Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences

Aouad, Ali; Segev, Danny

doi:10.1287/mnsc.2020.3664

Cited by 39 publications

(18 citation statements)

References 59 publications

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“…in the first page of results) but allow all consumers see the same set of products if they keep browsing down. Although the offer set is actually the same for all consumers, this policy has a similar effect in consumers as personalized assortments [Abeliuk et al, 2016, Gallego et al, 2020, Aouad and Segev, 2021, Berbeglia et al, 2021a. The reader interested in personalized pricing is referred to Elmachtoub et al [2021], Chen et al [2020] and Gallego and Berbeglia [2021] and references therein.…”

Section: Related Literaturementioning

confidence: 99%

Bounds, Heuristics, and Prophet Inequalities for Assortment Optimization

Gallego¹,

Berbeglia²

2021

Preprint

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Consider a clairvoyant firm that knows the products' valuations of each arriving consumer and offers them only the most profitable product they are willing to buy. How much more can such a firm make relative to a firm that offers all consumers the assortment that maximizes expected revenues? We show that for general discrete choice models, the ratio can be exponential in the number of products, but at most equal to the number of products for random utility models.We show that the ratio is at most 2 for the α-shaken multinomial logit (α-MNL) which includes the MNL and the general attraction model (GAM) as special cases. We also provide sufficient conditions for the ratio of at most 2 to hold for the latent class MNL, and in fact show that in the limit as the coefficient of variation of the utilities goes to infinity the bound is at most 1.5. For all of these cases the revenue-ordered heuristic yields the stated guarantees relevant to the clairvoyant firm.

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Section: Related Literaturementioning

confidence: 99%

Bounds, Heuristics, and Prophet Inequalities for Assortment Optimization

Gallego¹,

Berbeglia²

2021

Preprint

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“…Subsequently, Gallego et al (2020) developed a dynamic programming-based algorithm that attains an improved approximation ratio of 6/π 2 ≈ 0.607 and actually applies to a more general class of choice models. Focusing on the MNL setting, Aouad and Segev (2020) devised a PTAS via an approximate dynamic programming formulation. Closely related variants have been considered in additional papers, including those of Derakhshan et al (2018) and Flores et al (2019).…”

Section: Problem Formulationmentioning

confidence: 99%

An Approximate Dynamic Programming Approach to The Incremental Knapsack Problem

Aouad,

Segev

2020

Preprint

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We study the incremental knapsack problem, where one wishes to sequentially pack items into a knapsack whose capacity expands over a finite planning horizon, with the objective of maximizing time-averaged profits. While various approximation algorithms were developed under mitigating structural assumptions, obtaining non-trivial performance guarantees for this problem in its utmost generality has remained an open question thus far. In this paper, we devise a polynomial-time approximation scheme for general instances of the incremental knapsack problem, which is the strongest guarantee possible given existing hardness results. In contrast to earlier work, our algorithmic approach exploits an approximate dynamic programming formulation. Starting with a simple exponentially sized dynamic program, we prove that an appropriate composition of state pruning ideas yields a polynomially sized state space with negligible loss of optimality.The analysis of this formulation synthesizes various techniques, including new problem decompositions, parsimonious counting arguments, and efficient rounding methods, that may be of broader interest.

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“…Product Ranking. Recently, many papers have designed algorithms for product ranking (or display) that account for the impact of position bias on customer choice (Davis et al 2013, Abeliuk et al 2015, Aouad and Segev 2020, Abeliuk et al 2016, Gallego et al 2016, Lei et al 2018, Derakhshan et al 2018, Asadpour et al 2020. In contrast to our setting, the aforementioned works focus on the offline version of the product ranking problem, where the platform is aware of all the parameters that make up the customers' choice model (e.g., click probabilities).…”

Section: Related Workmentioning

confidence: 99%

Learning Product Rankings Robust to Fake Users

Golrezaei¹,

Manshadi²,

Schneider³

et al. 2020

Preprint

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In many online platforms, customers' decisions are substantially influenced by product rankings as most customers only examine a few top-ranked products. Concurrently, such platforms also use the same data corresponding to customers' actions to learn how these products must be ranked or ordered. These interactions in the underlying learning process, however, may incentivize sellers to artificially inflate their position by employing fake users, as exemplified by the emergence of click farms. Motivated by such fraudulent behavior, we study the ranking problem of a platform that faces a mixture of real and fake users who are indistinguishable from one another. We first show that existing learning algorithms-that are optimal in the absence of fake users-may converge to highly sub-optimal rankings under manipulation by fake users. To overcome this deficiency, we develop efficient learning algorithms under two informational environments: in the first setting, the platform is aware of the number of fake users, and in the second setting, it is agnostic to the number of fake users. For both these environments, we prove that our algorithms converge to the optimal ranking, while being robust to the aforementioned fraudulent behavior; we also present worst-case performance guarantees for our methods, and show that they significantly outperform existing algorithms. At a high level, our work employs several novel approaches to guarantee robustness such as: piq constructing product-ordering graphs that encode the pairwise relationships between products inferred from the customers' actions; and piiq implementing multiple levels of learning with a judicious amount of bi-directional cross-learning between levels. Overall, our results indicate that online platforms can effectively combat fraudulent users without incurring large costs by designing new learning algorithms that guarantee efficient convergence even when the platform is completely oblivious to the number and identity of the fake users.

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Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences

Cited by 39 publications

References 59 publications

Bounds, Heuristics, and Prophet Inequalities for Assortment Optimization

Bounds, Heuristics, and Prophet Inequalities for Assortment Optimization

An Approximate Dynamic Programming Approach to The Incremental Knapsack Problem

Learning Product Rankings Robust to Fake Users

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