Mean Field Game with Delay: A Toy Model
Department of Statistics & Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA
Work supported by NSF grants DMS-1409434 and DMS-1814091.
Author to whom correspondence should be addressed.
Received: 12 July 2018 / Revised: 17 August 2018 / Accepted: 20 August 2018 / Published: 1 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.
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MDPI and ACS Style
Fouque, J.-P.; Zhang, Z. Mean Field Game with Delay: A Toy Model. Risks 2018, 6, 90.
Fouque J-P, Zhang Z. Mean Field Game with Delay: A Toy Model. Risks. 2018; 6(3):90.
Fouque, Jean-Pierre; Zhang, Zhaoyu. 2018. "Mean Field Game with Delay: A Toy Model." Risks 6, no. 3: 90.
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