TY - JOUR
T1 - Social optima in leader-follower mean field linear quadratic control
AU - Huang, Jianhui
AU - Wang, Bing Chang
AU - Xie, Tinghan
N1 - Funding Information:
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.
Publisher Copyright:
© 2021 EDP Sciences, SMAI.
PY - 2021/3/1
Y1 - 2021/3/1
N2 - 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.
AB - 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.
KW - Forward-backward stochastic differential equation
KW - Leader-follower problem
KW - Linear quadratic control
KW - Social optimality
KW - Weakly-coupled stochastic system
UR - http://www.scopus.com/inward/record.url?scp=85101987560&partnerID=8YFLogxK
U2 - 10.1051/cocv/2020056
DO - 10.1051/cocv/2020056
M3 - Journal article
AN - SCOPUS:85101987560
SN - 1292-8119
VL - 27
SP - 1
EP - 31
JO - ESAIM - Control, Optimisation and Calculus of Variations
JF - ESAIM - Control, Optimisation and Calculus of Variations
M1 - 2020056
ER -