Linear-Quadratic-Gaussian Mixed Games with Continuum-Parametrized Minor Players

We consider a mean field linear-quadratic-Gaussian game with a major player and a large number of minor players parametrized by a continuum set. The mean field generated by the minor players is approximated by a random process depending only on the initial state and the Brownian motion of the major...

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Bibliographic Details
Published inSIAM journal on control and optimization Vol. 50; no. 5; pp. 2907 - 2937
Main Authors Nguyen, Son Luu, Huang, Minyi
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2012
Subjects
Approximation
Brownian motion
Decision making
Game theory
Population
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ISSN0363-0129
1095-7138
DOI10.1137/110841217

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Summary:We consider a mean field linear-quadratic-Gaussian game with a major player and a large number of minor players parametrized by a continuum set. The mean field generated by the minor players is approximated by a random process depending only on the initial state and the Brownian motion of the major player, and this leads to two limiting optimal control problems with random coefficients, which are solved subject to a consistency requirement on the mean field approximation. The set of decentralized strategies constructed from the limiting control problems has an $\varepsilon$-Nash equilibrium property when applied to the large but finite population model. [PUBLICATION ABSTRACT]
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ISSN:0363-0129
1095-7138
DOI:10.1137/110841217