On Boltzmann Type Equations in Socio-Economic Applications
Explore the application of kinetic and Boltzmann-type models in describing large interacting agent systems through this lecture from the Hausdorff Junior Trimester Program on Kinetic Theory. Delve into two specific applications: a continuous version of the Elo rating system and Boltzmann mean field games. Examine the behavior of solutions to the Boltzmann-type equation for the Elo rating model in scaling limits, supported by numerical experiments. Investigate a Boltzmann mean field game model for knowledge growth, where agents strategically allocate time between learning and production. Analyze the coupled system of a Boltzmann-type equation and a Hamilton-Jacobi Bellman equation, focusing on the existence of balanced growth path solutions.