Master Equation and the Convergence Problem in Mean Field Games: (AMS-201)

The book discusses the theory of mean field games, which are optimal control problems with a continuum of players, and their applications in various fields. It establishes the convergence of mean field games to Nash equilibria of differential games with finitely many players, and provides a complete self-contained analysis of the master equation, including common noise problems.

\n Format: Paperback / softback
\n Length: 224 pages
\n Publication date: 13 August 2019
\n Publisher: Princeton University Press
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Mean field games are optimal control problems with a continuum of players, each interacting with the whole statistical distribution of a population. While initially rooted in economics, these games have found applications in diverse fields such as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. These games are particularly interesting when the number of players becomes infinite, as they exhibit a convergence towards a limit known as the mean field limit.

The book establishes this convergence, which had been an open problem until now. It does so by developing a rigorous mathematical framework to describe the limit of the system associated with differential games with finitely many players. The master equation, a nonlocal transport equation in the space of measures, plays a central role in this analysis. The authors define a suitable notion of differentiability in this space and provide a comprehensive self-contained analysis of the master equation. They also address the case of common noise problems, where all players are affected by a common Brownian motion.

Furthermore, the book demonstrates how to use the master equation to prove the mean field limit. These groundbreaking results contribute to a unified theoretical framework for mean field games and have significant implications for understanding complex systems with many interacting agents.

The book is written for mathematicians and researchers interested in optimal control, game theory, and mathematical physics. It provides a comprehensive introduction to the theory of mean field games and assumes a basic knowledge of differential equations and measure theory. With its clear and concise presentation, the book is accessible to a wide audience and will be valuable to students, scholars, and professionals in these fields.

\n Weight: 390g\n
Dimension: 156 x 233 x 20 (mm)\n
ISBN-13: 9780691190716\n \n