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Mean Field Game with Delay: A Toy Model

Department of Statistics & Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA
Author to whom correspondence should be addressed.
Work supported by NSF grants DMS-1409434 and DMS-1814091.
Risks 2018, 6(3), 90;
Received: 12 July 2018 / Revised: 17 August 2018 / Accepted: 20 August 2018 / Published: 1 September 2018
(This article belongs to the Special Issue Systemic Risk in Finance and Insurance)
PDF [417 KB, uploaded 4 September 2018]


We study a toy model of linear-quadratic mean field game with delay. We “lift” the delayed dynamic into an infinite dimensional space, and recast the mean field game system which is made of a forward Kolmogorov equation and a backward Hamilton-Jacobi-Bellman equation. We identify the corresponding master equation. A solution to this master equation is computed, and we show that it provides an approximation to a Nash equilibrium of the finite player game. View Full-Text
Keywords: inter-bank borrowing and lending; stochastic game with delay; Nash equilibrium; master equation inter-bank borrowing and lending; stochastic game with delay; Nash equilibrium; master equation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Fouque, J.-P.; Zhang, Z. Mean Field Game with Delay: A Toy Model. Risks 2018, 6, 90.

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