MEAN FIELD GAMES: CONVERGENCE OF A FINITE DIFFERENCE METHOD

Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞ have been recently introduced by Lasry and Lions. Numerical methods for the approximation of the stationary and evolutive versions of such models have been proposed by the au...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 51; no. 5; pp. 2585 - 2612
Main Authors ACHDOU, YVES, CAMILLI, FABIO, CAPUZZO-DOLCETTA, ITALO
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Subjects
Applied mathematics
Approximation
Boundary conditions
Computer Science
Constraining
Convergence
Finite difference method
Games
Mathematical analysis
Mathematical models
Numerical Analysis
91A23
finite difference schemes
65M012
convergence AMS subject classifications 65M06
9108
Mean field games
49L25
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Summary:Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞ have been recently introduced by Lasry and Lions. Numerical methods for the approximation of the stationary and evolutive versions of such models have been proposed by the authors in previous works. Here, convergence theorems for these methods are proved under various assumptions on the coupling operator.
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ISSN:0036-1429
1095-7170
DOI:10.1137/120882421