Issue |
ESAIM: COCV
Volume 31, 2025
|
|
---|---|---|
Article Number | 8 | |
Number of page(s) | 27 | |
DOI | https://doi.org/10.1051/cocv/2024087 | |
Published online | 31 January 2025 |
ϵ-Nash equilibrium of anticipative large-population LQ game with partial observations
1
School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, PR China
2
School of Big Data and Computer Science, Guizhou Normal University, Guiyang 550025, PR China
* Corresponding author: yonghuizhou@gznu.edu.cn
Received:
14
January
2024
Accepted:
29
January
2024
In this paper, we study a class of large-population linear-quadratic game problem that is driven by an anticipative signal-observation system with a correlation between the initial value of the signal and the observation noise. Firstly, we utilize a method of enlargement of filtration to transform the anticipative signal-observation system into a higher-dimensional non-anticipative one, and construct an extended equivalent large-population adapted game problem. Secondly, for each individual, by separation principle, filtering theory, and squared compensatory technology, we derive a closed-form decentralized equilibrium strategy for a limiting adapted version with a freezing term instead of average state, and obtain a consistency condition consisting of a forward-backward stochastic differential system with the coefficients affected by the correlation function. Finally, we prove for the extended equivalent large-population adapted game, the ϵ-Nash equilibrium properties of the decentralized strategy designed by means of locally observed information.
Mathematics Subject Classification: 60H10 / 60H30 / 93E20
Key words: Anticipative large-population LQ game / partial observation / enlargement of filtration / decentralized equilibrium strategy / filtering equation / ϵ-Nash equilibrium
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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