A Stochastic Linear-Quadratic Leader-Follower Differential Game with Elephant Memory

TL;DR

This paper develops a stochastic linear-quadratic leader-follower differential game model incorporating elephant memory, deriving explicit feedback strategies via Riccati equations, and illustrating the approach with a dynamic advertising example.

Contribution

It introduces a novel stochastic differential game model with elephant memory and provides explicit solution methods using Riccati equations.

Findings

Explicit feedback strategies derived for the game.

Theoretical framework validated with a dynamic advertising example.

Extension of LQ differential games to include elephant memory effects.

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.