Stochastic evolutionary differential games toward a systems theory of behavioral social dynamics

Abstract

This paper proposes a systems approach to social sciences based on mathematical framework derived from a generalization of the mathematical kinetic theory and on theoretical tools of game theory. Social systems are modeled as a living evolutionary ensemble composed by many individuals, who express specific strategies, cooperate, compete and might aggregate into groups which pursue a common interest. A critical analysis on the complexity features of social system is developed and a differential structure is derived to provide a general framework toward modeling.

On Entropy Dynamics for Active “Living” Particles

“…Social systems: The dynamics of social systems constituted by many interacting entities can be modeled by the kinetic theory methods as shown in [28,34]. Mathematical models have been derived by assuming that the overall system is partitioned into groups of interest characterized by the economical or social strategy they share.…”

“…The number of entities (active particles) within each group of interest (functional subsystem) can be supposed to be constant when the said entities do not move across functional subsystems, while when this dynamics occurs the assumption simply refers to the total number of active particles. Applications are reviewed in [28], focusing on mathematical topics, and [35] with greater emphasis on economy and social sciences (see also [36]). Here, the functions f are probability distribution functions over discrete variables u.…”

“…General reasonings about entropy calculations have been developed in various papers, focusing, for instance, on biological systems [25][26][27] as well as social and financial markets [28,29]. Some papers show how models at the macroscopic scale can be derived from the underlying description at the microscopic scale delivered by kinetic theory models [25,30].…”

Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

“…While this choice is easy to handle with from a mathematical point of view, it naturally leads to eliminate a part of human behavior from the trading. Consequently, this simplification could introduce some fault into the model, since, in contrast to classical kinetic theory of rarefied gases, various aspects of human behavior play a substantial role into the mathematical modeling of socio-economic phenomena [1,7,8,9,10,11,41].…”

Asymmetric Contrarians in Opinion Dynamics

“…The modeling of opinion dynamics is one of the major topic of sociophysics studies [1][2][3][4][5][6][7][8][9][10][11]. Most discrete models consider the dynamics of two competing choices among identical agents, who all follow the same update rule while involved in a discussion with others.…”