Regularity Theory for Mean-Field Game Systems

Nonfiction, Science & Nature, Mathematics, Game Theory, Business & Finance, Economics, Theory of Economics
Cover of the book Regularity Theory for Mean-Field Game Systems by Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan, Springer International Publishing
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Author: Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan ISBN: 9783319389349
Publisher: Springer International Publishing Publication: September 14, 2016
Imprint: Springer Language: English
Author: Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan
ISBN: 9783319389349
Publisher: Springer International Publishing
Publication: September 14, 2016
Imprint: Springer
Language: English

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.

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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.

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