Stackelberg strategies for stochastic systems with multiple followers

In this paper, Stackelberg games for linear stochastic systems governed by Itô differential equations with multiple followers are investigated. Stackelberg strategies are developed under two different settings, that is, the followers act either cooperatively to attain Pareto optimality or non-cooperatively to arrive at a Nash equilibrium. After establishing the necessary conditions to obtain Stackelberg strategies by using sets of cross-coupled algebraic nonlinear matrix equations (CANMEs), two numerical algorithms are developed based on Newton's method and the semidefinite programming (SDP) problem to solve the CANMEs. Finally, a numerical example is solved to demonstrate the validity of the algorithms.