Semiorder preferences and price-oriented buyers in a Hotelling model

We modify the Hotelling model to introduce the possibility that insufficiently differentiated but not necessarily identical products may induce buyers to be price-oriented. Price-oriented buyers purchase the cheapest good independently of its characteristics (as in a Bertrand model), while non-price-oriented buyers purchase the good with the most attractive price-variety combination (as in a standard Hotelling model). This difference in behavior is motivated by the introduction of semiorder lexicographic preferences. When designing their products, sellers are uncertain as to what level of product differentiation makes buyers price-oriented. This increases sellers’ incentives to differentiate their products in comparison to a standard Hotelling model. Two counterintuitive results emerge. First, we show that despite sellers making less profit when buyers are price-oriented, their expected profits can increase when price-oriented buyers are more prevalent (in a stochastic sense). Second, in the presence of asymmetric costs the seller with the lowest costs may end up setting the highest price.