The Master Equation and the Convergence Problem in Mean Field Games: (AMS-201) (Annals of Mathematics Studies, 201) - Image 1

Price loading...

Princeton University Press The Master Equation and the Convergence Problem in Mean Field Games: (AMS-201) (Annals of Mathematics Studies, 201)

Name: The Master Equation and the Convergence Problem in Mean Field Games: (AMS-201) (Annals of Mathematics Studies, 201)
Brand: Princeton University Press

Differential Equations

Price History & Forecast

No Price Data Available

Price history will appear here once data is collected from Amazon.

Price Distribution

No price data available for histogram

Description

This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.

Product Specifications

Brand: Princeton University Press
Format: hardcover
ASIN: 0691190704
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Mathematical Analysis > Differential Equations
Domain: Amazon UK
Release Date: 13 August 2019
Listed Since: 23 October 2018

Barcode

No barcode data available

Princeton University Press The Master Equation and the Convergence Problem in Mean Field Games: (AMS-201) (Annals of Mathematics Studies, 201)

Price History & Forecast

No Price Data Available

Price Distribution

Description

Product Specifications

Barcode

Similar Products You Might Like

The Master Equation and the Convergence Problem in Mean Field Games: (AMS-201) (Annals of Mathematics Studies, 201)

Probabilistic Theory of Mean Field Games with Applications II: Mean Field Games with Common Noise and Master Equations: 84 (Probability Theory and Stochastic Modelling, 84)

Probabilistic Theory of Mean Field Games with Applications II: Mean Field Games with Common Noise and Master Equations: 84 (Probability Theory and Stochastic Modelling, 84)

Probabilistic Theory of Mean Field Games with Applications I: Mean Field FBSDEs, Control, and Games: 83 (Probability Theory and Stochastic Modelling, 83)

Mean Field Games: Ams Short Course, Mean Field Games, Agent Based Models to Nash Equilibria, January 13--14, 2020, Denver, Colorado: 78 (Proceedings of Symposia in Applied Mathematics)

Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems (SpringerBriefs in Mathematics)

Equilibrium Problems and Applications (Mathematics in Science and Engineering)

Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrödinger Equation (AM–154) (Annals of Mathematics Studies, 154)

Mean Field Games: Cetraro, Italy 2019: 2281 (Lecture Notes in Mathematics, 2281)

Intermittent Convex Integration for the 3D Euler Equations: (AMS-217) (Annals of Mathematics Studies, 217)

Semiclassical Soliton Ensembles for the Focusing Nonlinear Schrodinger Equation (Annals of Mathematics Studies, 154)

Analysis of Monge-Ampere Equations: 240 (Graduate Studies in Mathematics)

Game Theory, Alive

PDE Models for Multi-Agent Phenomena: 28 (Springer INdAM Series, 28)

Ordinary Differential Equations and Dynamical Systems (Graduate Studies in Mathematics)

Nonlinear Analysis, Differential Equations, and Applications: 173 (Springer Optimization and Its Applications, 173)

Higher-Order Time Asymptotics of Fast Diffusion in Euclidean Space: A Dynamical Systems Approach (Memoirs of the American Mathematical Society)

Princeton University Press Comparison Principles for PDEs (AMS-218)

Essentials of Brownian Motion and Diffusion (Mathematical Surveys and Monographs)

Analysis of Monge-Ampere Equations: 240.S (Graduate Studies in Mathematics)

Attractors for Equations of Mathematical Physics (Colloquium Publications)

Functional Analytic Techniques for Diffusion Processes (Springer Monographs in Mathematics)

Functional Analytic Techniques for Diffusion Processes (Springer Monographs in Mathematics)

Games and Dynamics in Economics: Essays in Honor of Akio Matsumoto