Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource

TL;DR

This paper develops a framework for solving linear quadratic mean field type control problems with common noise, linking them to mean field games, and applies it to an economic model of exhaustible resource production.

Contribution

It introduces a solution approach using Riccati equations for mean field type control with common noise and connects it to mean field games, with an application to resource economics.

Findings

Solution via Riccati equations for control and game problems

Connection established between mean field control and mean field games

Application to modeling exhaustible resource production

Abstract

We study a general linear quadratic mean field type control problem and connect it to mean field games of a similar type. The solution is given both in terms of a forward/backward system of stochastic differential equations and by a pair of Riccati equations. In certain cases, the solution to the mean field type control is also the equilibrium strategy for a class of mean field games. We use this fact to study an economic model of production of exhaustible resources. Keywords: mean field type control, mean field games, linear-quadratic, optimal control, riccati equations, exhaustible resource production