We analyze the evolution of fashion based on a network game model. Each agent in this model is 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 agents, 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.

See Also:

“The Logic of Fashion Cycles”
“Fashion and art cycles are driven by counter-dominance signals of elite competition: quantitative evidence from music styles”
“The hipster effect: When anticonformists all look the same”
“α-Rank: Multi-Agent Evaluation by Evolution”
“Assortative mating and the evolution of desirability covariation”
“StreetStyle: Exploring world-wide clothing styles from millions of photos”
“Optimal Distinctiveness Revisited: an integrative framework for understanding the balance between differentiation and conformity in individual and organizational identities”