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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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    as
    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. Garrett van Ryzin & Siddharth Mahajan, 1999. "On the Relationship Between Inventory Costs and Variety Benefits in Retail Assortments," Management Science, INFORMS, vol. 45(11), pages 1496-1509, November.
    7. 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.
    8. 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.
    9. 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.
    10. Ward Hanson & Kipp Martin, 1996. "Optimizing Multinomial Logit Profit Functions," Management Science, INFORMS, vol. 42(7), pages 992-1003, July.
    11. 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.
    12. 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.
    13. John R. Hauser & Steven P. Gaskin, 1984. "Application of the “Defender” Consumer Model," Marketing Science, INFORMS, vol. 3(4), pages 327-351.
    14. 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.
    15. 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.
    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. Tversky, Amos & Kahneman, Daniel, 1986. "Rational Choice and the Framing of Decisions," The Journal of Business, University of Chicago Press, vol. 59(4), pages 251-278, October.
    23. 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.
    24. 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:

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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. "The Limits of Personalization in Assortment Optimization," Papers 2109.14861, arXiv.org, revised Jun 2024.
    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. 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.
    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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