A mean-field game economic growth model

TL;DR

This paper develops a mean-field game model for economic growth involving rational agents with capital and consumer goods, analyzing strategies, equilibrium prices, and providing numerical methods for computation.

Contribution

It introduces a novel MFG framework for economic growth with detailed analysis of strategies and market equilibrium, including numerical solution techniques.

Findings

Existence and uniqueness of optimal strategies established.

Numerical methods for computing strategies and prices developed.

Model captures complex interactions in economic growth dynamics.

Abstract

Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent seeks to maximize their utility by taking into account statistical data of the total population. The individual actions drive the evolution of the players, and a market-clearing condition determines the relative price of capital and consumer goods. We study the existence and uniqueness of optimal strategies of the agents and develop numerical methods to compute these strategies and the equilibrium price.