The Master Equation and the Convergence Problem in Mean Field Games ― Ams-201
- 系列名：Annals of Mathematics Studies
- ISBN13：9780691190709
- 出版社：Princeton Univ Pr
- 作者：Pierre Cardaliaguet; Fran蔞is Delarue; Jean-michel Lasry; Pierre-Louis Lions
- 裝訂／頁數：精裝／192頁
- 規格：24.8cm*16.5cm*1.9cm (高/寬/厚)
- 出版日：2019/08/13
商品簡介
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 originating 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.
作者簡介
您曾經瀏覽過的商品
購物須知
外文書商品之書封，為出版社提供之樣本。實際出貨商品，以出版社所提供之現有版本為主。部份書籍，因出版社供應狀況特殊，匯率將依實際狀況做調整。
無庫存之商品，在您完成訂單程序之後，將以空運的方式為你下單調貨。為了縮短等待的時間，建議您將外文書與其他商品分開下單，以獲得最快的取貨速度，平均調貨時間為1~2個月。
為了保護您的權益，「三民網路書店」提供會員七日商品鑑賞期(收到商品為起始日)。
若要辦理退貨，請在商品鑑賞期內寄回，且商品必須是全新狀態與完整包裝(商品、附件、發票、隨貨贈品等)否則恕不接受退貨。