Technical Note—Multiproduct Pricing Under the Generalized Extreme Value Models with Homogeneous Price Sensitivity Parameters

Zhang, Heng; Rusmevichientong, Paat; Topaloğlu, Hüseyin

doi:10.1287/opre.2018.1740

Cited by 36 publications

(13 citation statements)

References 50 publications

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“…This was demonstrated for the MNL model (e.g., (Aydin and Ryan, 2000, Hopp and Xu, 2005, Maddah and Bish, 2007, Aydin and Porteus, 2008, Akçay et al, 2010), the NL model (e.g., Aydin and Ryan (2000), Hopp and Xu (2005), Maddah and Bish (2007), Aydin and Porteus (2008), Akçay et al (2010), Gallego and Wang (2014), Huh and Li (2015)), and the paired combinatorial logit (PCL) model (Li and Webster, 2017). Lately Zhang et al (2018) showed that this result actually holds for the entire family of generalized extreme value (GEV) models. This stream of research also includes studies in which pricing decisions are optimized jointly with other decisions such as assortment or scheduling decisions (e.g., Du et al (2016), Jalali et al (2019), Bertsimas et al (2020)).…”

Section: Choice-based Pricingmentioning

confidence: 90%

Stable allocations for choice-based collaborative price setting

Schlicher¹,

Lurkin²

2021

Preprint

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Horizontal agreements can fall within the scope of exemptions to antitrust competition if they are expected to create pro-consumer benefits. Inspired by such horizontal agreements, we introduce a cooperative game in which a set of transport operators can collectively decide at what price to offer sustainable urban mobility services to a pool of travelers. The travelers choose amongst the mobility services according to a multinomial logit model, and the operators aim at maximizing their joint profit under a constant market share constraint. After showing that various well-known allocation rules (i.e., proportional rules and the Shapley value) do not always generate core allocations, we present a core-guaranteeing allocation rule, the market share exchange rule. This rule first allocates to each transport operator the profit he or she generates under collaboration, and then subsequently compensates those transport operators that lose part of their market share, which is paid by the ones that receive some extra market share. This exchange of market share is facilitated by a unique price, which can be expressed as the additional return by cooperating per unit of market share. Finally, we show that, under some natural conditions, the market share exchange rule still sustains the collaboration when the transport operators need to pay back part of the joint profit to society.

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Section: Choice-based Pricingmentioning

confidence: 90%

Stable allocations for choice-based collaborative price setting

Schlicher¹,

Lurkin²

2021

Preprint

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“…Keller et al (2014) discussed similar concavity results under the general attraction demand model (GAM, which also subsumes the MNL model) and showed that constraints such as price bounds and price ladders could be added to the pricing problem as linear constraints in the market shares. Zhang et al (2018) discussed the multi-product pricing problem under the generalized extreme value (GEV) models (which subsumes the NL model). They showed that the problem could be formulated as a convex program with homogeneous price sensitivity parameters.…”

Section: Related Literaturementioning

confidence: 99%

Revenue Management Under the Markov Chain Choice Model with Joint Price and Assortment Decisions

Kleywegt¹,

Shao²

2022

Preprint

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Finding the optimal product prices and product assortment are two fundamental problems in revenue management. Usually, a seller needs to jointly determine the prices and assortment while managing a network of resources with limited capacity. However, there is not yet a tractable method to efficiently solve such a problem. Existing papers studying static joint optimization of price and assortment cannot incorporate resource constraints. Then we study the revenue management problem with resource constraints and price bounds, where the prices and the product assortments need to be jointly determined over time. We showed that under the Markov chain (MC) choice model (which subsumes the multinomial logit (MNL) model), we could reformulate the choice-based joint optimization problem as a tractable convex conic optimization problem. We also proved that an optimal solution with a constant price vector exists even with constraints on resources. In addition, a solution with both constant assortment and price vector can be optimal when there is no resource constraint.

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“…Assuming identical price sensitivities for all products, Chen and Jiang (2019) studied the joint assortment and pricing problem under the multilevel NL model with a capacity limit imposed on all products. Zhang et al (2018) showed that the constant markup property at the optimality holds under the generalized extreme value (GEV) models, including the MNL, NL, and PCL models. Despite the effort of these papers, the assumption that all products have the same price sensitivity is apparently not realistic and thus leads to a large gap in the literature that cannot be ignored (Erdem et al, 2002).…”

Section: Literature Reviewmentioning

confidence: 99%

“…From another point of view, most of the literature is based on an exact preference function from buying a product associated with characteristics such as price and quality, while the constraint sometimes is too strict to accurately describe real situations. Only two papers considered the general choice probability function: Wang (2012) (based on the MNL model) and Zhang et al (2018) (based on the GEV model). These two studies, however, were also based on the identical price sensitivity assumption.…”

Section: Literature Reviewmentioning

confidence: 99%

Pricing optimization and competition under the linear nested stochastic choice model

et al. 2021

Naval Research Logistics

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In this article, we investigate the pricing optimization of firms selling multiple alternatives to the market where consumer purchase behavior follows the linear nested stochastic choice (LNSC) model. As a special case of the nested stochastic choice (NSC) model, LNSC similarly features a two‐step Luce procedure. Considering differentiated price sensitivities in a non‐exact preference function form, the present research specifically shows that, for any product in each nest, the adjusted markup is constant under certain conditions; and the adjusted nest‐level markup is constant among nests under another sufficient condition. The “loss‐leader” effect is observed, which indicates that it may be optimal to price a product with a negative adjusted markup or even a negative margin to attract more attention to the corresponding nest. Based on these results, the pricing optimization can be simplified to a single‐variable problem where the objective function is unimodal. Then, a special case with an exponential preference function is discussed along with its concavity of the total expected profit. The above results are also used to construct the oligopoly multiproduct price competition and characterize the Nash equilibrium. Finally, a series of sensitivity analyses are conducted to reveal the impacts of key parameters on the optimal solutions.

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Technical Note—Multiproduct Pricing Under the Generalized Extreme Value Models with Homogeneous Price Sensitivity Parameters

Cited by 36 publications

References 50 publications

Stable allocations for choice-based collaborative price setting

Stable allocations for choice-based collaborative price setting

Revenue Management Under the Markov Chain Choice Model with Joint Price and Assortment Decisions

Pricing optimization and competition under the linear nested stochastic choice model

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