Mean-field games for high-density crowds: The discount factor reproduces experiments but raises numerical issues

Among the various types of crowd models, mean-field games have proved especially appropriate to reproduce some experimental results in high density crowds that involve anticipation on a time scale longer than usually involved in collision avoidance. It is possible to tune the level of anticipation with a so-called discount factor. However, the introduction of such a discount factor raises numerical issues close to solid boundaries (walls). A way to circumvent the difficulty is presented.