Noncooperative Game in Multi-controller System under Delayed and Asymmetric Information

TL;DR

This paper develops a method to find Nash equilibria in multi-controller systems with delayed and asymmetric information, using a common-private information approach and iterative Riccati equations.

Contribution

It introduces a novel decoupling technique for control and estimation in complex information structures, enabling explicit equilibrium solutions.

Findings

The proposed method converges to a steady-state solution.

Richer information sets lead to reduced costs for players.

Numerical examples validate the theoretical results.

Abstract

We address a noncooperative game problem in multi-controller system under delayed and asymmetric information structure. Under these conditions, the classical separation principle fails as estimation and control design become strongly coupled, complicating the derivation of an explicit Nash equilibrium. To resolve this, we employ a common-private information decomposition approach, effectively decoupling control inputs and state estimation to obtain a closed-form Nash equilibrium. By applying a forward iterative method, we establish the convergence of the coupled Riccati and estimation error covariance recursions, yielding both the steady-state Kalman filter and the Nash equilibrium. Furthermore, we quantify the impact of asymmetric information, proving that a richer information set reduces the costs for the corresponding player. Finally, numerical examples are provided to demonstrate the effectiveness of the results.