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Linear-Quadratic Delayed Mean-Field Social Optimization

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Abstract

A linear quadratic (LQ) stochastic optimization problem with delay involving weakly-coupled large population is investigated in this paper. Different to classic mean field (MF) game, here agents cooperate with each other to minimize the so-called social objective. With the aid of delayed person-by-person optimality principle, one arrives at an auxiliary LQ delayed control problem by decentralized information. A decentralized strategy is obtained by feat of an MF type anticipated forward-backward stochastic differential delay equation (AFBSDDE) consistency condition. The discounting method with delay feature is employed to solve the consistency condition system. Finally, by some estimates of AFBSDDEs we derive the asymptotic social optimality.

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Funding

This work was supported by the National Key R &D Program of China (No. 2022YFA1006104), the National Natural Science Foundation of China (Nos. 12022108, 11971267, 12001320, 12371447, 11831010, 61961160732), the Natural Science Foundation of Shandong Province (Nos. ZR2022JQ01, ZR2019ZD42), the Taishan Scholars Climbing Program of Shandong (No. TSPD20210302), the Taishan Scholars Young Program of Shandong (No. TSQN202211032), the Distinguished Young Scholars Program and the Young Scholars Program of Shandong University.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, Shandong, 250100, China

    Tianyang Nie & Zhen Wu

  2. School of Management, Shandong University, Jinan, Shandong, 250100, China

    Shujun Wang

Authors
  1. Tianyang Nie
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  2. Shujun Wang
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  3. Zhen Wu
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by TN, SW and ZW. The first draft of the manuscript was written by TN and SW, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Shujun Wang.

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Nie, T., Wang, S. & Wu, Z. Linear-Quadratic Delayed Mean-Field Social Optimization. Appl Math Optim 89, 4 (2024). https://doi.org/10.1007/s00245-023-10067-5

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