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Article: Linear-Quadratic Mean Field Games

TitleLinear-Quadratic Mean Field Games
Authors
Issue Date2016
PublisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0022-3239
Citation
Journal of Optimization Theory and Applications, 2016, v. 169 n. 2, p. 496-529 How to Cite?
AbstractWe provide a comprehensive study of a general class of linear-quadratic mean field games. We adopt the adjoint equation approach to investigate the unique existence of their equilibrium strategies. Due to the linearity of the adjoint equations, the optimal mean field term satisfies a forward---backward ordinary differential equation. For the one-dimensional case, we establish the unique existence of the equilibrium strategy. For a dimension greater than one, by applying the Banach fixed point theorem under a suitable norm, a sufficient condition for the unique existence of the equilibrium strategy is provided, which is independent of the coefficients of controls in the underlying dynamics and is always satisfied whenever the coefficients of the mean field term are vanished, and hence, our theories include the classical linear-quadratic stochastic control problems as special cases. As a by-product, we also establish a neat and instructive sufficient condition, which is apparently absent in the literature and only depends on coefficients, for the unique existence of the solution for a class of nonsymmetric Riccati equations. Numerical examples of nonexistence of the equilibrium strategy will also be illustrated. Finally, a similar approach has been adopted to study the linear-quadratic mean field type stochastic control problems and their comparisons with mean field games.
Persistent Identifierhttp://hdl.handle.net/10722/234644
ISSN
2015 Impact Factor: 1.16
2015 SCImago Journal Rankings: 0.898

 

DC FieldValueLanguage
dc.contributor.authorBensoussan, A-
dc.contributor.authorSung, K.J.-
dc.contributor.authorYam, S.C.P.-
dc.contributor.authorYung, SP-
dc.date.accessioned2016-10-14T13:48:14Z-
dc.date.available2016-10-14T13:48:14Z-
dc.date.issued2016-
dc.identifier.citationJournal of Optimization Theory and Applications, 2016, v. 169 n. 2, p. 496-529-
dc.identifier.issn0022-3239-
dc.identifier.urihttp://hdl.handle.net/10722/234644-
dc.description.abstractWe provide a comprehensive study of a general class of linear-quadratic mean field games. We adopt the adjoint equation approach to investigate the unique existence of their equilibrium strategies. Due to the linearity of the adjoint equations, the optimal mean field term satisfies a forward---backward ordinary differential equation. For the one-dimensional case, we establish the unique existence of the equilibrium strategy. For a dimension greater than one, by applying the Banach fixed point theorem under a suitable norm, a sufficient condition for the unique existence of the equilibrium strategy is provided, which is independent of the coefficients of controls in the underlying dynamics and is always satisfied whenever the coefficients of the mean field term are vanished, and hence, our theories include the classical linear-quadratic stochastic control problems as special cases. As a by-product, we also establish a neat and instructive sufficient condition, which is apparently absent in the literature and only depends on coefficients, for the unique existence of the solution for a class of nonsymmetric Riccati equations. Numerical examples of nonexistence of the equilibrium strategy will also be illustrated. Finally, a similar approach has been adopted to study the linear-quadratic mean field type stochastic control problems and their comparisons with mean field games.-
dc.languageeng-
dc.publisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0022-3239-
dc.relation.ispartofJournal of Optimization Theory and Applications-
dc.rightsThe final publication is available at Springer via http://dx.doi.org/[insert DOI]-
dc.titleLinear-Quadratic Mean Field Games-
dc.typeArticle-
dc.identifier.emailYung, SP: spyung@hku.hk-
dc.identifier.authorityYung, SP=rp00838-
dc.identifier.doi10.1007/s10957-015-0819-4-
dc.identifier.hkuros269433-
dc.identifier.volume169-
dc.identifier.issue2-
dc.identifier.spage496-
dc.identifier.epage529-
dc.publisher.placeUnited States-

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