Role assignment is an important task in Role-Based Collaboration (RBC) and Adaptive Collaboration. There are many variations in the process of role assignment. An introduction of any new requirement leads to a significant change in the process and the complexity of the algorithm of role assignment. This paper formally identifies a group of problems in role assignment when multiple agents are involved; proposes initial solutions; conducts simulations and experiments to reveal the complexity of collective group role assignment, and indicates future work activities. The contributions of this paper include formal provision of taxonomy for collective group role assignment and indication of the complexities arising from of this type of problem through simulations and experiments.