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arXiv · 1905.09564

Linear-Quadratic Mixed Stackelberg-Nash Stochastic Differential Game with Major-Minor Agents

Kehan Si·James Huang·Zhen Wu
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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.

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Kehan Si, James Huang, Zhen Wu. 2019-05-23. Linear-Quadratic Mixed Stackelberg-Nash Stochastic Differential Game with Major-Minor Agents. https://arxiv.org/abs/1905.09564

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