Work

Linear-quadratic-Gaussian mean-field games driven by Poisson jumps with major and minor agents

Year: 2025

Type: article

Abstract: This paper studies mean-field linear-quadratic-Gaussian (LQG) games with a major agent and a large number of minor agents, where each agent's state process is driven by a Poisson random measure and independent Brownian motion. The major and minor agents were coupled via both their state dynamics as well as in their individual cost functionals. By the Nash certainty equivalence (NCE) methodology, two limiting control problems were constructed and the decentralized strategies were derived through the consistency condition. The $ \epsilon $-Nash equilibrium property of the obtained decentralized strategies was shown for a finite $ N $ population system where $ \epsilon = O(1/\sqrt{N}) $. A numerical example was presented to illustrate the consistency of the mean-field estimation and the impact of the population's collective behavior.

Source: AIMS Mathematics

DOI: 10.3934/math.2025503

Authors: Ruimin Xu, Kaiyue Dong, Jingyu Zhang, Ying Zhou

Institutions: Qilu University of Technology, Shandong Academy of Sciences

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province, Shandong Academy of Sciences, Qilu University of Technology