Overview
- Authors:
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Diogo A. Gomes
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CEMSE Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
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Edgard A. Pimentel
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Department of Mathematics, Universidade Federal de Sao Carlos, São Carlos, Brazil
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Vardan Voskanyan
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CEMSE Division, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
- Details key elements of the regularity theory for mean-field games
- Presents a series of techniques for well-posedness
- Explores stationary and time-dependent MFGs through a series of a-priori estimates?
- Includes supplementary material: sn.pub/extras
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Table of contents (11 chapters)
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- Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Pages 1-8
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- Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Pages 9-14
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- Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Pages 15-37
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- Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Pages 39-61
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- Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Pages 63-76
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- Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Pages 77-95
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- Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Pages 97-103
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- Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Pages 105-109
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- Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Pages 111-123
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- Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Pages 125-130
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- Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
Pages 131-144
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Back Matter
Pages 145-156
About this book
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.
Reviews
“This book is concerned with mean field game systems, or MFG systems for short. Such systems describe an infinite number of rational agents in competition. … The book is an accesible introduction to MFG systems, readable by anyone with a basic knowledge of partial differential equations.” (Teemu Lukkari, Mathematical Reviews, October, 2017)