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

It has been proven that the displayed anticipation pattern of a dense crowd crossed by an intruder can be successfully described by a minimal Mean-Field Games model. However, experiments show that when pedestrians have limited knowledge, the global anticipation dynamics becomes less optimal. Here we reproduce this with the same MFG model, with the addition of only one parameter, a discount factor $\gamma$ that tells the time scale of agents' anticipation. We present a comparison between the discounted MFG and the experimental data, also providing new analytic results and important insight about how the introduction of $\gamma$ modifies the model.