Theory, Implementations, and Applications of Mean Field Games: the Second Generation

The first goal of the original proposal was the development of new stochastic and numerical methods for the equilibrium analyses of the theory of Mean Field Games and Mean Field Control. Motivated by a wide spectrum of applications ranging from population dynamics and social networks, to communications and cybersecurity, it will advance the understanding of complex stochastic systems by introducing and developing new mathematical theories and associated computational algorithms. Its ambition is to provide a quantum leap to the state of the current understanding of Mean Field Games. Building on the results of the first generation of investigations, it proposes an ambitious research program whose goal is to define the second generation of equilibrium analyses of these complex stochastic systems. For example, now that we understand the concept of master equation, we plan to fully develop its theory by taking advantage of our newly acquired calculus on spaces of probability measures to produce asymptotic expansions and numerical algorithms, and investigate convergence rates, including models with delay of crucial importance in many logistic applications of interest to the Air Force.