Mean Field Production Output Control with Sticky Prices: Nash and Social Solutions

TL;DR

This paper applies mean field control to optimize production in markets with many firms, considering both competitive and cooperative strategies, and demonstrates their asymptotic optimality through theoretical analysis and numerical examples.

Contribution

It introduces a mean field control framework for production with sticky prices, deriving decentralized strategies for Nash and social optima, and analyzes their asymptotic properties.

Findings

Nash and social optimal strategies asymptotically attained

Performance of strategies estimated using passivity property

Numerical comparison of market prices and outputs

Abstract

This paper presents an application of mean field control to dynamic production optimization. Both noncooperative and cooperative solutions are considered. We first introduce a market of a large number of agents (firms) with sticky prices and adjustment costs. By solving auxiliary limiting optimal control problems subject to consistent mean field approximations, two sets of decentralized strategies are obtained and further shown to asymptotically attain Nash equilibria and social optima, respectively. The performance estimate of the social optimum strategies exploits a passivity property of the underlying model. A numerical example is given to compare market prices, firms' outputs and costs under two two solution frameworks.