We propose a new microscopic crowd motion model based on Game-Theoretic principles, from which we derive an Inhibition-Based model for evacuation situations. Each individual is supposed to have a desired velocity that they adapt to the behavior of neighbors that influence them. Possible adapted velocities are defined as instantaneous Nash equilibria: each individual does their best with respect to a personal objective (desired velocity), considering the behavior of the neighbors that influence them (to avoid overlapping). We address theoretical and modeling issues in various situations, in particular when each individual is influenced by all their neighbors, and in the case where the influence relations are structured in a hierarchical way. The second particular case is used to define the Inhibition-Based model.
Nous proposons un nouveau modèle microscopique de mouvement de foule basé sur la théorie des jeux, à partir duquel nous dérivons une version particulière dédiée aux situations d’évacuation, basée sur un principe d’inhibition. Nous supposons que chaque individu a une certaine vitesse souhaitée qu’il adapte en fonction du comportement des voisins qui l’influencent. Les vitesses adaptées possibles sont définies comme des équilibres de Nash instantanés : chaque individu fait de son mieux par rapport à un objectif personnel (vitesse souhaitée), en tenant compte du comportement des voisins qui l’influencent (pour éviter un chevauchement avec eux). Nous abordons des questions relatives à la modélisation ainsi que les aspects théoriques du problème dans diverses situations, en particulier dans le cas où chaque individu est influencé par tous ses voisins, et dans le cas où les relations d’influence entre les individus ont une structure hiérarchique. Le second cas particulier fait l’objet du modèle basé sur un principe d’inhibition.
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Bertrand Maury 1; Fatima Al Reda 1
CC-BY 4.0
@article{CRMATH_2021__359_9_1071_0,
author = {Bertrand Maury and Fatima Al Reda},
title = {Game-Theoretic and {Inhibition-Based} models for crowd motion},
journal = {Comptes Rendus. Math\'ematique},
pages = {1071--1083},
publisher = {Acad\'emie des sciences, Paris},
volume = {359},
number = {9},
year = {2021},
doi = {10.5802/crmath.224},
language = {en},
}
Bertrand Maury; Fatima Al Reda. Game-Theoretic and Inhibition-Based models for crowd motion. Comptes Rendus. Mathématique, Volume 359 (2021) no. 9, pp. 1071-1083. doi : 10.5802/crmath.224. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.224/
[1] Numerical Analysis and Optimization. An Introduction to Mathematical Modelling and Numerical Simulation, Numerical Mathematics and Scientific Computation, Oxford University Press, 2007 (translation from the French by Alan Craig) | Zbl
[2] Generalized Nash equilibrium problems, 4OR, Volume 5 (2007) no. 3, pp. 173-210 | DOI | MR | Zbl
[3] Experimental evidence of the “Faster Is Slower” effect, Transportation Research Procedia, Volume 2 (2014), pp. 760-767 | DOI
[4] Simulating dynamical features of escape panic, Nature, Volume 407 (2000) no. 6803, pp. 487-490 | DOI
[5] Handling of contacts in crowd motion simulations, raffic and granular flow ’07. Selected papers based on the presentations at the international conference (TFG 2007), Orsay, France, June 20–22, 2007 (Cécile Appert-Rolland, ed.), Springer, 2009, pp. 171-180 | Zbl
[6] A discrete contact model for crowd motion, ESAIM, Math. Model. Numer. Anal., Volume 45 (2011) no. 1, pp. 145-168 | DOI | Numdam | MR | Zbl
[7] Equilibrium points in n-person games, Proc. Natl. Acad. Sci. USA, Volume 36 (1950) no. 1, pp. 48-49 | DOI | MR | Zbl
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