Leader-follower stochastic differential game with asymmetric information and applications

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• 作者：Jingtao Shi^a ; ^{shijingtao@sdu.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Guangchen Wang^b ; ¹ ; ^{wguangchen@sdu.edu.cn" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Jie Xiong^c ; ^{jiexiong@umac.mo" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Leader&ndash ; follower stochastic differential game ; Asymmetric information ; Filtering ; Conditional mean-field forward&ndash ; backward stochastic differential equation ; Partial information linear&ndash ; quadratic control ; Open-loop Stackelberg equilibrium
• 刊名：Automatica
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：63
• 期：Complete
• 页码：60-73
• 全文大小：611 K

文摘

This paper is concerned with a leader–follower stochastic differential game with asymmetric information, where the information available to the follower is based on some sub-user=111111111&_pii=S0005109815004112&_rdoc=1&_issn=00051098&md5=1c9f671267c8b5eaae6e2437dc86dc1f" title="Click to view the MathML source">σ$\sigma$-algebra of that available to the leader. Such kind of game problem has wide applications in finance, economics and management engineering such as newsvendor problems, cooperative advertising and pricing problems. Stochastic maximum principles and verification theorems with partial information are obtained, to represent the Stackelberg equilibrium. As applications, a linear–quadratic leader–follower stochastic differential game with asymmetric information is studied. It is shown that the open-loop Stackelberg equilibrium admits a state feedback representation if some system of Riccati equations is solvable.