Mean field social optima in production output adjustment

This paper studies social optima in the model of dynamic production competition by the mean field methodology. The objective of all agents (firms) is to optimize a social cost. We first introduce a market of a large number of firms with sticky prices and adjustment costs. The cost of each agent has indefinite state weights. By solving an auxiliary limiting optimal control problem subject to consistent mean field approximations, a set of decentralized strategies is obtained and further shown to be asymptotically optimal. The performance estimate will exploit a passivity property of the underlying model.