Linear-Quadratic Mean Field Games with a Major Player: Nash certainty equivalence versus master equations

TL;DR

This paper compares three solution approaches for linear-quadratic mean field games with a major player, establishing their equivalence and clarifying their relationships within the rich structure of such models.

Contribution

It demonstrates the equivalence between Nash certainty equivalence, master equations, and asymptotic solvability in LQ mean field games with a major player.

Findings

Established the equivalence between NCE, master equations, and asymptotic solvability.

Clarified the relationships among different solution frameworks for major-minor mean field games.

Enhanced understanding of solution methods in complex LQ mean field game models.

Abstract

Mean field games with a major player were introduced in (Huang, 2010) within a linear-quadratic (LQ) modeling framework. Due to the rich structure of major-minor player models, the past ten years have seen significant research efforts for different solution notions and analytical techniques. For LQ models, we address the relation between three solution frameworks: the Nash certainty equivalence (NCE) approach in (Huang, 2010), master equations, and asymptotic solvability, which have been developed starting with different ideas. We establish their equivalence relationships.