Discounted Mean-Field Game model of a dense static crowd with variable information crossed by an intruder

TL;DR

This paper extends a mean-field game model of dense crowds crossing an intruder by introducing a discount factor, enabling it to replicate various behaviors observed in experiments with different pedestrian knowledge levels.

Contribution

The addition of a discount factor parameter to the mean-field game model captures a wider range of crowd behaviors influenced by pedestrian knowledge.

Findings

The discount factor $eta$ significantly affects crowd dynamics.

The model with $eta$ matches experimental observations.

Analytic insights into the role of $eta$ in behavior modification.

Abstract

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 $\gamma$, 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 $\gamma$ modifies the model.