Existence of k -People Stable Alliance in n -Player Cooperative Games
This paper considers the existence of a stable k-cooperative alliance with a nonempty core in an n-person cooperative game on the premise that the Nash negotiation solution is the distribution criterion. First, the situation of a two-person alliance is examined, and the concept of stable two-person alliance is given and further proves that there must be a stable two-person alliance in n-person cooperative games. Then, analyze the stable k-man alliance and give a sufficient condition for the existence of a stable k-person alliance. Further, an algorithm is designed to find a match equivalent to the existence of a stable k-league alliance. In addition, this article also provides sufficient conditions for the benefits of all players in a k-man alliance to lie in its internal suballiance. Finally, an example is given to verify the feasibility of the theory and method in this paper.
Journal of Testing and Evaluation
Tao, Zheng; Hu, Yuanwei; Pan, Ziyi; Zhao, Junyi; and Xing, Dongao, "Existence of k -People Stable Alliance in n -Player Cooperative Games" (2021). Kean Publications. 1005.