A Stochastic Linear-Quadratic Leader-Follower Differential Game with Elephant Memory
Optimization and Control
2025-02-19 v1
Abstract
This paper is concerned with a stochastic linear-quadratic leader-follower differential game with elephant memory. The model is general in that the state equation for both the leader and the follower includes the elephant memory of the state and the control, which are part of the diffusion term. Under certain assumptions, the state feedback representation of the open-loop Stackelberg strategy is derived by introducing two Riccati equations and a special matrix-valued equation. Finally, theoretical results are illustrated by means of an example concerning a dynamic advertising problem with elephant memory.
Keywords
Cite
@article{arxiv.2502.12437,
title = {A Stochastic Linear-Quadratic Leader-Follower Differential Game with Elephant Memory},
author = {Xinpo Li and Jingtao Shi},
journal= {arXiv preprint arXiv:2502.12437},
year = {2025}
}
Comments
28 pages, 2 figures