Linear–Quadratic Mean-Field-Type Games: Jump–Diffusion Process With Regime Switching

Abstract

In this paper, we study a linear–quadratic mean-field-type game problem under jump–diffusion–regime switching state dynamics that include mean-field terms in the states and in the cost function. In the cost functional, we consider conditional variance of both the states and control actions, mean of both states and control actions, and covariance terms. The underlying problem is solved in a semiexplicit way by using the direct method.