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arXiv · 1710.02916

Linear-Quadratic-Gaussian Mixed Mean-field Games with Heterogeneous Input Constraints

Ying Hu·Jianhui Huang·Tianyang Nie
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Abstract

We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex subsets $Γ_{k}$ of $\mathbb{R}^{m}.$ The decentralized strategies for individual agents and consistency condition system are represented in an unified manner through a class of mean-field forward-backward stochastic differential equations involving projection operators on $Γ_{k}$. The well-posedness of consistency system is established in both the local and global cases by the contraction mapping and discounting method respectively. Related $\varepsilon-$Nash equilibrium property is also verified.

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Ying Hu, Jianhui Huang, Tianyang Nie. 2017-10-09. Linear-Quadratic-Gaussian Mixed Mean-field Games with Heterogeneous Input Constraints. https://arxiv.org/abs/1710.02916

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