Backward-forward linear-quadratic mean-field Stackelberg games

Abstract This paper studies a controlled backward-forward linear-quadratic-Gaussian (LQG) large population system in Stackelberg games. The leader agent is of backward state and follower agents are forward state. dominating as its enters those agents. On the other hand, state-average all affects cost functional agent. In reality, followers may represent two typical types participants involved market price formation: supplier producers. differs from standard MFG literature mainly due to structure here. By variational analysis, consistency condition can be represented by some fully-coupled stochastic differential equations (BFSDEs) with high dimensional block an open-loop sense. Next, we discuss well-posedness such BFSDE virtue contraction mapping method. Consequently, obtain decentralized strategies for which proved satisfy ε -Nash equilibrium property.