On the Sequence of Customer Acquisitions and Pricing in the Model of Sales

The basic models of price dispersion due to Butters (1977) and Varian (1980), further developed by Narasimhan (1988), have been applied to a broad range of issues in industrial organization and marketing. Much of the previous research assumes that the captive and switcher segments are exogenously symmetric or asymmetric. We embed the Varian (1980) model in a broader setting that considers how captive/switcher customer segments are determined through customer acquisition. The customer segments are symmetric if sellers acquire customers simultaneously with setting prices. If customers are acquired before prices are set, then the equilibrium customer segments are asymmetric unless customer acquisitions are randomized and the marginal cost of customer acquisition increases at a sufficiently slow rate. If prices are set before customers are acquired, then the equilibrium customer segments are almost certainly asymmetric. With constant returns to scale, the customer segments are symmetric only if sellers acquire customers simultaneously with setting prices. * City University of Hong Kong; † Hanyang University; †† National University of Singapore. Corresponding author: Ivan Png, Department of Information Systems, National University of Singapore, 3 Science Drive 2, Singapore 117543, Tel: +65 6516-6807; http://www.comp.nus.edu.sg/~ipng/. This is an extensively revised version of an earlier paper with Il Horn Hann, “Sales and Promotions: A More General Model”. We thank seminar participants at Boston University, INSEAD, Tsinghua University, Chinese University of Hong Kong, and the University of Bern, Ioana Chioveanu, Bai Chong En, Yuxin Chen, and especially John Morgan for helpful advice and suggestions.