Incomplete Information Linear-Quadratic Mean-Field Games and Related Riccati Equations

TL;DR

This paper investigates linear-quadratic mean-field games with incomplete information, deriving decentralized strategies via Riccati equations and analyzing their equilibrium properties under common noise influence.

Contribution

It introduces a novel framework for mean-field games with incomplete information, incorporating common noise and control-dependent diffusion, and provides explicit strategies and equilibrium analysis.

Findings

Decentralized strategies are derived using Riccati equations.

The well-posedness of the mean-field consistency system is established.

An application to network security demonstrates the approach.

Abstract

We study a class of linear-quadratic mean-field games with incomplete information. For each agent, the state is given by a linear forward stochastic differential equation with common noise. Moreover, both the state and control variables can enter the diffusion coefficients of the state equation. We deduce the open-loop adapted decentralized strategies and feedback decentralized strategies by mean-field forward-backward stochastic differential equation and Riccati equations, respectively. The well-posedness of the corresponding consistency condition system is obtained and the limiting state-average turns out to be the solution of a mean-field stochastic differential equation driven by common noise. We also verify the $\varepsilon$-Nash equilibrium property of the decentralized control strategies. Finally, a network security problem is studied to illustrate our results as an application.