Communications in Information and Systems

Volume 21 (2021)

Number 3

Linear-quadratic mean field games with a major player: Nash certainty equivalence versus master equations

Pages: 441 – 471



Minyi Huang (School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada)


Mean field games with a major player were introduced in [26] 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 [26], master equations, and asymptotic solvability, which have been developed starting with different ideas. We establish their equivalence relationships.

This work is supported in part by Natural Sciences and Engineering Research Council (NSERC) of Canada.

Received 27 May 2020

Published 4 June 2021