I. Introduction
Mean-field-type games have been studied in [1]–[4], where the assumption about having a large number of decision makers is not longer required. Mean-field-type games address problems involving both mean and variance of the system state and the control inputs. Indeed, both mean and variance terms might also be involved in the system dynamics. The problem incorporating these mean-variance terms is associated to the paradigm established by H. Markowitz, 1990 Nobel Laureate in Economics, on the mean-variance portfolio selection problem [5]. In addition, mean-field-type control has also been studied in the literature. For instance, discrete-time mean-field-type control problems are addressed using a Lagrange and operator approach for finite and infinite time horizon in [6] and [7], respectively. In contrast, maximum principle is used to solve mean-field-type control problems in [8], [9].