Existence of value functions of differential games with incomplete information in partially order spaces. (4th May 2023)

• Record Type: Journal Article
• Authors: Shao, Menghao; Hong, Shihuang; Cao, Xiaoyu; Luo, Xinggang
• Is Part Of: Optimization. Volume 72:Number 5(2023)
• Page Start: 1285
• Page End: 1307
• Publication Date: 2023-05-04
• Subjects: Two-person zero-sum differential game -- incomplete information -- generalized contraction -- probability distribution -- value function; 49L25 -- 49L99; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.2011867
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we consider a two-person zero-sum differential game with incomplete information on the initial state, namely, the first player has a private information while the second player knows only a probability distribution on the initial state, and obtain the existence of its value functions. The main novelty lies in the method for which we apply a generalized weak contraction for dynamic systems and terminal cost functions instead of the Lipschitz contractive condition on a partially ordered metric space.