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Article: Linear-Quadratic Mean Field Games
Title | Linear-Quadratic Mean Field Games |
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Authors | |
Keywords | Adjoint equations Linear quadratic Mean field games Mean field type stochastic control problems |
Issue Date | 2016 |
Publisher | Springer 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? |
Abstract | We 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 Identifier | http://hdl.handle.net/10722/234644 |
ISSN | 2021 Impact Factor: 2.189 2020 SCImago Journal Rankings: 1.109 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Bensoussan, A | - |
dc.contributor.author | Sung, K.J. | - |
dc.contributor.author | Yam, S.C.P. | - |
dc.contributor.author | Yung, SP | - |
dc.date.accessioned | 2016-10-14T13:48:14Z | - |
dc.date.available | 2016-10-14T13:48:14Z | - |
dc.date.issued | 2016 | - |
dc.identifier.citation | Journal of Optimization Theory and Applications, 2016, v. 169 n. 2, p. 496-529 | - |
dc.identifier.issn | 0022-3239 | - |
dc.identifier.uri | http://hdl.handle.net/10722/234644 | - |
dc.description.abstract | We 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.language | eng | - |
dc.publisher | Springer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0022-3239 | - |
dc.relation.ispartof | Journal of Optimization Theory and Applications | - |
dc.rights | The final publication is available at Springer via http://dx.doi.org/[insert DOI] | - |
dc.subject | Adjoint equations | - |
dc.subject | Linear quadratic | - |
dc.subject | Mean field games | - |
dc.subject | Mean field type stochastic control problems | - |
dc.title | Linear-Quadratic Mean Field Games | - |
dc.type | Article | - |
dc.identifier.email | Yung, SP: spyung@hku.hk | - |
dc.identifier.authority | Yung, SP=rp00838 | - |
dc.identifier.doi | 10.1007/s10957-015-0819-4 | - |
dc.identifier.scopus | eid_2-s2.0-84945273282 | - |
dc.identifier.hkuros | 269433 | - |
dc.identifier.volume | 169 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 496 | - |
dc.identifier.epage | 529 | - |
dc.identifier.isi | WOS:000374861300008 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 0022-3239 | - |