Stable Beneficial Group Activity Formation

Computational models are one of the very powerful tools for expressing everyday situations that are derived from human interactions. In this paper, an investigation of the problem of forming beneficial groups based on the members' preferences and the coordinator's own strategy is presented . It is assumed that a coordinator has a good intention behind trimming members' preferences to meet the ultimate goal of forming the group. His strategy is justified and evaluated by Nash stability. There are two variations of the problem: the Anonymous Stable Beneficial Group Activity Formation and the General Stable Beneficial Group Activity Formation. The computational complexity of solving both variations has been analyzed. Finding stable groups needs non-polynomial time algorithm to be solved. A polynomial time solution is presented and enhanced with examples. Keywords—computational models; group formation; members' preferences; Nash stability