Mean Field Social Control for Production Output Adjustment with Noisy Sticky Prices

This paper is concerned with mean field social control for dynamic production adjustment. We first introduce a social control problem with many firms in a market, where the price is sticky and affected by random shocks. By tackling a centralized social control problem, we obtain a system of coupled forward–backward stochastic differential equations (FBSDEs). Decoupling the FBSDEs and applying mean field approximations, we design a set of decentralized strategies in terms of two Riccati equations. Such a set of decentralized strategies is shown to have asymptotic social optimality. The infinite-horizon problem is further considered and a neat condition is given to ensure asymptotic optimality of decentralized strategies.