Shelf space strategy in long-tail markets

Shelf space strategy in long-tail markets R. Alexander Bentley Anthropology Department, Durham University Durham DH1 3HN UK r.a.bentley@durham.ac.uk Paul Ormerod Institute of Advanced Study, Durham University Volterra Consulting Ltd. London SW14 8AE, UK pormerod@volterra.co.uk Mark E. Madsen Department of Anthropology, University of Washington Seattle, WA 98195 USA madsenm@u.washington.edu October 30, 2018 Abstract The Internet is known to have had a powerful impact on on-line retailer strategies in markets characterised by long-tail distribution of sales [1]. Such retailers can exploit the long tail of the market, since they are effectively without physical limit on the number of choices on offer. Here we examine two extensions of this phenomenon. First, we introduce turnover into the long-tail distribution of sales. Although over any given period such as a week or a month, the distribution is right-skewed and often power law distributed, over time there is considerable turnover in the rankings of sales of individual products. Second, we establish some initial results on the implications for shelf-space strategy of physical retailers in such markets. 1 Introduction In his recent book, The Long Tail, Chris Anderson [2] qualitatively reviews how the Internet changes the dynamics of markets characterized by long-tailed distributions of sales, such that a few titles sell enormous amounts and most titles (the long tail) sell very little (Figure 1). Recog- nized at least since the early 20th century [32, 23, 44] long-tailed distributions (and, specifically, power law distributions) in economics and society have been an exceedingly popular subject in the last 15 years [10, 4, 5, 9, 18, 19, 25, 24, 26, 27, 29]. Although power laws have become a well-worn subject, with multiple potential causes rec- ognized [26], Anderson [1, 2] usefully identified a profound transition associated with the rise of Internet retailers, who can exploit the long tail of the market, as they are effectively without physical limit on the number of choices they can offer. A retailer in a physical building, of course, 1 arXiv:0808.1655v2 [q-fin.GN] 19 Aug 2008 Figure 1: Anderson’s [1, 2] model of profit thresholds in an economy characterised by power law sales distributions, and physical retailers (real items from real shelves), digital retailers (digital goods from digital shelves) and hybrid retailers (physical goods from digital shelves). cannot afford the space to stock the low-selling items beyond some point in the long tail (Figure 1). In a simplified sense, if a retailer has space for y different items in the store, then a reasonable strategy is to stock the top y best-selling items, as determined by market data. In contrast, an Internet retailer can sell items within the long tail, which can yield sales (area under the curve) comparable to those of the physical retailers selling the blockbusters at the top end (Figure 1). Of course, in practice a retailer may want to follow alternative strategies from the one of stocking the top y products. Profit margins, for example, might be higher on certain products with low sales, the retailer may feel that specializing in a ‘niche’ in the particular market may increase the chances of survival, and so on. But for a retailer selling into the mass market, a good initial strategy to consider is one of selling the top y items. It is this strategy which we analyse and for which we establish initial results. A crucial factor to take into account is the turnover in the sales (and hence the rankings) of individual products. The distribution in Figure 1 is of course a stylized representation of the power law distribution of sales at a given point in time. Over time, the relative popularity of the sales of the individual products will change. So although the distribution of sales may look very similar over time, taking snapshots of it at different points in time, the positions of the individual items within it will vary. Indeed, in most fashion markets new items will constantly enter the market. We consider a fashion-based model of consumer choice which is capable of generating power law distributions of sales such as are observed in practice, and which takes into account both turnover over time in the relative sales of a given set of items, and innovation in the sense that entirely new items become offered for sale. The model has antecedents in the neutral model of population dynamics in biology [20, 28], but its relevance to long-tail consumer markets has been demonstrated by studies that show that the model is capable of explaining both the distribution of outcomes and the turnover over time in, for example, pop music, first names and dog breeds in the United States [21, 22, 6]. 2 2 A fashion based model of consumer choice Standard consumer choice theory in economics assumes atomised individuals exercise choice in an attempt to maximise utility subject to a budget constraint. In this approach, given an indi- vid

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