2022/04/07 by Jiang, Chunmei, Li, Tongqing, Yu, Jie
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2204.03300
We study a mean field game problem arising from the production control for multiple firms with price stickiness in the commodity market. The price dynamics for each firm is described as a (controlled) jump-diffusion process with mean-field interaction. Each firm aims to maximize her expectation of cumulative net profit coupled with each other through price processes. By solving the limiting control problem and a fixed-point problem, we construct an explicit approximating Nash equilibrium when the number of firms grows large.