Conservation laws and asymptotic behavior of a model of social dynamics

A conservative social dynamics model is developed within a discrete kinetic framework for active particles, which has been proposed in [M.L. Bertotti, L. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Mod. Meth. Appl. Sci. 14 (2004) 1061–1084]. The model concerns a society in which individuals, distinguished by a scalar variable (the activity) which expresses their social state, undergo competitive and/or cooperative interactions. The evolution of the discrete probability distribution over the social state is described by a system of nonlinear ordinary differential equations. The asymptotic trend of their solutions is investigated both analytically and computationally. Existence, stability and attractivity of certain equilibria are proved.