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Title: | Backward-forward linear-quadratic mean-field games with major and minor agents | Authors: | Huang, JH Wang, SJ Wu, Z |
Issue Date: | 2016 | Source: | Probability uncertainty and quantitative risk, 2016, v. 1, 8, p. 1-27 | Abstract: | This paper studies the backward-forward linear-quadratic-Gaussian (LQG) games with major and minor agents (players). The state of major agent follows a linear backward stochastic differential equation (BSDE) and the states of minor agents are governed by linear forward stochastic differential equations (SDEs). The major agent is dominating as its state enters those of minor agents. On the other hand, all minor agents are individually negligible but their state-average affects the cost functional of major agent. The mean-field game in such backward-major and forward-minor setup is formulated to analyze the decentralized strategies. We first derive the consistency condition via an auxiliary mean-field SDEs and a 3x2 mixed backward-forward stochastic differential equation (BFSDE) system. Next, we discuss the wellposedness of such BFSDE system by virtue of the monotonicity method. Consequently, we obtain the decentralized strategies for major and minor agents which are proved to satisfy the epsilon-Nash equilibrium property. | Keywords: | Backward-forward stochastic differential equation (BFSDE) Consistency condition Epsilon-Nash equilibrium Large-population system Major-minor agent Mean-field game |
Publisher: | Springer | Journal: | Probability uncertainty and quantitative risk | ISSN: | 2367-0126 | DOI: | 10.1186/s41546-016-0009-9 | Rights: | © The Author(s). 2016 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The following publication Huang, J. H., Wang, S. J., & Wu, Z. (2016). Backward-forward linear-quadratic mean-field games with major and minor agents. Probability Uncertainty and Quantitative Risk, 1, 8, 1-27 is available at https://dx.doi.org/10.1186/s41546-016-0009-9 |
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