Mean Field Game with Delay: A Toy Model

Jean-Pierre Fouque and Zhaoyu Zhang
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Jean-Pierre Fouque: Department of Statistics & Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA
Zhaoyu Zhang: Department of Statistics & Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA

Risks, 2018, vol. 6, issue 3, 1-17

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.

Keywords: inter-bank borrowing and lending; stochastic game with delay; Nash equilibrium; master equation (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

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