Nash‐Based Stackelberg Strategy Under H∞ Constraint for Discrete‐time Stochastic Mean‐Field Systems

ABSTRACT

This paper is devoted to infinite‐horizon linear‐quadratic Nash‐based Stackelberg strategy under constraint for discrete‐time stochastic mean‐field systems. We use the Stackelberg game approach to deal with multiple inputs with one leader and multiple followers. Using the theory of exact observability, we obtain two main results. The first one is the sufficient conditions for the optimization of decision makers in terms of generalized algebraic Riccati equations (GAREs). The second one is the necessary conditions for the existence of a set of Nash‐based Stackelberg strategies under the constraint via cross‐coupled algebraic equations. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed results.