Multi-Layer Mean-Field-Type Games Driven by Five Noises

Gaussian and Poisson noises have been widely studied in mean-field-type game theory. In this paper, we examine the effect of the noise in the equilibrium strategies. We show that the equilibrium strategies obtained under states driven by Brownian motions, Fractional Brownian motions, Gauss-Volterra and Poisson processes no longer provide equilibrium when mixed with Rosenblatt noises. The result suggests a careful understanding of the noise structures involved in the quantities of interests in the state dynamics before approximating it by standard Gaussian noises.