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Mathematics > Optimization and Control

arXiv:1403.3999 (math)
[Submitted on 17 Mar 2014]

Title:Mean Field Linear-Quadratic-Gaussian (LQG) Games: Major and Minor Players

Authors:Jianhui Huang, Shujun Wang, Zhen Wu
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Abstract:This paper is concerned with a backward-forward stochastic differential equation (BFSDE) system, in which a large number of negligible agents are coupled in their dynamics via state average. Here some BSDE is introduced as the dynamics of major player, while dynamics of minor players are described by SDEs. Some auxiliary mean-field SDEs (MFSDEs) and a $3\times2$ mixed forward-backward stochastic differential equation (FBSDE) system are considered and analyzed instead of involving the fixed-point analysis as in other mean-field games. We also derive the decentralized strategies which are shown to satisfy the $\epsilon$-Nash equilibrium property.
Comments: 17 pages
Subjects: Optimization and Control (math.OC); Probability (math.PR)
Cite as: arXiv:1403.3999 [math.OC]
  (or arXiv:1403.3999v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1403.3999

Submission history

From: Shujun Wang [view email]
[v1] Mon, 17 Mar 2014 04:54:24 UTC (13 KB)
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