Open-Loop Stackelberg Games for Stochastic Systems

Hiroaki MUKAIDANI  Hua XU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.4   pp.989-995
Publication Date: 2017/04/01
Online ISSN: 1745-1337
Type of Manuscript: PAPER
Category: Systems and Control
Keyword: 
Stackelberg games,  cross-coupled forward-backward stochastic differential equations (CFBSDEs),  open-loop strategy,  Newton's method,  

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Summary: 
This paper investigates open-loop Stackelberg games for a class of stochastic systems with multiple players. First, the necessary conditions for the existence of an open-loop Stackelberg strategy set are established using the stochastic maximum principle. Such conditions can be represented as solvability conditions for cross-coupled forward-backward stochastic differential equations (CFBSDEs). Second, in order to obtain the open-loop strategy set, a computational algorithm based on a four-step scheme is developed. A numerical example is then demonstrated to show the validity of the proposed method.