Mean Field Games

ISBN-13: 9781470455866

Francois Delarue

Opis

This volume is based on lectures delivered at the 2020 AMS Short Course ""Mean Field Games: Agent Based Models to Nash Equilibria,"" held January 13-14, 2020, in Denver, Colorado. Mean field game theory offers a robust methodology for studying large systems of interacting rational agents. It has been extraordinarily successful and has continued to develop since its inception. The six chapters that make up this volume provide an overview of the subject, from the foundations of the theory to applications in economics and finance, including computational aspects. The reader will find a pedagogical introduction to the main ingredients, from the forward-backward mean field game system to the master equation. Also included are two detailed chapters on the connection between finite games and mean field games, with a pedestrian description of the different methods available to solve the convergence problem. The volume concludes with two contributions on applications of mean field games and on existing numerical methods, with an opening to machine learning techniques.

Spis treści

• An overview of the theory of mean field games: R. P. Malhame and C. Graves, Mean Field Games: A paradigm for individual-mass interctions
• F. Delarue, Mean field games and master equation
• Connection with games with finitely many players: D. Lacker, The mean field game convergence problem
• K. Ramanan, Refined convergence results for interacting diffusions and mean-field games
• Applications and numerical methods: R. Carmona, Applications of Mean Field Games in financial engineering and economic theory
• M. Lauriere, Numerical methods for mean field games and mean field type control
• F. Delarue, Index