Retail Price Competition with Product Fit Uncertainty and Assortment Selection

For many products, consumers need to physically experience them in order to assess their own valuations. We study how the equilibrium pricing among competing retailers depend upon assortments when consumers must search for this sort of fit information and are heterogeneous in their shopping behaviors. Specifically, we consider a market that consists of two retailers and two possible products. A consumer is either loyal to one of the retailers or is a shopper who follows a rational dynamic search process based on the prices and available assortments. We demonstrate how the retailers' equilibrium pricing strategies depend upon their assortment choices and the resulting search process. Among other things, we show that, when the retailers carry non-overlapping assortments, as search cost increases, the equilibrium pricing strategy changes from a low price with no discounting, to a high price with deep discounting. Furthermore, we find that when a full line retailer competes with a limited line retailer, a strategy of discounting only the common product can dominate one of discounting both products together. This is not the case when his rival also carries the full product line.