# Linear quadratic leader-follower stochastic differential games for mean-field switching diffusions

arXiv: https://arxiv.org/abs/2208.00347 · HTML: https://mlsanity.com/paper/2208.00347/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2022.

## Built on by (most cited first, 2 of 2)

- [Entropy Regularized Reinforcement Learning for Zero-Sum Stochastic Differential Games in a Regime-Switching Jump-Diffusion Process](https://mlsanity.com/paper/2606.28669/) (2026)
- [Entropy-Regularized Reinforcement Learning for Linear-Quadratic Stackelberg Differential Games in Regime-Switching Diffusion Models](https://mlsanity.com/paper/2606.28671/) (2026)

## Abstract (arXiv)

In this paper, we consider a linear quadratic (LQ) leader-follower stochastic differential game for regime switching diffusions with mean-field interactions. One of the salient features of this paper is that conditional mean-field terms are included in the state equation and cost functionals. Based on stochastic maximum principles (SMPs), the follower's problem and the leader's problem are solved sequentially and an open-loop Stackelberg equilibrium is obtained. Further, with the help of the so-called four-step scheme, the corresponding Hamiltonian systems for the two players are decoupled and then the open-loop Stackelberg equilibrium admits a state feedback representation if some new-type Riccati equations are solvable.