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

Abstract

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.

Mean‐field games for multiagent systems with multiplicative noises

“…For instance, R is allowed to be negative in Section 4. In the work of Wang and Huang, is not semipositive definite.…”

Indefinite Linear Quadratic Mean Field Social Control with Multiplicative Noise

“…By combining mean field approximations and individual best response, the dimensionality difficulty can be overcome. Mean field games and control have found wide applications, including smart grids [29], [10], finance, economics [15], [9], [40], [22], and social networks [5], etc.…”

“…The state weight Q and control weight R in the cost functional are not limited to be positive semi-definite. In fact, an indefinite Q or R may naturally occur in a wide class of practical problems, including production adjustment [40], uncertain systems [17], and portfolio selection [53].…”

Robust linear quadratic mean field social control: A direct approach

“…The mean field game (MFG) [9,34], a very powerful tool in solving problems with large-population characteristic, is applied in many fields such as information technology and engineering [15,28,31], crowd motion [1,8,33], finance and economics [13,19,47,49], vaccination and medicine [5,12,21,24,35], especially for the following recent papers connected to the COVID-19 pandemic [2,14,17]. The mean field optimal control problem, a special class of control problems, is introduce in [6,11].…”