  This paper is devoted to a high-dimensional mixed leadership stochastic
differential game on a finite horizon in feedback information mode, where the
control variables enter into the diffusion term of state equation. A
verification theorem for the feedback Stackelberg-Nash equilibrium is obtained
by using a system of coupled and fully nonlinear parabolic partial differential
equations. We apply the verification theorem to deal with a dynamic innovation
and pricing decision problem where the buyer acts as the leader in the pricing
decisions and the dynamic model is stochastic. Via the solutions of coupled
Riccati equations, we explicitly express the feedback equilibrium strategies of
innovation and pricing. And by analysis, the local existence and uniqueness of
the solutions of the coupled Riccati equations is derived. We also conduct some
numerical analyses to discuss the effects of model parameters on the feedback
equilibrium strategies.
