There are indeed connections between the invariant measure approximation of MV-SDEs and mean-field game theory that offer avenues for further exploration. Mean-field game theory deals with the study of strategic interactions among a large number of agents, where each agent's behavior depends on the distribution of the entire population. In the context of MV-SDEs, the invariant measure represents the long-term distribution of the system, capturing the collective behavior of all particles. By drawing parallels between the invariant measure approximation and mean-field game theory, researchers can potentially leverage insights from one field to enhance understanding in the other. Exploring these connections further could lead to the development of novel methodologies for analyzing and solving both MV-SDEs and mean-field games, offering new perspectives on complex systems with interacting components.