On the kinetic and stochastic games theory for active particles: Some reasonings on open large living systems

This paper deals with some developments of the mathematical kinetic theory for active particles to model large systems of interacting entities whose microscopic state includes not only geometric and mechanical variables but also peculiar functions or specific activities. The analysis is specifically focused on modelling living open systems in view of optimization, control problems, and derivation of macroscopic equations from the underlying microscopic description.