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ItemPricing policies for selling indivisible storable goods to strategic consumersBerbeglia, G ; Rayaprolu, G ; Vetta, A (Springer (part of Springer Nature), 2019-03)We study the dynamic pricing problem faced by a monopolistic retailer who sells a storable product to forward-looking consumers. In this framework, the two major pricing policies (or mechanisms) studied in the literature are the preannounced (commitment) pricing policy and the contingent (threat or history dependent) pricing policy. We analyse and compare these pricing policies in the setting where the good can be purchased along a finite time horizon in indivisible atomic quantities. First, we show that, given linear storage costs, the retailer can compute an optimal preannounced pricing policy in polynomial time by solving a dynamic program. Moreover, under such a policy, we show that consumers do not need to store units in order to anticipate price rises. Second, under the contingent pricing policy rather than the preannounced pricing mechanism, (i) prices could be lower, (ii) retailer revenues could be higher, and (iii) consumer surplus could be higher. This result is surprising, in that these three facts are in complete contrast to the case of a retailer selling divisible storable goods (Dudine et al. in Am Econ Rev 96(5):1706–1719, 2006). Third, we quantify exactly how much more profitable a contingent policy could be with respect to a preannounced policy. Specifically, for a market with N consumers, a contingent policy can produce a multiplicative factor of Ω(logN) more revenues than a preannounced policy, and this bound is tight.
ItemAssortment optimization under the Sequential Multinomial Logit ModelBerbeglia, G ; Flores, A ; Hentenryck, PV (Elsevier, 2019-03-16)We study the assortment optimization problem under the Sequential Multinomial Logit (SML), a discrete choice model that generalizes the Multinomial Logit (MNL). Under the SML model, products are partitioned into two levels, to capture differences in attractiveness, brand awareness and, or visibility of the products in the market. When a consumer is presented with an assortment of products, she first considers products in the first level and, if none of them is purchased, products in the second level are considered. This model is a special case of the Perception-Adjusted Luce Model (PALM) recently proposed by Echenique et al. (2018). It can explain many behavioral phenomena such as the attraction, compromise, similarity effects and choice overload which cannot be explained by the MNL model or any discrete choice model based on random utility. In particular, the SML model allows violations to regularity which states that the probability of choosing a product cannot increase if the offer set is enlarged. This paper shows that the seminal concept of revenue-ordered assortment sets, which contain an optimal assortment under the MNL model, can be generalized to the SML model. More precisely, the paper proves that all optimal assortments under the SML are revenue-ordered by level, a natural generalization of revenue-ordered assortments that contains, at most, a quadratic number of assortments. As a corollary, assortment optimization under the SML is polynomial-time solvable.
ItemThe finite horizon, undiscounted, durable goods monopoly problem with finitely many consumersBerbeglia, G ; Sloan, P ; Vetta, A (Elsevier, 2019-05-01)We study the uncommitted durable goods monopoly problem when there are finitely many consumers, a finite horizon, and no discounting. In particular we characterize the set of strong-Markov subgame perfect equilibria that satisfy the skimming property. We show that in any such equilibrium the profits are not less than static monopoly profits; and at most the static monopoly profits plus the monopoly price. When each consumer is small relative to the market, profits are then approximately the same as those of a static monopolist which sets a single price. Finally, we extend the equilibrium characterization to games with an arbitrary discount factor.