Reference groups and product line decisions: An experimental investigation of limited editions and product proliferation

Some luxury goods manufacturers offer limited editions of their products, whereas some others market multiple product lines. Researchers have found that reference groups shape consumer evaluations of these product categories. Yet little empirical research has examined how reference groups affect the product line decisions of firms. Indeed, in a field setting it is quite a challenge to isolate reference group effects from contextual effects and correlated effects. In this paper, we propose a parsimonious model that allows us to study how reference groups influence firm behavior and that lends itself to experimental analysis. With the aid of the model we investigate the behavior of consumers in a laboratory setting where we can focus on the reference group effects after controlling for the contextual and correlated effects. The experimental results show that in the presence of strong reference group effects, limited editions and multiple products can help improve firms' profits. Furthermore, the trends in the purchase decisions of our participants point to the possibility that they are capable of introspecting close to two steps of thinking at the outset of the game and then learning through reinforcement mechanisms. © 2010 INFORMS.

Sticky central limit theorems on open books

Given a probability distribution on an open book (a metric space obtained by gluing a disjoint union of copies of a half-space along their boundary hyperplanes), we define a precise concept of when the Fréchet mean (barycenter) is sticky. This nonclassical phenomenon is quantified by a law of large numbers (LLN) stating that the empirical mean eventually almost surely lies on the (codimension 1 and hence measure 0) spine that is the glued hyperplane, and a central limit theorem (CLT) stating that the limiting distribution is Gaussian and supported on the spine.We also state versions of the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on the spine) and partly sticky (i.e., is, on the spine but not sticky). © Institute of Mathematical Statistics, 2013.