Discounted Mean-Field Game model of a dense static crowd with variable information crossed by an intruder
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909170902499328 |
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| author | Butano, Matteo Appert-Rolland, Cécile Ullmo, Denis |
| author_facet | Butano, Matteo Appert-Rolland, Cécile Ullmo, Denis |
| contents | It was demonstrated in [Bonnemain et al., Phys. Rev. E 107, 024612 (2023)] that the anticipation pattern displayed by a dense crowd crossed by an intruder can be successfully described by a minimal Mean-Field Games model. However, experiments show that changes in the pedestrian knowledge significantly modify the dynamics of the crowd. Here, we show that the addition of a single parameter, the discount factor $γ$, which gives a lower weight to events distant in time, is sufficient to observe the whole variety of behaviors observed in the experiments. We present a comparison between the discounted MFG and the experimental data, also providing new analytic results and insight about how the introduction of $γ$ modifies the model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08945 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Discounted Mean-Field Game model of a dense static crowd with variable information crossed by an intruder Butano, Matteo Appert-Rolland, Cécile Ullmo, Denis Physics and Society Statistical Mechanics It was demonstrated in [Bonnemain et al., Phys. Rev. E 107, 024612 (2023)] that the anticipation pattern displayed by a dense crowd crossed by an intruder can be successfully described by a minimal Mean-Field Games model. However, experiments show that changes in the pedestrian knowledge significantly modify the dynamics of the crowd. Here, we show that the addition of a single parameter, the discount factor $γ$, which gives a lower weight to events distant in time, is sufficient to observe the whole variety of behaviors observed in the experiments. We present a comparison between the discounted MFG and the experimental data, also providing new analytic results and insight about how the introduction of $γ$ modifies the model. |
| title | Discounted Mean-Field Game model of a dense static crowd with variable information crossed by an intruder |
| topic | Physics and Society Statistical Mechanics |
| url | https://arxiv.org/abs/2302.08945 |