Linear-Quadratic Mixed Stackelberg-Nash Stochastic Differential Game with Major-Minor Agents
Optimization and Control
2019-05-28 v2
Abstract
We consider a controlled linear-quadratic (LQ) large-population system with mixture of three types agents: major leader, minor leaders and minor followers. The Stackelberg-Nash-Cournot (SNC) approximate equilibrium is studied by a major-minor mean-field game (MFG) coupled with a leader-follower Stackelberg game. By variational method, the SNC approximate equilibrium strategy can be represented by some forward-backward-stochastic-differential-equations (FBSDEs) in the open-loop sense. And we pay great effort to give the feedback form of the open-loop strategy by some Riccati equations.
Keywords
Cite
@article{arxiv.1905.09564,
title = {Linear-Quadratic Mixed Stackelberg-Nash Stochastic Differential Game with Major-Minor Agents},
author = {Kehan Si and James Huang and Zhen Wu},
journal= {arXiv preprint arXiv:1905.09564},
year = {2019}
}