Lecture Marie Therese Wolfram: On Boltzmann type equations in socio economic applications

The lecture was held within the of the Hausdorff Junior Trimester Program: Kinetic Theory

Abstract:
In this talk we discuss how kinetic or so-called Boltzmann type models can be used to describe the dynamics of large interacting agents systems. We focus on two applications – a continuous
version of the Elo rating system and so-called Boltzmann mean field games. In the Elo rating model players are characterised by their intrinsic strength and official rating, which are updated after each game. We discuss the behaviour of solutions to the corresponding Boltzmann type equation in suitable scaling limits and illustrate the dynamics with numerical experiments. In the second part we introduce a Boltzmann mean field game model for knowledge growth. Here agents are rational individuals, who determine how much time they spend on learning via binary interactions or producing goods with the knowledge level they already have. This results in a coupled system of a Boltzmann type equation and a Hamilton-Jacobi Bellman equation. We discuss the analysis of this system, especially the existence of so-called balanced growth path solutions.