000			05037cam a2200781 i 4500
001			on1105145193
003			OCoLC
005			20220908100159.0
006			m o d
007			cr cnu|||unuuu
008			190620s2019 nju ob 001 0 eng d
040			_aN$T _beng _erda _epn _cN$T _dN$T _dOCLCF _dJSTOR _dYDX _dEBLCP _dUKAHL _dDEGRU _dBRX _dGZS _dGZM _dOCLCQ _dGZS _dIEEEE _dOCLCO _dOCLCA _dOCLCQ _dOCLCO
019			_a1107577676
020			_a9780691193717 _q(electronic bk.)
020			_a0691193711 _q(electronic bk.)
020			_z9780691190709
029	1		_aAU@ _b000065541790
035			_a(OCoLC)1105145193 _z(OCoLC)1107577676
037			_a22573/ctvcjdck6 _bJSTOR
037			_a9452505 _bIEEE
050		4	_aQA269
072		7	_aMAT _x003000 _2bisacsh
072		7	_aMAT _x029000 _2bisacsh
072		7	_aMAT _x011000 _2bisacsh
072		7	_aMAT _x007020 _2bisacsh
082	0	4	_a519.3 _223
049			_aMAIN
100	1		_aCardaliaguet, Pierre, _eauthor. _965350
245	1	4	_aThe master equation and the convergence problem in mean field games / _cPierre Cardaliaguet, Fran�cois Delarue, Jean-Michel Lasry, Pierre-Louis Lions.
264		1	_aPrinceton, New Jersey : _bPrinceton University Press, _c2019.
264		4	_c�2019
300			_a1 online resource
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aAnnals of mathematics studies ; _vNumber 201
504			_aIncludes bibliographical references and index.
588	0		_aOnline resource; title from PDF title page (EBSCO, viewed June 21, 2019).
505	0	0	_tFrontmatter -- _tContents -- _tPreface -- _t1. Introduction -- _t2. Presentation of the Main Results -- _t3. A Starter: The First-Order Master Equation -- _t4. Mean Field Game System with a Common Noise -- _t5. The Second-Order Master Equation -- _t6. Convergence of the Nash System -- _tA. Appendix -- _tReferences -- _tIndex
520			_aThis 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.
590			_aIEEE _bIEEE Xplore Princeton University Press eBooks Library
650		0	_aGame theory. _96996
650		0	_aDifferential equations. _965351
650		0	_aMean field theory. _922729
650		6	_aTh�eorie des jeux. _965352
650		6	_a�Equations diff�erentielles. _965353
650		6	_aTh�eorie de champ moyen. _965354
650		7	_aMATHEMATICS _xApplied. _2bisacsh _95811
650		7	_aMATHEMATICS _xProbability & Statistics _xGeneral. _2bisacsh _95812
650		7	_aMATHEMATICS _xGame Theory. _2bisacsh _965355
650		7	_aDifferential equations. _2fast _0(OCoLC)fst00893446 _965351
650		7	_aGame theory. _2fast _0(OCoLC)fst00937501 _96996
650		7	_aMean field theory. _2fast _0(OCoLC)fst01013145 _922729
655		4	_aElectronic books. _93294
700	1		_aDelarue, Fran�cois, _d1976- _eauthor. _965356
700	1		_aLasry, J. M., _eauthor. _965357
700	1		_aLions, P. L. _q(Pierre-Louis), _eauthor. _965358
776	0	8	_iPrint version: _aCardaliaguet, Pierre. _tMaster Equation and the Convergence Problem in Mean Field Games : (ams-201). _dPrinceton : Princeton University Press, �2019 _z9780691190709
830		0	_aAnnals of mathematics studies ; _vno. 201. _965359
856	4	0	_uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=9452505
938			_aAskews and Holts Library Services _bASKH _nAH36452254
938			_aDe Gruyter _bDEGR _n9780691193717
938			_aProQuest Ebook Central _bEBLB _nEBL5791799
938			_aEBSCOhost _bEBSC _n2030557
938			_aYBP Library Services _bYANK _n16161200
942			_cEBK
994			_a92 _bINTKS
999			_c81445 _d81445