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Schrödinger approach to Mean Field Games with negative coordination
by Thibault Bonnemain, Thierry Gobron, Denis Ullmo
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Submission summary
| Authors (as registered SciPost users): | Thibault Bonnemain · Denis Ullmo |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2006.01221v1 (pdf) |
| Date submitted: | 2020-06-05 02:00 |
| Submitted by: | Ullmo, Denis |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled agents in interaction. Here we consider such systems when the interactions between agents result in a negative coordination and analyze the behavior of the associated system of coupled PDEs using the now well established correspondence with the non linear Schr\"odinger equation. We focus on the long optimization time limit and on configurations such that the game we consider goes through different regimes in which the relative importance of disorder, interactions between agents and external potential varies, which makes possible to get insights on the role of the forward-backward structure of the Mean Field Game equations in relation with the way these various regimes are connected.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2020-7-19 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2006.01221v1, delivered 2020-07-19, doi: 10.21468/SciPost.Report.1838
Strengths
1) Well performed and interesting, on a topical subject
2) Well written, review like paper on a trans-disciplinary subject
Weaknesses
1) Method seems restricted to the very special case of quadratic games
2) Quite technical paper
Report
I suggest acceptance of this paper essentially as it
Requested changes
Maybe discuss if and how these methods can be adapted to more general cases: non quadratic games; time dependent potential U_0.
Report #1 by Anonymous (Referee 1) on 2020-7-13 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2006.01221v1, delivered 2020-07-13, doi: 10.21468/SciPost.Report.1825
Strengths
1) original
2) well written
Weaknesses
1) very technical so quite limited readership
Report
yes
Requested changes
1) list of minor details in my attached report