A Three-level Stochastic Linear-quadratic Stackelberg Differential Game with Asymmetric Information

TL;DR

This paper develops a three-level stochastic linear-quadratic Stackelberg differential game model with asymmetric information among three players, providing a new equilibrium solution framework using Riccati equations.

Contribution

It introduces a novel three-level Stackelberg game with asymmetric information and derives a feedback equilibrium using a system of Riccati equations.

Findings

Derived explicit feedback Stackelberg equilibrium

Established the role of asymmetric information in hierarchical decision-making

Proposed a new Riccati-based solution method

Abstract

This paper is concerned with a three-level stochastic linear-quadratic Stackelberg differential game with asymmetric information, in which three players participate credited as Player 1, Player 2 and Player 3. Player 3 acts as the leader of Player 2 and Player 1, Player 2 acts as the leader of Player 1 and Player 1 acts as the follower. The asymmetric information considered is: the information available to Player 1 is based on the sub-$\sigma$-algebra of the information available to Player 2, and the information available to Player 2 is based on the sub-$\sigma$-algebra of the information available to Player 3. By maximum principle of forward-backward stochastic differential equations and optimal filtering, feedback Stackelberg equilibrium of the game is given with the help of a new system consisting of three Riccati equations.