  We derive a hierarchy of kinetic and macroscopic models from a noisy variant
of the heuristic behavioral Individual-Based Model of Moussaid et al, PNAS
2011, where the pedestrians are supposed to have constant speeds. This IBM
supposes that the pedestrians seek the best compromise between navigation
towards their target and collisions avoidance. We first propose a kinetic model
for the probability distribution function of the pedestrians. Then, we derive
fluid models and propose three different closure relations. The first two
closures assume that the velocity distribution functions are either a Dirac
delta or a von Mises-Fisher distribution respectively. The third closure
results from a hydrodynamic limit associated to a Local Thermodynamical
Equilibrium. We develop an analogy between this equilibrium and Nash equilibia
in a game theoretic framework. In each case, we discuss the features of the
models and their suitability for practical use.
