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

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.

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

Received 27 May 2020

Published 4 June 2021