Linear Quadratic Mean Field Games -- Part I: The Asymptotic Solvability Problem

Abstract

This paper investigates the so-called asymptotic solvability problem in linear quadratic (LQ) mean field games. The model has asymptotic solvability if for all sufficiently large population sizes, the corresponding game has a set of feedback Nash strategies subject to a mild regularity requirement. We provide a necessary and sufficient condition and show that in this case the solution converges to a mean field limit. This is accomplished by developing a re-scaling method to derive a low dimensional ordinary differential equation (ODE) system, where a non-symmetric Riccati ODE has a central role.

arXiv commentPresented at the 23rd MTNS Internat. Symposium, Hong Kong, July 2018

References in corpus (1)

• Limiting Behavior of LQ Deterministic Infinite Horizon Nash Games with Symmetric Players as the Number of Players goes to Infinity

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