Linear-Quadratic Non-zero Sum Differential Game with Asymmetric Delayed Information

TL;DR

This paper studies a linear-quadratic differential game with two players experiencing different delays in information, deriving a Nash equilibrium using stochastic maximum principle and discretisation methods.

Contribution

It introduces a novel approach to handle asymmetric delayed information in non-zero sum differential games and derives the equilibrium explicitly.

Findings

Established the stochastic Hamiltonian system with delays

Derived the state-estimate feedback Nash equilibrium

Linked forward-backward processes under asymmetric delays

Abstract

This paper is concerned with a linear-quadratic non-zero sum differential game with asymmetric delayed information. To be specific, two players exist time delays simultaneously which are different, leading the dynamical system being an asymmetric information structure. By virtue of stochastic maximum principle, the stochastic Hamiltonian system is given which is a delayed forward-backward stochastic differential equation. Utilizing discretisation approach and backward iteration technique, we establish the relationship between forward and backward processes under asymmetric delayed information structure and obtain the state-estimate feedback Nash equilibrium of our problem.