Modelling of Individual Behaviour in the DeGroot--Friedkin Self-Appraisal Dynamics on Social Network

The DeGroot-Friedkin model describes how an individual's self-confidence in his or her own opinion evolves as that individual participates in a group discussing a sequence of topics; as the individual has more impact or less impact (termed social power) on a given topic discussion, his or her self-confidence increases or decreases due to the process of reflected self-appraisal. This paper proposes a broad generalisation of the DeGroot-Friedkin model by allowing each individual's self-appraisal process to be distorted by behavioural characteristics such as humility. We establish the generalised dynamical model for the evolution of individuals' social power (a measure of an individual's contribution to each topic discussion). For some types of individuals, whom we term “humble” and “unreactive”, results are provided on the existence of equilibria, whether such equilibria are unique, and convergence to said equilibria. Simulations are used to illustrate that networks of “emotional” individuals, who at times act like humble individuals and at other times like arrogant individuals, can have at least two attractive equilibria.