Mean Field Game with Delay: a Toy Model

Jean-Pierre Fouque; Zhaoyu Zhang

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arXiv · 1807.04795

Mean Field Game with Delay: a Toy Model

Jean-Pierre Fouque·Zhaoyu Zhang

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Abstract

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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Jean-Pierre Fouque, Zhaoyu Zhang. 2018-07-12. Mean Field Game with Delay: a Toy Model. https://arxiv.org/abs/1807.04795

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