Approximating Nash Equilibrium for Production Control with Sticky Price

TL;DR

This paper develops an explicit approximation method for Nash equilibria in a mean field game modeling production control among many firms with sticky prices, using jump-diffusion processes and fixed-point analysis.

Contribution

It introduces a novel approach to approximate Nash equilibria in a mean field game with price stickiness and jump-diffusion dynamics, applicable to large numbers of firms.

Findings

Explicit Nash equilibrium approximation constructed for large firm populations

Method handles price stickiness and jump-diffusion dynamics effectively

Provides insights into optimal production control in commodity markets

Abstract

We study a mean field game problem arising from the production control for multiple firms with price stickiness in the commodity market. The price dynamics for each firm is described as a (controlled) jump-diffusion process with mean-field interaction. Each firm aims to maximize her expectation of cumulative net profit coupled with each other through price processes. By solving the limiting control problem and a fixed-point problem, we construct an explicit approximating Nash equilibrium when the number of firms grows large.