This talk is based on research with my colleagues Anamaria Berea and Bill Rand at the University of Maryland's Center for Complexity in Business. We all know that fashions come and go. A fashion may be "hot" one year, copied by everybody the next year, and then gone soon after. Why is that? To help answer the question, we build a mathematical model that describes fashion adoption behavior. Based on a small set of reasonable assumptions, derivations using differential equations show the inevitability of a fashion rising and then falling. The mechanism of the model is based on the existence of an "in group" and an "out group." The in group may be thought of as the rich, celebrities, etc. When a fashion gets a foothold among the in group it is more attractive to both the in group and the out group. At that point the out group starts to adopt the fashion, and as a result the in group is less interested in it. Fewer in group members now adopt the fashion, and eventually even the out group finds it less attractive, because the fashion is less popular among the in group. Thus the adoption curve goes up, and then goes down, for both the in group and the out group. We also show, using derivations, that the in group peak must occur before the out group peak. We further examine this scenario using agent-based models, to explore the conditions that affect how quickly all of this happens. Our conclusion is that the ups and downs of fashion may not just be based on whimsy. They may result instead from rational decisions by customers seeking to identify with the in group.

• Roland T. Rust(University of Maryland)