arXiv:1807.04795 Abstract | arXiv Analytics

arXiv:1807.04795 [math.PR]Abstract References Reviews Resources

Mean Field Game with Delay: a Toy Model

Published 2018-07-12Version 1

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.

Categories: math.PR

Subjects: 91A15, 91G80, 60G99

Keywords: toy model, linear-quadratic mean field game, mean field game system, finite player game, infinite dimensional space

Related articles: Most relevant | Search more

arXiv:1310.7845 [math.PR] (Published 2013-10-29, updated 2014-03-28)

Kullback-Leibler Approximation for Probability Measures on Infinite Dimensional Spaces

Frank Pinski, Gideon Simpson, Andrew Stuart, Hendrik Weber

arXiv:1906.01220 [math.PR] (Published 2019-06-04)

Snackjack: A toy model of blackjack

Stewart N. Ethier, Jiyeon Lee

arXiv:2412.04336 [math.PR] (Published 2024-12-05)

On the Replica Symmetry of a Variant of the Sherrington-Kirkpatrick Spin Glass