Mean Field Social Control for Production Output Adjustment with Noisy Sticky Prices
DYNAMIC GAMES AND APPLICATIONS(2023)
Abstract
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.
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