In this paper, we consider infinite horizon linear-quadratic Stackelberg games for a discrete-time stochastic system with multiple decision makers. Necessary conditions for the existence of the Stackelberg strategy set are derived in terms of the solvability of cross-coupled stochastic algebraic equations (CSAEs). As an important application, the hierarchical Hoo-constraint control problem for the infinite horizon discrete time stochastic system with multiple channel inputs is solved using the Stackelberg game approach. Computational methods for solving the CSAEs are also discussed. A numerical example is provided to demonstrate the usefulness of the proposed algorithms. (C) 2016 Elsevier Ltd. All rights reserved.