We study firms that sell multiple differentiated substitutable products and customers whose purchase behavior follows a Nested Logit model, of which the Multinomial Logit model is a special case. Customers make purchasing decision sequentially under the Nested Logit model: they first select a nest of products and subsequently purchase a product within the selected nest. We consider the general Nested Logit model with product-differentiated price sensitivities and general nest coefficients. The problem is to price the products to maximize the expected total profit. We show that the adjusted markup, defined as price minus cost minus the reciprocal of price sensitivity, is constant for all products within a nest at optimality. This reduces the problem's dimension to a single variable per nest. We also show that each nest has an adjusted nest-level markup that is nest invariant, which further reduces the problem to a single variable optimization of a continuous function over a bounded interval. We provide conditions for this function to be uni-modal. We also use this result to simplify the oligopolistic multi-product price competition and characterize the Nash equilibrium. Furthermore, we extend to more general attraction functions including the linear utility and the multiplicative competitive interaction model, and show that the same technique can significantly simplify the multi-product pricing problems under the Nested Attraction model.

Consumers search for product information to resolve valuation uncertainties before purchase. We incorporate search cost into consumer choice models and study the two-stage consider-then-choose policy. In the first stage, a consumer forms her consideration set by balancing utility uncertainty and search cost. In the second stage, she evaluates all products in her consideration set and chooses the one with the highest net utility. We show that the revenue-ordered assortment (i.e., the offer set that includes products in the revenue-decreasing order) fails to be optimal, although it can obtain at least half the optimal revenue. We propose a k-quasi-attractiveness-ordered assortment and show that it can be arbitrarily near optimal for the market share maximization problem. The assortment problems with search cost are generally NP-hard, so we develop efficient approximation or relatively fast exact algorithms for a variety of assortment problems under the consider-then-choose models with search cost. For the joint assortment planning and pricing problem with homogeneous consumers, we show that the intrinsic-utility-ordered assortment and the quasi-same-price policy, which charges the same price for all products except at most one, are optimal. The online appendix is available at https://doi.org/10.1287/mnsc.2017.2790 . This paper was accepted by Gad Allon, operations management.

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Network externality arises when the utility of a product depends not only on its attributes but also on the number of consumers who purchase the same product. In this paper, we study consumer choice models that endogenize such network externality. We first characterize the choice probabilities under such models and conduct studies on comparative statics. Then we investigate the assortment optimization problem under such choice models. Although the problem is generally NP-hard, we show that a new class of assortments, called quasi-revenue-ordered assortments, which consist of a revenue-ordered assortment plus at most one additional item, are optimal under mild conditions. We also propose an iterative estimation method to calibrate such choice models, for both uncensored and censored data cases. An empirical study on a mobile game data set shows that our proposed model can provide better fits for the data, increase the prediction accuracy for consumer choices, and potentially increase revenue. This paper was accepted by Noah Gans, stochastic models and simulation.

Problem definition: In this paper, we develop an integrated framework to study a firm’s joint decisions on product price, quality, and service duration in a variety of monopolistic and competitive scenarios. Academic/practical relevance: Product price, quality, and ancillary service (such as maintenance and factory warranty) are arguably among the most important factors consumers consider when making a purchase decision. Meanwhile, they are also seen as effective instruments for firms to achieve market segmentation. We consider a cost structure for a firm in which the service cost depends on the product quality level. In particular, if quality is associated with product reliability (respectively, complexity), the service cost would decrease (increase) in the quality level. Methodology: We adopt the widely used multinomial logit model and the nested logit model to study consumers’ choice behavior and employ mixed-integer optimization and game theory to conduct analyses. Results: We find that with multiple substitutable products being offered, it is sufficient for a firm to provide only two maximally differentiated service durations at optimality. The quality of each product should be set at a level such that the marginal utility to consumers equals the marginal cost to the firm, independent of the decisions on other products, whereas the pricing decision should take into account all products. In addition, consumer surplus increases when the firm can make more decisions. Managerial implications: Regardless of product substitution and market competition, the optimal quality level and service duration for each product can be determined independently of other products. Moreover, service differentiation can benefit consumers and improve the firm’s profitability at the same time.