Discrete‐time indefinite mean field linear quadratic games with multiplicative noise

Abstract

AbstractThis paper considers discrete‐time mean field linear quadratic games with multiplicative noises, where the weighting matrices in the cost functions are allowed to be indefinite. First, by expanding the dimension of the systems, we present the necessary and sufficient condition for the existence of Nash equilibrium. Second, by solving the limiting optimal control problem, we design a set of decentralized control strategies, which is shown to be an ‐Nash equilibrium. Finally, a numerical example is given to illustrate the effectiveness of the proposed control strategies.