A Linear-quadratic Mean-Field Stochastic Stackelberg Differential Game with Random Exit Time

TL;DR

This paper develops a novel linear-quadratic mean-field stochastic Stackelberg differential game model with a leader who can exit at a random time, and derives the explicit Stackelberg solution using backward induction and optimal control techniques.

Contribution

It introduces a new mean-field Stackelberg game model with random exit time and provides a method to explicitly solve for the Stackelberg equilibrium.

Findings

Derived explicit Stackelberg solutions for the model.

Utilized backward induction, maximum principle, and verification theorem.

Addressed the leader's strategic stopping decision in the game.

Abstract

In this paper, we investigate a new model of a linear-quadratic mean-field stochastic Stackelberg differential game with one leader and two followers, in which the leader is allowed to stop her strategy at a random time. Our overarching goal is to find the Stackelberg solution of the leader and followers for such a model. By employing the backward induction method, the state equation is divided into two-stage equations. Moreover, by using the maximum principle and the verification theorem, the Stackelberg solution is obtained for such a model.