| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 18 | |
| Number of page(s) | 23 | |
| DOI | https://doi.org/10.1051/cocv/2025007 | |
| Published online | 20 March 2025 | |
Stationary Mean Field Games on networks with sticky transition conditions
1
Univ Rennes, INSA, CNRS, IRMAR – UMR 6625, Rennes F-35000, France
2
Dip. di Ingegneria e Geologia, Università degli Studi “G. d’Annunzio” Chieti-Pescara, viale Pindaro 42, 65127 Pescara Italy
* Corresponding Author: fabio.camilli@unich.it
Received:
28
June
2024
Accepted:
14
January
2025
We study stochastic Mean Field Games on networks with sticky transition conditions. In this setting, the diffusion process governing the agent’s dynamics can spend finite time both in the interior of the edges and at the vertices. The corresponding generator is subject to limitations concerning second-order derivatives and the invariant measure breaks down into a combination of an absolutely continuous measure within the edges and a sum of Dirac measures positioned at the vertices. Additionally, the value function, solution to the Hamilton-Jacobi-Bellman equation, satisfies generalized Kirchhoff conditions at the vertices.
Mathematics Subject Classification: 35R02 / 49N80 / 91A16
Key words: Mean Field Games / networks / Markov processes / sticky points
© The authors. Published by EDP Sciences, SMAI 2025
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