LQG Mean Field Games with a Major Agent: Nash Certainty Equivalence versus Probabilistic Approach

Understand

Mean field game (MFG) systems consisting of a major agent and a large number of minor agents were introduced in (Huang, 2010) in an LQG setup.

• The Nash certainty equivalence was used to obtain a Markovian closed-loop Nash equilibrium for the limiting system when the number of minor agents tends to infinity.
• In the past years several approaches to major--minor mean field game problems have been developed, principally (i) the Nash certainty equivalence and analytic approach, (ii) master equations, (iii) asymptotic solvability, and (iv) the probabilistic approach.
• For the LQG case, the recent work (Huang, 2021) establishes the equivalency of the Markovian closed-loop Nash equilibrium obtained via (i) with those obtained via (ii) and (iii).