  Macroscopic models of crowd flow incorporating individual pedestrian choices
present many analytic and computational challenges. Anisotropic interactions
are particularly subtle, both in terms of describing the correct "optimal"
direction field for the pedestrians and ensuring that this field is uniquely
defined. We develop sufficient conditions, which establish a range of "safe"
densities and parameter values for each model. We illustrate our approach by
analyzing several established intra-crowd and inter-crowd models. For the
two-crowd case, we also develop sufficient conditions for the uniqueness of
Nash Equilibria in the resulting non-zero-sum game.
