Stackelberg Stochastic Differential Game with Asymmetric Noisy Observations

TL;DR

This paper studies a Stackelberg stochastic differential game with asymmetric noisy observations, deriving equilibrium strategies for a leader and follower with different observation capabilities.

Contribution

It introduces a novel framework for Stackelberg games with asymmetric noisy observations and derives explicit equilibrium strategies using Riccati equations.

Findings

Explicit equilibrium strategies derived for the game.

State estimate feedback representation obtained.

Theoretical results validated through a linear-quadratic example.

Abstract

This paper is concerned with a Stackelberg stochastic differential game with asymmetric noisy observation, with one follower and one leader. In our model, the follower cannot observe the state process directly, but could observe a noisy observation process, while the leader can completely observe the state process. Open-loop Stackelberg equilibrium is considered. The follower first solve an stochastic optimal control problem with partial observation, the maximum principle and verification theorem are obtained. Then the leader turns to solve an optimal control problem for a conditional mean-field forward-backward stochastic differential equation, and both maximum principle and verification theorem are proved. An linear-quadratic Stackelberg stochastic differential game with asymmetric noisy observation is discussed to illustrate the theoretical results in this paper. With the aid of some Riccati equations, the open-loop Stackelberg equilibrium admits its state estimate feedback representation.