The Cooperative Mean Field Game for Production Control with Sticky Price

Lijun Bo , Tongqing Li

Communications in Mathematics and Statistics ›› : 1 -18.

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Communications in Mathematics and Statistics ›› : 1 -18. DOI: 10.1007/s40304-023-00370-6
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The Cooperative Mean Field Game for Production Control with Sticky Price

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Abstract

We study a cooperative 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 the so-called social rewards which is defined by the average of individual rewards for all firms. By solving the limiting control problem for the representative firm and an associated fixed-point problem, we construct an explicit approximating optimal strategy when the number of firms grows large.

Keywords

Production control / Sticky price / Social rewards / Cooperative mean field game

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Lijun Bo,Tongqing Li. The Cooperative Mean Field Game for Production Control with Sticky Price. Communications in Mathematics and Statistics 1-18 DOI:10.1007/s40304-023-00370-6

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National Natural Science Foundation of China(11971368)

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