$\epsilon$-Nash Equilibria for Major Minor LQG Mean Field Games with Partial Observations of All Agents

TL;DR

This paper develops a framework for $ ext{epsilon}$-Nash equilibria in major-minor linear-quadratic-Gaussian mean field games with partial observations, addressing recursive estimation challenges and establishing equilibrium existence.

Contribution

It introduces a novel analysis of partial observation patterns in major-minor LQG mean field games and proves the existence of $ ext{epsilon}$-Nash equilibria using the Separation Principle.

Findings

Existence of $ ext{epsilon}$-Nash equilibria established.

Control laws for agents are derived under partial observations.

Recursive estimation of the major agent's state is incorporated.

Abstract

The partially observed major minor LQG and nonlinear mean field game (PO MM LQG MFG) systems where it is assumed the major agent's state is partially observed by each minor agent, and the major agent completely observes its own state have been analysed in the literature. In this paper, PO MM LQG MFG problems with general information patterns are studied where (i) the major agent has partial observations of its own state, and (ii) each minor agent has partial observations of its own state and the major agent's state. The assumption of partial observations by all agents leads to a new situation involving the recursive estimation by each minor agent of the major agent's estimate of its own state. For a general case of indefinite LQG MFG systems, the existence of $\epsilon$-Nash equilibria together with the individual agents' control laws yielding the equilibria are established via the Separation Principle.