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An asymmetric information mean‐field type linear‐quadratic stochastic Stackelberg differential game with one leader and two followers
Author(s) -
Wang Guangchen,
Wang Yu,
Zhang Susu
Publication year - 2020
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2585
Subject(s) - stackelberg competition , differential game , stochastic differential equation , mathematics , riccati equation , type (biology) , state (computer science) , differential equation , mathematical optimization , mathematical economics , mathematical analysis , algorithm , ecology , biology
Summary This paper is concerned with an asymmetric information linear‐quadratic (AILQ) stochastic Stackelberg differential game with one leader and two followers, where the game system is governed by mean‐field type stochastic differential equation (MF‐SDE). With the help of two systems of Riccati equations, the followers solve a MF‐type stochastic LQ game problem with partial information first, and then, the leader turns to address an optimal control problem driven by linear MF‐type forward‐backward stochastic differential filtering equation (MF‐FBSDFE). By maximum principle, direct construction method and optimal filtering, the open‐loop Stackelberg solution is expressed as a feedback form of state, state estimation, and state mean.