Cooperative differential games with continuous updating using Hamilton–Jacobi–Bellman equation. (2nd November 2021)

• Record Type: Journal Article
• Authors: Petrosian, Ovanes; Tur, Anna; Wang, Zeyang; Gao, Hongwei
• Is Part Of: Optimization methods and software. Volume 36:Number 6(2021)
• Page Start: 1099
• Page End: 1127
• Publication Date: 2021-11-02
• Subjects: Differential game with continuous updating -- differential game with dynamic updating -- cooperative differential game with continuous updating -- cooperative differential game with dynamic updating -- time consistency -- cooperative strategies -- characteristic function; 49L20 -- 49N70 -- 91A12 -- 91A23; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1802456
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : This paper examines a class of cooperative differential games with continuous updating. Here it is assumed that at each time instant players have or use information about the game structure defined for a closed time interval with fixed duration. The current time continuously evolves with the updating interval. The main problems considered in a cooperative setting with continuous updating is how to define players' cooperative behaviour, how to construct a cooperative trajectory, how to define the characteristic function and how to arrive at a cooperative solution. This paper also addresses the properties of the solution and presents some techniques to fix the process by which a cooperative solution is constructed. Theoretical results are demonstrated on a differential game model of non-renewable resource extraction, initial and continuous updating versions are also considered. Comparison of cooperative strategies, trajectories, characteristic functions and corresponding Shapley values is presented.