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Approximation algorithms for product framing and pricing

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  • Gallego, Guillermo
  • Li, Anran
  • Truong, Van-Anh
  • Wang, Xinshang

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

  • Gallego, Guillermo & Li, Anran & Truong, Van-Anh & Wang, Xinshang, 2020. "Approximation algorithms for product framing and pricing," LSE Research Online Documents on Economics 101983, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:101983
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    File URL: http://eprints.lse.ac.uk/101983/
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    1. Eric J. Johnson & Wendy W. Moe & Peter S. Fader & Steven Bellman & Gerald L. Lohse, 2004. "On the Depth and Dynamics of Online Search Behavior," Management Science, INFORMS, vol. 50(3), pages 299-308, March.
    2. Kalyan Talluri & Garrett van Ryzin, 2004. "Revenue Management Under a General Discrete Choice Model of Consumer Behavior," Management Science, INFORMS, vol. 50(1), pages 15-33, January.
    3. Shugan, Steven M, 1980. "The Cost of Thinking," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 7(2), pages 99-111, Se.
    4. Juan Feng & Hemant K. Bhargava & David M. Pennock, 2007. "Implementing Sponsored Search in Web Search Engines: Computational Evaluation of Alternative Mechanisms," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 137-148, February.
    5. John R. Hauser, 1978. "Testing the Accuracy, Usefulness, and Significance of Probabilistic Choice Models: An Information-Theoretic Approach," Operations Research, INFORMS, vol. 26(3), pages 406-421, June.
    6. Hongmin Li & Woonghee Tim Huh, 2011. "Pricing Multiple Products with the Multinomial Logit and Nested Logit Models: Concavity and Implications," Manufacturing & Service Operations Management, INFORMS, vol. 13(4), pages 549-563, October.
    7. Chiang, Jeongwen & Chib, Siddhartha & Narasimhan, Chakravarthi, 1998. "Markov chain Monte Carlo and models of consideration set and parameter heterogeneity," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 223-248, November.
    8. Gérard P. Cachon & Christian Terwiesch & Yi Xu, 2005. "Retail Assortment Planning in the Presence of Consumer Search," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 330-346, August.
    9. Ward Hanson & Kipp Martin, 1996. "Optimizing Multinomial Logit Profit Functions," Management Science, INFORMS, vol. 42(7), pages 992-1003, July.
    10. Shashi Mittal & Andreas S. Schulz, 2013. "A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One," Operations Research, INFORMS, vol. 61(2), pages 386-397, April.
    11. Michael R. Baye & J. Rupert J. Gatti & Paul Kattuman & John Morgan, 2009. "Clicks, Discontinuities, and Firm Demand Online," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 18(4), pages 935-975, December.
    12. John R. Hauser & Steven P. Gaskin, 1984. "Application of the “Defender” Consumer Model," Marketing Science, INFORMS, vol. 3(4), pages 327-351.
    13. James M. Davis & Guillermo Gallego & Huseyin Topaloglu, 2014. "Assortment Optimization Under Variants of the Nested Logit Model," Operations Research, INFORMS, vol. 62(2), pages 250-273, April.
    14. Manrai, Ajay K. & Andrews, Rick L., 1998. "Two-stage discrete choice models for scanner panel data: An assessment of process and assumptions," European Journal of Operational Research, Elsevier, vol. 111(2), pages 193-215, December.
    15. Juan José Miranda Bront & Isabel Méndez-Díaz & Gustavo Vulcano, 2009. "A Column Generation Algorithm for Choice-Based Network Revenue Management," Operations Research, INFORMS, vol. 57(3), pages 769-784, June.
    16. Wallace J. Hopp & Xiaowei Xu, 2005. "Product Line Selection and Pricing with Modularity in Design," Manufacturing & Service Operations Management, INFORMS, vol. 7(3), pages 172-187, August.
    17. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    18. Guillermo Gallego & Huseyin Topaloglu, 2014. "Constrained Assortment Optimization for the Nested Logit Model," Management Science, INFORMS, vol. 60(10), pages 2583-2601, October.
    19. Erik Brynjolfsson & Astrid Dick & Michael Smith, 2010. "A nearly perfect market?," Quantitative Marketing and Economics (QME), Springer, vol. 8(1), pages 1-33, March.
    20. Guillermo Gallego & Ruxian Wang, 2014. "Multiproduct Price Optimization and Competition Under the Nested Logit Model with Product-Differentiated Price Sensitivities," Operations Research, INFORMS, vol. 62(2), pages 450-461, April.
    21. Paat Rusmevichientong & Zuo-Jun Max Shen & David B. Shmoys, 2010. "Dynamic Assortment Optimization with a Multinomial Logit Choice Model and Capacity Constraint," Operations Research, INFORMS, vol. 58(6), pages 1666-1680, December.
    22. Anindya Ghose & Sha Yang, 2009. "An Empirical Analysis of Search Engine Advertising: Sponsored Search in Electronic Markets," Management Science, INFORMS, vol. 55(10), pages 1605-1622, October.
    23. Animesh Animesh & Siva Viswanathan & Ritu Agarwal, 2011. "Competing “Creatively” in Sponsored Search Markets: The Effect of Rank, Differentiation Strategy, and Competition on Performance," Information Systems Research, INFORMS, vol. 22(1), pages 153-169, March.
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    Cited by:

    1. Gerardo Berbeglia & Alvaro Flores & Guillermo Gallego, 2021. "The Refined Assortment Optimization Problem," Papers 2102.03043, arXiv.org.
    2. Mahsa Derakhshan & Negin Golrezaei & Vahideh Manshadi & Vahab Mirrokni, 2022. "Product Ranking on Online Platforms," Management Science, INFORMS, vol. 68(6), pages 4024-4041, June.
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    4. 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.
    5. 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.
    6. 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.
    7. Guillermo Gallego & Gerardo Berbeglia, 2021. "Bounds, Heuristics, and Prophet Inequalities for Assortment Optimization," Papers 2109.14861, arXiv.org, revised Oct 2023.
    8. Santiago R. Balseiro & Antoine Désir, 2023. "Incentive-Compatible Assortment Optimization for Sponsored Products," Management Science, INFORMS, vol. 69(8), pages 4668-4684, August.
    9. 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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    More about this item

    Keywords

    analysis of algorithms; choice models; marketing; pricing;
    All these keywords.

    JEL classification:

    • J50 - Labor and Demographic Economics - - Labor-Management Relations, Trade Unions, and Collective Bargaining - - - General

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