The project is devoted to the study of Kinetic Mean Field Games (KMFGs), i.e. the limit of cooperative or non-cooperative games in very large populations, composed of interacting individuals, where each individual has a small influence on the global behaviour of the system and where the behaviour of the system depends on additional (internal) variables.

    The methods which will be used include the most recent developments in kinetic theory, as well as the strategies developed in the last years for macroscopic mean field games.

    Moreover, through the identification of a scale parameter, it is interesting to obtain the limit, as the parameter tends to zero, of the system. The main goal here is to justify the relationships between kinetic and macroscopic mean field game theory. This research direction will be the analogous, in Mean Field Game theory, of the study on the hydrodynamical limits of kinetic equations, a research program proposed by Hilbert in his famous lecture delivered at the International Congress of Mathematicians, in Paris in 1900 (this problem is known as Hilbert's sixth problem).

    Particular emphasis will be addressed to the numerical simulation of KMFG systems. The new hardware tools have made possible an easy access to manycore computing. Hence, the impact of many-core architectures on the design of numerical methods requires a new paradigm in the conception of the codes, since standard discretization methods (mesh, array data structures, sparse matrices, memory) have been designed and optimized on the assumption of a sustainable CPU-global memory model.