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Mean-Field Linear-Quadratic-Gaussian (LQG) Games for Stochastic Integral Systems

Authors :
Jianhui Huang
Tianxiao Wang
Xun Li
Source :
IEEE Transactions on Automatic Control. 61:2670-2675
Publication Year :
2016
Publisher :
Institute of Electrical and Electronics Engineers (IEEE), 2016.

Abstract

In this technical note, we formulate and investigate a class of mean-field linear-quadratic-Gaussian (LQG) games for stochastic integral systems. Unlike other literature on mean-field games where the individual states follow the controlled stochastic differential equations (SDEs), the individual states in our large-population system are characterized by a class of stochastic Volterra-type integral equations. We obtain the Nash certainty equivalence (NCE) equation and hence derive the set of associated decentralized strategies. The $\epsilon$ -Nash equilibrium properties are also verified. Due to the intrinsic integral structure, the techniques and estimates applied here are significantly different from those existing results in mean-field LQG games for stochastic differential systems. For example, some Fredholm equation in the mean-field setup is introduced for the first time. As for applications, two types of stochastic delayed systems are formulated as the special cases of our stochastic integral system, and relevant mean-field LQG games are discussed.

Details

ISSN :
15582523 and 00189286
Volume :
61
Database :
OpenAIRE
Journal :
IEEE Transactions on Automatic Control
Accession number :
edsair.doi...........05865c780b6ed2ff656e781d36e6f2c8
Full Text :
https://doi.org/10.1109/tac.2015.2506620