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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 intrudercan be successfully described by a minimal Mean-Field Games model. However,experiments show that changes in the pedestrian knowledge significantly modifythe dynamics of the crowd. Here, we show that the addition of a singleparameter, the discount factor $\gamma$, which gives a lower weight to eventsdistant in time, is sufficient to observe the whole variety of behaviorsobserved in the experiments. We present a comparison between the discounted MFGand the experimental data, also providing new analytic results and insightabout how the introduction of $\gamma$ modifies the model.

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