subjects:
Computer Science - Computer Science and Game Theory
Mathematics - Dynamical Systems
Online Access:Get full text
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Summary:The asymptotic behaviour of deterministic logit dynamics in heterogeneous routing games is analyzed. It is proved that in directed multigraphs with parallel routes, and in series composition of such multigraphs, the dynamics admits a globally asymptotically stable fixed point. Moreover, the unique fixed point of the dynamics approaches the set of Wardrop equilibria, as the noise vanishes. The result relies on the fact that the dynamics of aggregate flows is monotone, and its Jacobian is strictly diagonally dominant by columns.
DOI:10.48550/arxiv.1912.02007