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arXiv · 2208.00347

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

Siyu Lv·Jie Xiong·Xin Zhang
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Abstract

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.

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Siyu Lv, Jie Xiong, Xin Zhang. 2022-07-31. Linear quadratic leader-follower stochastic differential games for mean-field switching diffusions. https://arxiv.org/abs/2208.00347

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