IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v69y2021i1p164-174.html
   My bibliography  Save this article

Technical Note—Global Robust Stability in a General Price and Assortment Competition Model

Author

Listed:
  • Awi Federgruen

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • Ming Hu

    (Rotman School of Management, University of Toronto, Toronto, Ontario M5S 3E6, Canada)

Abstract

We analyze a general but parsimonious price competition model for an oligopoly in which each firm offers any number of products. The demand volumes are general piecewise affine functions of the full price vector, generated as the “regular” extension of a base set of affine functions. The model specifies a product assortment , along with their prices and demand volumes, in contrast to most commonly used demand models, such as the multinomial logit model or any of its variants. We show that a special equilibrium in this model has global robust stability . This means that, from any starting point, the market converges to this equilibrium when firms use a particular response mapping to dynamically adjust their own prices in response to their competitors’ prices. The mapping involves each firm optimizing its own prices over a limited subset of possible prices and requires each firm to only know the demand function and cost structure for its own products (but not for other firms’ products).

Suggested Citation

  • Awi Federgruen & Ming Hu, 2021. "Technical Note—Global Robust Stability in a General Price and Assortment Competition Model," Operations Research, INFORMS, vol. 69(1), pages 164-174, January.
    • Handle: RePEc:inm:oropre:v:69:y:2021:i:1:p:164-174
    DOI: 10.1287/opre.2020.2001
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/opre.2020.2001
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2020.2001?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. al-Nowaihi, A. & Levine, P. L., 1985. "The stability of the cournot oligopoly model: A reassessment," Journal of Economic Theory, Elsevier, vol. 35(2), pages 307-321, August.
    2. R. D. Theocharis, 1960. "On the Stability of the Cournot Solution on the Oligopoly Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(2), pages 133-134.
    3. Awi Federgruen & Ming Hu, 2015. "Multi-Product Price and Assortment Competition," Operations Research, INFORMS, vol. 63(3), pages 572-584, June.
    4. Oecd, 2007. "Resale below Cost Laws and Regulations," OECD Journal: Competition Law and Policy, OECD Publishing, vol. 9(1), pages 169-255.
    5. Zhijun Chen & Patrick Rey, 2012. "Loss Leading as an Exploitative Practice," American Economic Review, American Economic Association, vol. 102(7), pages 3462-3482, December.
    6. Øyvind Thomassen & Howard Smith & Stephan Seiler & Pasquale Schiraldi, 2017. "Multi-category Competition and Market Power: A Model of Supermarket Pricing," American Economic Review, American Economic Association, vol. 107(8), pages 2308-2351, August.
    7. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    8. Timothy W. McGuire & Richard Staelin, 1983. "An Industry Equilibrium Analysis of Downstream Vertical Integration," Marketing Science, INFORMS, vol. 2(2), pages 161-191.
    9. Awi Federgruen & Ming Hu, 2019. "Stability in a general oligopoly model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 90-102, February.
    10. K. Okuguchi, 1964. "The Stability of The Cournot Oligopoly Solution: A Further Generalization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(2), pages 143-146.
    11. F. H. Hahn, 1962. "The Stability of the Cournot Oligopoly Solution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(4), pages 329-331.
    12. Cumbul, Eray & Virág, Gábor, 2018. "Multilateral limit pricing in price-setting games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 250-273.
    13. Omar Besbes & Denis Sauré, 2016. "Product Assortment and Price Competition under Multinomial Logit Demand," Production and Operations Management, Production and Operations Management Society, vol. 25(1), pages 114-127, January.
    14. Timothy W. McGuire & Richard Staelin, 2008. "An Industry Equilibrium Analysis of Downstream Vertical Integration," Marketing Science, INFORMS, vol. 27(1), pages 115-130, 01-02.
    15. 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.
    16. Awi Federgruen & Ming Hu, 2016. "Technical Note—Sequential Multiproduct Price Competition in Supply Chain Networks," Operations Research, INFORMS, vol. 64(1), pages 135-149, February.
    17. Okuguchi, Koji & Yamazaki, Takeshi, 2008. "Global stability of unique Nash equilibrium in Cournot oligopoly and rent-seeking game," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1204-1211, April.
    18. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, April.
    19. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    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. Koji Okuguchi & Takeshi Yamazaki, 2018. "Existence of Unique Equilibrium in Cournot Mixed Oligopoly," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-13, September.
    2. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    3. Mamada, Robert & Perrings, Charles, 2020. "The effect of emission charges on output and emissions in dynamic Cournot duopoly," Economic Analysis and Policy, Elsevier, vol. 66(C), pages 370-380.
    4. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    5. Hefti, Andreas, 2016. "On the relationship between uniqueness and stability in sum-aggregative, symmetric and general differentiable games," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 83-96.
    6. Eiichi Chuman, 2008. "Stability And Instability Of The Coucrnot Equilibrium," Australian Economic Papers, Wiley Blackwell, vol. 47(3), pages 259-263, September.
    7. Awi Federgruen & Ming Hu, 2019. "Stability in a general oligopoly model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(1), pages 90-102, February.
    8. Quan Zheng & Xiajun Amy Pan & Asoo J. Vakharia, 2021. "Product Decoys: A Supply Chain Perspective," Production and Operations Management, Production and Operations Management Society, vol. 30(9), pages 2858-2870, September.
    9. 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.
    10. Awi Federgruen & Ming Hu, 2016. "Technical Note—Sequential Multiproduct Price Competition in Supply Chain Networks," Operations Research, INFORMS, vol. 64(1), pages 135-149, February.
    11. Chuman, Eiichi, 2010. "Comparing Cournot and Stackelberg Duopoly," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 51(2), pages 59-73, December.
    12. Gao, Xing & Zhong, Weijun & Mei, Shue, 2012. "On local stability of Cournot models with simultaneous and sequential decisions," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 207-212.
    13. Romana L. Autrey & Francesco Bova & David A. Soberman, 2014. "Organizational Structure and Gray Markets," Marketing Science, INFORMS, vol. 33(6), pages 849-870, November.
    14. Niu, Baozhuang & Ruan, Yiyuan & Zeng, Fanzhuo, 2022. "Promoting remanufacturing through subsidy and environment tax: Channel co-opetition, incentive alignment and regulation optimization," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 166(C).
    15. Cars H. Hommes & Marius I. Ochea & Jan Tuinstra, 2018. "Evolutionary Competition Between Adjustment Processes in Cournot Oligopoly: Instability and Complex Dynamics," Dynamic Games and Applications, Springer, vol. 8(4), pages 822-843, December.
    16. Noriaki Matsushima & Akira Miyaoka, 2013. "Who benefits from resale-below-cost laws?," ISER Discussion Paper 0875, Institute of Social and Economic Research, Osaka University.
    17. Quan Zheng & Xiajun Amy Pan & Asoo J. Vakharia, 2020. "Common Retailer Channel Revisited: The Role of Supply Network Size," Production and Operations Management, Production and Operations Management Society, vol. 29(9), pages 2175-2181, September.
    18. Koji Okuguchi, 2012. "General Analysis of Cournot Mixed Oligopoly with Partial Privatization," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 2(1), pages 48-62, June.
    19. Bervoets, Sebastian & Faure, Mathieu, 2019. "Stability in games with continua of equilibria," Journal of Economic Theory, Elsevier, vol. 179(C), pages 131-162.
    20. Sun, Yiqi & Wu, Zhengping & Zhu, Wanshan, 2022. "When do firms benefit from joint price and lead-time competition?," European Journal of Operational Research, Elsevier, vol. 302(2), pages 497-517.

    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:inm:oropre:v:69:y:2021:i:1:p:164-174. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.