Existence and uniqueness of solutions to a Cauchy problem modeling the dynamics of socio-political conflicts

This paper presents the analysis of a system of ordinary differential equations modeling a socio-political competition toward a possible onset of extreme conflicts. The dependent variable is a probability density distribution, while the equations are characterized by quadratic type nonlinearities. The model was derived within the framework of the kinetic theory for active particles, where interactions are modeled according to game-theoretical tools. Global existence and uniqueness of the solutions to the initial value problem related to the model are proved in a special case. The main tool used is the Banach–Caccioppoli fixed point theorem.