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Explore how game theory and mean-field games can model high-density crowd behavior in this 56-minute mathematical lecture. Learn about the application of mean-field hypothesis to make large-scale pedestrian dynamics tractable, examining how individuals compete for space in dense crowds of up to 6 pedestrians per square meter. Discover how this approach successfully reproduces experimental results of crowd deformation by intruders, capturing pedestrian anticipation behaviors that traditional crowd models failed to explain. Understand the key role of the anticipation horizon parameter in accounting for varying levels of pedestrian information and how this differs fundamentally from granular matter behavior. Examine the numerical challenges that arise when implementing mean-field game models for crowd dynamics, with insights from joint research conducted at LPTMS (Laboratoire de Physique Théorique et Modèles Statistiques).
