Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations

Li Chen, Peipei Zhou and Hua Xiao ()
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Li Chen: School of Science, China University of Mining and Technology, Beijing 100083, China
Peipei Zhou: School of Science, China University of Mining and Technology, Beijing 100083, China
Hua Xiao: School of Mathematics and Statistics, Shandong University, Weihai 264209, China

Mathematics, 2023, vol. 11, issue 13, 1-18

Abstract: In this paper, we study a kind of Stackelberg game where the controlled systems are described by backward stochastic differential delayed equations (BSDDEs). By introducing a new kind of adjoint equation, we establish the sufficient verification theorem for the optimal strategies of the leader and the follower in a general case. Then, we focus on the linear–quadratic (LQ) backward Stackelberg game with delay. The backward Stackelberg equilibrium is presented by the generalized fully coupled anticipated forward–backward stochastic differential delayed Equation (AFBSDDE), which is composed of anticipated stochastic differential equations (ASDEs) and BSDDEs. Moreover, we obtain the unique solvability of the AFBSDDE using the continuation method. As an application of the theoretical results, the pension fund problem with delay effect is considered.

Keywords: Stackelberg game; state delay; forward–backward stochastic differential equation; linear–quadratic problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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