Robust Incentive Stackelberg Mean Field Stochastic Linear-Quadratic Differential Game with Model Uncertainty

TL;DR

This paper develops a robust incentive Stackelberg mean field game framework with model uncertainty, providing decentralized strategies and verifying their asymptotic optimality through theoretical analysis and a numerical example.

Contribution

It introduces a novel approach combining zero-sum game theory, mean field approximation, and duality to solve robust incentive Stackelberg games with model uncertainty.

Findings

Derived the leader's limiting cost functional and saddle points representation.

Established decentralized strategies for followers and the consistency condition system.

Verified the asymptotic robust incentive optimality of the strategies through a numerical example.

Abstract

This paper investigates a robust incentive Stackelberg stochastic differential game problem for a linear-quadratic mean field system, where the model uncertainty appears in the drift term of the leader's state equation. Moreover, both the state average and control averages enter into the leader's dynamics and cost functional. Based on the zero-sum game approach, mean field approximation and duality theory, firstly the representation of the leader's limiting cost functional and the closed-loop representation of decentralized open-loop saddle points are given, via decoupling methods. Then by convex analysis and the variational method, the decentralized strategies of the followers' auxiliary limiting problems and the corresponding consistency condition system are derived. Finally, applying decoupling technique, the leader's approximate incentive strategy set is obtained, under which the asymptotical robust incentive optimality of the decentralized mean field strategy is verified. A numerical example is given to illustrate the theoretical results.