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Article

Mean Field Game with Delay: A Toy Model

Department of Statistics & Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA
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Author to whom correspondence should be addressed.
Work supported by NSF grants DMS-1409434 and DMS-1814091.
Risks 2018, 6(3), 90; https://doi.org/10.3390/risks6030090
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)
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
MDPI and ACS Style

Fouque, J.-P.; Zhang, Z. Mean Field Game with Delay: A Toy Model. Risks 2018, 6, 90. https://doi.org/10.3390/risks6030090

AMA Style

Fouque J-P, Zhang Z. Mean Field Game with Delay: A Toy Model. Risks. 2018; 6(3):90. https://doi.org/10.3390/risks6030090

Chicago/Turabian Style

Fouque, Jean-Pierre, and Zhaoyu Zhang. 2018. "Mean Field Game with Delay: A Toy Model" Risks 6, no. 3: 90. https://doi.org/10.3390/risks6030090

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