Abstract
We consider a class of linear-quadratic-Gaussian mean-field games having a major agent and numerous heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex subsets Γk of Rm. The decentralized strategies of individual agents and the consistency condition system are represented in a unified manner through a class of mean-field forward-backward stochastic differential equations involving projection operators on Γk. The well-posedness of the consistency system is established in both the local and global cases through the contraction mapping and discounting methods, respectively. A related ε-Nash-equilibrium property is also verified.
Original language | English |
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Pages (from-to) | 2835-2877 |
Number of pages | 43 |
Journal | SIAM Journal on Control and Optimization |
Volume | 56 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1 Aug 2018 |
Keywords
- Forward-backward stochastic differential equation
- Input constraint
- Linear-quadratic mixed mean-field games
- Projection operator
- Ε-Nash equilibrium
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics