Dynamic Task Performance, Cohesion, and Communications in Human Groups

In the study of the behavior of human groups, it has been observed that there is a strong interaction between the cohesiveness of the group, its performance when the group has to solve a task, and the patterns of communication between the members of the group. Developing mathematical and computational tools for the analysis and design of task-solving groups that are not only cohesive but also perform well is of importance in social sciences, organizational management, and engineering. In this paper, we model a human group as a dynamical system whose behavior is driven by a task optimization process and the interaction between subsystems that represent the members of the group interconnected according to a given communication network. These interactions are described as attractions and repulsions among members. We show that the dynamics characterized by the proposed mathematical model are qualitatively consistent with those observed in real-human groups, where the key aspect is that the attraction patterns in the group and the commitment to solve the task are not static but change over time. Through a theoretical analysis of the system we provide conditions on the parameters that allow the group to have cohesive behaviors, and Monte Carlo simulations are used to study group dynamics for different sets of parameters, communication topologies, and tasks to solve.