Kinetic modelling of multiple interactions in socio-economic systems

TL;DR

This paper extends kinetic modeling to socio-economic systems by incorporating multiple interactions among agents, proposing a linearisation approach that simplifies analysis while preserving key system features.

Contribution

It introduces a linearisation strategy for modeling multiple interactions in socio-economic kinetic systems, maintaining essential aggregate properties.

Findings

Linearisation simplifies the kinetic description of socio-economic interactions.

The approach preserves equilibrium distributions of the system.

Multiple interactions can be effectively modeled beyond binary collisions.

Abstract

Unlike the classical kinetic theory of rarefied gases, where microscopic interactions among gas molecules are described as binary collisions, the modelling of socio-economic phenomena in a multi-agent system naturally requires to consider, in various situations, multiple interactions among the individuals. In this paper, we collect and discuss some examples related to economic and gambling activities. In particular, we focus on a linearisation strategy of the multiple interactions, which greatly simplifies the kinetic description of such systems while maintaining all their essential aggregate features, including the equilibrium distributions.