Evolutionary dynamics of behavior in social networks

In this paper, we use evolutionary dynamics to understand the origin of social norms and dominant behavioral and cultural trends in social networks that lead to emergence of "hubs" such as few companies, politicians, celebrities, and fashion trends with overwhelming popular support. We define the notion of "behavior networks" and introduce a novel social choice model (i.e. mutation model) for evolutionary dynamics of behavior in social networks that exhibits a rich set of emergent phases of evolution. For behavioral networks with Watts-Strogatz small-world topology covering a broad range from highly clustered nearest-neighbor graphs to random graphs, we demonstrate the existence of S-shape phase transition curves relating diversity of behaviors to the mutation rate. This curve suggests the emergence of four key phases of behavior in the society ranging from one or a few dominant behaviors to collapse (or lack of dominance). Preliminary stability analysis and characterization of properties of equilibria are provided that suggest the proposed social choice model is plausible.