Mean field production output control with sticky prices: Nash and social solutions

This paper presents an application of mean field control to dynamic production optimization with sticky prices and adjustment costs. Both noncooperative and cooperative solutions are considered. 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. A numerical example is given to compare market prices, firms’ outputs and costs under the two solution frameworks