We consider the problem of a retailer managing a category of vertically differentiated products. The retailer has to pay a fixed cost for each product included in the assortment and a variable cost per product sold. Quality levels, fixed, and variable costs are exogenously determined. Customers differ in their valuation of quality and choose the product (if any) that maximizes their utility. First, we consider a setting in which the selling prices are also fixed. We find that the optimal set of products to offer depends on the distribution of customer valuations and might include dominated products, that is, products which are less attractive than at least one other product, on every possible dimension. We develop an efficient algorithm to identify an optimal assortment. Second, we consider a setting in which the retailer also determines the selling prices. We show that in this case the optimal assortment does not include any dominated product and does not vary with the distribution of customer valuations when there is no fixed cost. We develop several efficient algorithms to identify an optimal assortment and optimally price the products. We also test the applicability of our methods with realistic data for two product categories.

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Probabilistic selling can improve a seller’s profit by recognizing consumers’ salient thinking behavior.

We consider a firm managing a category of vertically differentiated goods, that is, products which differ with respect to an attribute for which all consumers prefer more to less. The goods can be sold individually, in which case they are referred to as components, or in bundles. The firm chooses the assortment of components and bundles and their selling prices to maximize profit. We show that each bundling strategy (pure components, pure bundling or mixed bundling) can be optimal and obtain closed‐form expressions for the optimal selling prices. We provide insights on the structure of the optimal assortment and prices. In particular, we show that, when consumers benefit from consuming the components jointly, the products in the optimal assortment form nested sets. When consumers do not benefit from the joint consumption of components, the bundles should be offered at a positive discount. We find that bundling vertically differentiated products can significantly improve profits, even if consumers do not benefit from consuming the components jointly. The value of bundling comes from increased sales: a firm, which understands that its customers may buy multiple types of components, offers bundles of components, incentivizing customers to buy more.

This study is motivated by the ubiquitous practical existence of common retailer distribution channels (e.g., a grocery store offering multiple brands of the same product). Demand interdependence (product substitutability) among various brands is critical and thus we investigate its impact on firms’ profits. Using an economic framework with manufacturers operating as Stackelberg leaders, our analysis reveals unique and substantive insights dependent on the underlying market demand structure, and in some cases, the extent of supply coverage. For the Spence–Dixit–Vives demand structure, we find that competing manufacturers prefer to offer brands with low levels of substitutability while retailer’s preferences are moderated by the interaction effect between the number of competing brands and level of product substitutability (essentially the retailer prefers high levels of substitutability when the number of brands is “small," and vice versa). For the Shubik–Levitan demand structure, manufacturers may prefer high or low levels of product substitutability depending on the extent of supply coverage while the retailer always prefers high levels of product substitutability. These findings offer useful prescriptions for category management and persuasive advertising.