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Approximation Algorithms for Product Framing and Pricing

Author

Listed:
  • Guillermo Gallego

    (Industrial Engineering and Decision Analytics, Hong Kong University of Science and Technology, Hong Kong)

  • Anran Li

    (London School of Economics and Political Science, London WC2A 2AE, United Kingdom)

  • Van-Anh Truong

    (Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Xinshang Wang

    (Alibaba Group, San Mateo, California 94402, Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200240, China)

Abstract

We propose one of the first models of “product framing” and pricing. Product framing refers to the way consumer choice is influenced by how the products are framed or displayed. We present a model in which a set of products is displayed or framed into a set of virtual web pages. We assume that consumers consider only products in the top pages with different consumers willing to see different numbers of pages. Consumers select a product, if any, from these pages following a general choice model. We show that the product-framing problem is NP-hard. We derive algorithms with guaranteed performance relative to an optimal algorithm under reasonable assumptions. Our algorithms are fast and easy to implement. We also present structural results and design algorithms for pricing under framing effects for the multinomial logit model. We show that, for profit maximization problems, at optimality, products are displayed in descending order of their value gap and in ascending order of their markups.

Suggested Citation

  • Guillermo Gallego & Anran Li & Van-Anh Truong & Xinshang Wang, 2020. "Approximation Algorithms for Product Framing and Pricing," Operations Research, INFORMS, vol. 68(1), pages 134-160, January.
    • Handle: RePEc:inm:oropre:v:68:y:2020:i:1:p:134-160
    DOI: 10.1287/opre.2019.1875
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    Cited by:

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    3. Ningyuan Chen & Adam N. Elmachtoub & Michael L. Hamilton & Xiao Lei, 2021. "Loot Box Pricing and Design," Management Science, INFORMS, vol. 67(8), pages 4809-4825, August.
    4. Ali Aouad & Daniela Saban, 2023. "Online Assortment Optimization for Two-Sided Matching Platforms," Management Science, INFORMS, vol. 69(4), pages 2069-2087, April.
    5. Ali Aouad & Danny Segev, 2021. "Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences," Management Science, INFORMS, vol. 67(6), pages 3519-3550, June.
    6. Guillermo Gallego & Gerardo Berbeglia, 2021. "The Limits of Personalization in Assortment Optimization," Papers 2109.14861, arXiv.org, revised Jun 2024.
    7. Santiago R. Balseiro & Antoine Désir, 2023. "Incentive-Compatible Assortment Optimization for Sponsored Products," Management Science, INFORMS, vol. 69(8), pages 4668-4684, August.
    8. Giovanni Compiani & Gregory Lewis & Sida Peng & Peichun Wang, 2024. "Online Search and Optimal Product Rankings: An Empirical Framework," Marketing Science, INFORMS, vol. 43(3), pages 615-636, May.
    9. Kris J. Ferreira & Sunanda Parthasarathy & Shreyas Sekar, 2022. "Learning to Rank an Assortment of Products," Management Science, INFORMS, vol. 68(3), pages 1828-1848, March.
    10. Haihao Lu & Luyang Zhang, 2024. "The Power of Linear Programming in Sponsored Listings Ranking: Evidence from Field Experiments," Papers 2403.14862, arXiv.org.
    11. Berbeglia, Franco & Berbeglia, Gerardo & Van Hentenryck, Pascal, 2021. "Market segmentation in online platforms," European Journal of Operational Research, Elsevier, vol. 295(3), pages 1025-1041.

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