Closed-Loop Stackelberg Strategy for Linear-Quadratic Leader-Follower Game

TL;DR

This paper derives an explicit linear closed-loop Stackelberg strategy with one-step memory for linear-quadratic leader-follower games using Riccati equations and the constrained maximum principle, demonstrating improved performance over feedback strategies.

Contribution

It introduces a novel explicit solution for the closed-loop Stackelberg strategy with one-step memory in linear-quadratic games, addressing solvability challenges.

Findings

Explicit linear closed-loop strategy derived

Strategy outperforms feedback strategies in numerical tests

Uses Riccati equations and maximum principle for solution

Abstract

This paper is concerned with the closed-loop Stackelberg strategy for linear-quadratic leader-follower game. Completely different from the open-loop and feedback Stackelberg strategy, the solvability of the closed-loop solution even the linear case remains challenging. The main contribution of the paper is to derive the explicitly linear closed-loop Stackelberg strategy with one-step memory in terms of Riccati equations. The key technique is to apply the constrained maximum principle to the leader-follower game and explicitly solve the corresponding forward and backward difference equations. Numerical examples verify the effectiveness of the results, which achieves better performance than feedback strategy.