Retraction

Abstract

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.