| Issue |
ESAIM: COCV
Volume 27, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
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|
|---|---|---|
| Article Number | S12 | |
| Number of page(s) | 31 | |
| DOI | https://doi.org/10.1051/cocv/2020056 | |
| Published online | 01 March 2021 | |
Social optima in leader-follower mean field linear quadratic control*
1
Department of Applied Mathematics, The Hong Kong Polytechnic University,
Hong Kong, PR China.
2
School of Control Science and Engineering, Shandong University,
Jinan, PR China.
** Corresponding author: tinghan.xie@connect.polyu.hk
Received:
23
January
2020
Accepted:
18
August
2020
This paper investigates a linear quadratic mean field leader-follower team problem, where the model involves one leader and a large number of weakly-coupled interactive followers. The leader and the followers cooperate to optimize the social cost. Specifically, for any strategy provided first by the leader, the followers would like to choose a strategy to minimize social cost functional. Using variational analysis and person-by-person optimality, we construct two auxiliary control problems. By solving sequentially, the auxiliary control problems with consistent mean field approximations, we can obtain a set of decentralized social optimality strategy with help of a class of forward-backward consistency systems. The relevant Stackelberg equilibrium is further proved under some proper conditions.
Mathematics Subject Classification: 91A12 / 91A23 / 91A25 / 93E03 / 93E20
Key words: Leader-follower problem / weakly-coupled stochastic system / linear quadratic control / social optimality / forward-backward stochastic differential equation
The first author acknowledges the financial support from: RGC 153005/14P, 153275/16P, P0030808; the second author acknowledges the support from: NNSF of China: 61773241; the third author acknowledges the support from: P0008686, P0031044; the authors also acknowledge the support from: the PolyU-SDU Joint Research Centre on Financial Mathematics.
© EDP Sciences, SMAI 2021
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