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Analysis of learning dynamics in heterogeneous routing games

Tommaso Toso

Analysis of learning dynamics in heterogeneous routing games.

Rel. Giacomo Como. Politecnico di Torino, Corso di laurea magistrale in Ingegneria Matematica, 2021

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The main focus of this work is the analysis of the asymptotic behavior of deterministic logit dynamics in heterogeneous routing games defined on two-terminal directed multigraphs. We provide three distinct results. The first one states that this dynamics admits a globally asymptotically stable fixed point when noise is sufficiently high. The second result, instead, shows that the fixed points of the dynamics always approach the set of Wardrop equilibria of the associated routing game, as noise vanishes. Finally, the third and last result says that fixed points are locally asymptotically stable, again for a sufficiently low noise level, when they converge to Wardrop equilibria consisting in flow distributions in which every users' population has a single optimal path to travel along.

Relators: Giacomo Como
Academic year: 2021/22
Publication type: Electronic
Number of Pages: 53
Corso di laurea: Corso di laurea magistrale in Ingegneria Matematica
Classe di laurea: New organization > Master science > LM-44 - MATHEMATICAL MODELLING FOR ENGINEERING
Aziende collaboratrici: UNSPECIFIED
URI: http://webthesis.biblio.polito.it/id/eprint/19868
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