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

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