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

Author

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  • 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
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    References listed on IDEAS

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    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. Awi Federgruen & Ming Hu, 2015. "Multi-Product Price and Assortment Competition," Operations Research, INFORMS, vol. 63(3), pages 572-584, June.
    3. Oecd, 2007. "Resale below Cost Laws and Regulations," OECD Journal: Competition Law and Policy, OECD Publishing, vol. 9(1), pages 169-255.
    4. Zhijun Chen & Patrick Rey, 2012. "Loss Leading as an Exploitative Practice," American Economic Review, American Economic Association, vol. 102(7), pages 3462-3482, December.
    5. Timothy W. McGuire & Richard Staelin, 1983. "An Industry Equilibrium Analysis of Downstream Vertical Integration," Marketing Science, INFORMS, vol. 2(2), pages 161-191.
    6. 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.
    7. 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.
    8. Cumbul, Eray & Virág, Gábor, 2018. "Multilateral limit pricing in price-setting games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 250-273.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    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.
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