Fashion and Homophily

We analyze the evolution of fashion based on a network game model. Each agent in this model is either a conformist or a rebel. A conformist prefers to take the action most common among her neighboring agents, whereas a rebel prefers the opposite. When there is only one type of agent, the model possesses an exact potential function, implying that fashion cycles are unlikely to emerge in a homogeneous population. The homophily index, a measure of segregation in networks with multiple types of nodes, is shown to play a key role in the emergence of fashion cycles. Our main finding is that a lower homophily index, in general, promotes the emergence of fashion cycles. We establish this result through a potential analysis, a partial potential analysis, and a stability analysis of a system of ordinary differential equations that is approximated from a stochastic best response dynamic. Numerical simulations based on a variety of networks confirm that the approximate analysis is reliable