  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.
