@inbook{798a3b8fe36d4288942fb52e889491b5,

title = "Non-local Mean-Field Games: Existence",

abstract = "MFGs where the Hamilton–Jacobi equation depends on the distribution of players in a non-local way make up an important group of problems. In many examples, this dependence is given by regularizing convolution operators. We split the discussion of non-local problems into two cases. First, we consider first-order MFGs. Here, semiconcavity bounds and the optimal control characterization of the Hamilton–Jacobi equation are the main tools. Next, we examine second-order MFGs. Here, the regularizing effects of parabolic equations and the L2 stability of the Fokker–Planck equation are the main ingredients of the proof.",

keywords = "Borel Probability Measure, Jacobi Equation, Parabolic Equation, Planck Equation, Viscosity Solution",

author = "Gomes, {Diogo A.} and Pimentel, {Edgard A.} and Vardan Voskanyan",

note = "Publisher Copyright: {\textcopyright} 2016, Springer International Publishing Switzerland.",

year = "2016",

doi = "10.1007/978-3-319-38934-9_10",

language = "English (US)",

series = "SpringerBriefs in Mathematics",

publisher = "Springer Science and Business Media B.V.",

pages = "125--130",

booktitle = "SpringerBriefs in Mathematics",

address = "Germany",

}