Abstract
This paper is devoted to a mixed leadership stochastic differential game on a finite horizon in feedback information mode, where the control variables enter into the diffusion term of the 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. A necessary condition for the feedback Stackelberg–Nash equilibrium is obtained as well. Theoretic results are applied 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, feedback equilibrium strategies of innovation and pricing are explicitly expressed. Not only the local existence and uniqueness of the solutions of the coupled Riccati equations, but also some sufficient conditions for the existence of their solutions, are obtained. Some numerical simulation results are given to discuss the effects of model parameters on the feedback equilibrium strategies.
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