LEADER 03830nam 22006015 450 001 9910254083503321 005 20200704074335.0 010 $a3-319-38934-3 024 7 $a10.1007/978-3-319-38934-9 035 $a(CKB)3710000000861960 035 $a(DE-He213)978-3-319-38934-9 035 $a(MiAaPQ)EBC4689364 035 $a(PPN)195512227 035 $a(EXLCZ)993710000000861960 100 $a20160914d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRegularity Theory for Mean-Field Game Systems /$fby Diogo A. Gomes, Edgard A. Pimentel, Vardan Voskanyan 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (XIV, 156 p. 4 illus. in color.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 311 $a3-319-38932-7 320 $aIncludes bibliographical references and index. 327 $aPreface -- Introduction -- Explicit solutions, special transformations, and further examples -- Estimates for the Hamilton-Jacobi equation -- Estimates for the Transport and Fokker-Planck equations -- The nonlinear adjoint method -- Estimates for MFGs -- A priori bounds for stationary models -- A priori bounds for time-dependent models -- A priori bounds for models with singularities -- Non-local mean-field games - existence -- Local mean-field games - existence -- References -- Index. 330 $aBeginning with a concise introduction to the theory of mean-field games (MFGs), this book presents the key elements of the regularity theory for MFGs. It then introduces a series of techniques for well-posedness in the context of mean-field problems, including stationary and time-dependent MFGs, subquadratic and superquadratic MFG formulations, and distinct classes of mean-field couplings. It also explores stationary and time-dependent MFGs through a series of a-priori estimates for solutions of the Hamilton-Jacobi and Fokker-Planck equation. It shows sophisticated a-priori systems derived using a range of analytical techniques, and builds on previous results to explain classical solutions. The final chapter discusses the potential applications, models and natural extensions of MFGs. As MFGs connect common problems in pure mathematics, engineering, economics and data management, this book is a valuable resource for researchers and graduate students in these fields. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aGame theory 606 $aEconomic theory 606 $aSystem theory 606 $aGame Theory, Economics, Social and Behav. Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13011 606 $aEconomic Theory/Quantitative Economics/Mathematical Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/W29000 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 615 0$aGame theory. 615 0$aEconomic theory. 615 0$aSystem theory. 615 14$aGame Theory, Economics, Social and Behav. Sciences. 615 24$aEconomic Theory/Quantitative Economics/Mathematical Methods. 615 24$aSystems Theory, Control. 676 $a530.1595 700 $aGomes$b Diogo A$4aut$4http://id.loc.gov/vocabulary/relators/aut$0756063 702 $aPimentel$b Edgard A$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aVoskanyan$b Vardan$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254083503321 996 $aRegularity Theory for Mean-Field Game Systems$92141277 997 $aUNINA