IDEAS home Printed from https://ideas.repec.org/a/bla/popmgt/v30y2021i9p3272-3283.html
   My bibliography  Save this article

Price Competition Under Mixed Multinomial Logit Demand: Sufficiency Conditions for Validating the Model

Author

Listed:
  • Chung‐seung Lee
  • Metin Çakanyildirim

Abstract

This study is motivated by a fundamental question among researchers: do price data correspond to a pure strategy Nash equilibrium of an estimated econometric model of Bertrand competition? The affirmative answer to this question is essential for validating the estimated model. Despite the extensive empirical applications of Bertrand competition over the last three decades, answering the question remains a daunting task for the researchers. This study takes a step to fill this gap, identifying a set of easy‐to‐verify and easy‐to‐interpret conditions under which, by checking how closely the price data fit the system of first‐order conditions, one can easily obtain an answer to the question.

Suggested Citation

  • Chung‐seung Lee & Metin Çakanyildirim, 2021. "Price Competition Under Mixed Multinomial Logit Demand: Sufficiency Conditions for Validating the Model," Production and Operations Management, Production and Operations Management Society, vol. 30(9), pages 3272-3283, September.
  • Handle: RePEc:bla:popmgt:v:30:y:2021:i:9:p:3272-3283
    DOI: 10.1111/poms.13428
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/poms.13428
    Download Restriction: no

    File URL: https://libkey.io/10.1111/poms.13428?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    2. 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.
    3. Anindya Ghose & Sang Pil Han, 2014. "Estimating Demand for Mobile Applications in the New Economy," Management Science, INFORMS, vol. 60(6), pages 1470-1488, June.
    4. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    5. repec:ebl:ecbull:v:12:y:2005:i:12:p:1-4 is not listed on IDEAS
    6. Guillermo Gallego & Woonghee Tim Huh & Wanmo Kang & Robert Phillips, 2006. "Price Competition with the Attraction Demand Model: Existence of Unique Equilibrium and Its Stability," Manufacturing & Service Operations Management, INFORMS, vol. 8(4), pages 359-375, June.
    7. Margaret Aksoy-Pierson & Gad Allon & Awi Federgruen, 2013. "Price Competition Under Mixed Multinomial Logit Demand Functions," Management Science, INFORMS, vol. 59(8), pages 1817-1835, August.
    8. Volker Nocke & Nicolas Schutz, 2018. "Multiproduct‐Firm Oligopoly: An Aggregative Games Approach," Econometrica, Econometric Society, vol. 86(2), pages 523-557, March.
    9. Fernando Bernstein & Awi Federgruen, 2004. "A General Equilibrium Model for Industries with Price and Service Competition," Operations Research, INFORMS, vol. 52(6), pages 868-886, December.
    10. Hongmin Li & Scott Webster & Nicholas Mason & Karl Kempf, 2019. "Product-Line Pricing Under Discrete Mixed Multinomial Logit Demand," Service Science, INFORMS, vol. 21(1), pages 14-28, January.
    11. 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.
    12. Ward Hanson & Kipp Martin, 1996. "Optimizing Multinomial Logit Profit Functions," Management Science, INFORMS, vol. 42(7), pages 992-1003, July.
    13. Raphael Thomadsen, 2005. "Existence of pure strategy equilibria among geographically dispersed firms," Economics Bulletin, AccessEcon, vol. 12(12), pages 1-4.
    14. W. Ross Morrow & Steven J. Skerlos, 2011. "Fixed-Point Approaches to Computing Bertrand-Nash Equilibrium Prices Under Mixed-Logit Demand," Operations Research, INFORMS, vol. 59(2), pages 328-345, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yangyang Xie & Lei Xie & Meng Lu & Houmin Yan, 2021. "Performance‐Price‐Ratio Utility: Market Equilibrium Analysis and Empirical Calibration Studies," Production and Operations Management, Production and Operations Management Society, vol. 30(5), pages 1442-1456, May.
    2. Hai Jiang & Rui Chen & He Sun, 2017. "Multiproduct price optimization under the multilevel nested logit model," Annals of Operations Research, Springer, vol. 254(1), pages 131-164, July.
    3. Margaret Aksoy-Pierson & Gad Allon & Awi Federgruen, 2013. "Price Competition Under Mixed Multinomial Logit Demand Functions," Management Science, INFORMS, vol. 59(8), pages 1817-1835, August.
    4. Schlicher, Loe & Lurkin, Virginie, 2022. "Stable allocations for choice-based collaborative price setting," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1242-1254.
    5. Woonghee T. Huh & Hongmin Li, 2023. "Product‐line pricing with dual objective of profit and consumer surplus," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1223-1242, April.
    6. Torsten J. Gerpott & Jan Berends, 2022. "Competitive pricing on online markets: a literature review," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(6), pages 596-622, December.
    7. Hongmin Li & Scott Webster & Gwangjae Yu, 2020. "Product Design Under Multinomial Logit Choices: Optimization of Quality and Prices in an Evolving Product Line," Manufacturing & Service Operations Management, INFORMS, vol. 22(5), pages 1011-1025, September.
    8. 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.
    9. Xavier D’Haultfœuille & Isis Durrmeyer & Philippe Février, 2019. "Automobile Prices in Market Equilibrium with Unobserved Price Discrimination," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(5), pages 1973-1998.
    10. Maxime C. Cohen & Renyu Zhang, 2022. "Competition and coopetition for two‐sided platforms," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 1997-2014, May.
    11. Schuur, Peter & Badur, Bertan & Sencer, Asli, 2021. "An explicit Nash equilibrium for a market share attraction game," Operations Research Perspectives, Elsevier, vol. 8(C).
    12. 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.
    13. Volker Nocke & Nicolas Schutz, 2018. "Multiproduct‐Firm Oligopoly: An Aggregative Games Approach," Econometrica, Econometric Society, vol. 86(2), pages 523-557, March.
    14. Juan Pérez & Héctor López-Ospina, 2022. "Competitive Pricing for Multiple Market Segments Considering Consumers’ Willingness to Pay," Mathematics, MDPI, vol. 10(19), pages 1-32, October.
    15. 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.
    16. Ruben van de Geer & Arnoud V. den Boer, 2022. "Price Optimization Under the Finite-Mixture Logit Model," Management Science, INFORMS, vol. 68(10), pages 7480-7496, October.
    17. 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.
    18. Woonghee Tim Huh & Hongmin Li, 2015. "Technical Note—Pricing Under the Nested Attraction Model with a Multistage Choice Structure," Operations Research, INFORMS, vol. 63(4), pages 840-850, August.
    19. Xiaobo Li & Hailong Sun & Chung Piaw Teo, 2022. "Convex Optimization for Bundle Size Pricing Problem," Management Science, INFORMS, vol. 68(2), pages 1095-1106, February.
    20. Kameng Nip & Changjun Wang & Zizhuo Wang, 2022. "Competitive and Cooperative Assortment Games under Markov Chain Choice Model," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1033-1051, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:popmgt:v:30:y:2021:i:9:p:3272-3283. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1937-5956 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.