Regularity Theory for Mean-Field Game Systems (SpringerBriefs in Mathematics)

Author: Gomes, Diogo A. A.

Brand: Springer

Edition: 1st ed. 2016

Number Of Pages: 170

EAN: 9783319389325

Release Date: 22-09-2016

Package Dimensions: 9.3 x 6.1 x 0.4 inches

Languages: English

Binding: paperback

Part Number: 44838126

Details: Beginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields.