TY - BOOK ID - 32842123 TI - Probabilistic Theory of Mean Field Games with Applications II : Mean Field Games with Common Noise and Master Equations AU - Carmona, René. AU - Delarue, François. PY - 2018 SN - 3319564366 3319564358 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Mean field theory. KW - Game theory. KW - Mathematics. KW - Partial differential equations. KW - Calculus of variations. KW - Probabilities. KW - Economic theory. KW - Probability Theory and Stochastic Processes. KW - Calculus of Variations and Optimal Control; Optimization. KW - Partial Differential Equations. KW - Economic Theory/Quantitative Economics/Mathematical Methods. KW - Many-body problem KW - Statistical mechanics KW - Games, Theory of KW - Theory of games KW - Mathematical models KW - Mathematics KW - Distribution (Probability theory. KW - Mathematical optimization. KW - Differential equations, partial. KW - Economic theory KW - Political economy KW - Social sciences KW - Economic man KW - Partial differential equations KW - Optimization (Mathematics) KW - Optimization techniques KW - Optimization theory KW - Systems optimization KW - Mathematical analysis KW - Maxima and minima KW - Operations research KW - Simulation methods KW - System analysis KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - Isoperimetrical problems KW - Variations, Calculus of KW - Probability KW - Statistical inference KW - Combinations KW - Chance KW - Least squares KW - Mathematical statistics KW - Risk UR - https://www.unicat.be/uniCat?func=search&query=sysid:32842123 AB - This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games. ER -