Three-Level Multi-Leader-Follower Incentive Stackelberg Differential Game with $H_\infty$ Constraint

TL;DR

This paper develops a hierarchical incentive Stackelberg differential game framework with $H_ fty$ constraints, optimizing system performance under worst-case disturbances using control theory and game analysis.

Contribution

It introduces a novel three-level incentive Stackelberg game model incorporating $H_ fty$ constraints and provides a method to derive the optimal strategies using advanced control and convex analysis techniques.

Findings

Established the existence of the incentive strategy set.

Derived the top leader's team-optimal solution.

Validated the approach with a numerical example.

Abstract

This paper is concerned with a three-level multi-leader-follower incentive Stackelberg game with $H_\infty$ constraint. Based on $H_2/H_\infty$ control theory, we firstly obtain the worst-case disturbance and the team-optimal strategy by dealing with a nonzero-sum stochastic differential game. The main objective is to establish an incentive Stackelberg strategy set of the three-level hierarchy in which the whole system achieves the top leader's team-optimal solution and attenuates the external disturbance under $H_\infty$ constraint. On the other hand, followers on the bottom two levels in turn attain their state feedback Nash equilibrium, ensuring incentive Stackelberg strategies while considering the worst-case disturbance. By convex analysis theory, maximum principle and decoupling technique, the three-level incentive Stackelberg strategy set is obtained. Finally, a numerical example is given to illustrate the existence of the proposed strategy set.