An individual-based evolutionary dynamics model for networked social behaviors

In this paper, an evolutionary dynamics model over a graph of connected individuals choosing between multiple behaviors is developed. This model emphasizes the individuality of the nodes, which arrive at individual behavioral choices primarily based on subjective individual preferences as well as individual mutation characteristics. We use the replicator-mutator dynamical equations to model the process of building individual behavioral inclinations. A dynamic graph, whose vertices are the individual members of society, is then constructed and the weighted adjacency matrix and individual fitness parameters are used to effect a social interaction model that is itself modeled based on the replicator-mutator dynamical equations. A notion of social diversity is defined for this individual-based social choice model. The individual-based social evolutionary model presented here relates to and generalizes three previous models appearing in the literature: the replicator-mutator social choice model, consensus algorithms, and an evolutionary dynamic model on graphs. The basic properties and conditions for the emergence of an absolutely dominant behavior over the social network are derived, and how the proposed model generalizes and relates to other work is also discussed.