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Learning and Pricing with Models That Do Not Explicitly Incorporate Competition

Author

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  • William L. Cooper

    (Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, Minnesota 55455)

  • Tito Homem-de-Mello

    (School of Business, Universidad Adolfo Ibañez, Santiago 7941169, Region Metropolitana, Chile)

  • Anton J. Kleywegt

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract
In revenue management research and practice, demand models are used that describe how demand for a seller’s products depends on the decisions, such as prices, of that seller. Even in settings where the demand for a seller’s products also depends on decisions of other sellers, the models often do not explicitly account for such decisions. It has been conjectured in the revenue management literature that such monopoly models may incorporate the effects of competition, because the parameter estimates of the monopoly models are based on data collected in the presence of competition. In this paper we take a closer look at such a setting to investigate the behavior of parameter estimates and decisions if monopoly models are used in the presence of competition. We consider repeated pricing games in which two competing sellers use mathematical models to choose the prices of their products. Over the sequence of games, each seller attempts to estimate the values of the parameters of a demand model that expresses demand as a function only of its own price using data comprised only of its own past prices and demand realizations. We analyze the behavior of the sellers’ parameter estimates and prices under various assumptions regarding the sellers’ knowledge and estimation procedures, and we identify situations in which (a) the sellers’ prices converge to the Nash equilibrium associated with knowledge of the correct demand model, (b) the sellers’ prices converge to the cooperative solution, and (c) the sellers’ prices have many potential limit points that are neither the Nash equilibrium nor the cooperative solution and that depend on the initial conditions. We compare the sellers’ revenues at potential limit prices with their revenues at the Nash equilibrium and the cooperative solution, and we show that it is possible for sellers to be better off when using a monopoly model than at the Nash equilibrium.

Suggested Citation

  • William L. Cooper & Tito Homem-de-Mello & Anton J. Kleywegt, 2015. "Learning and Pricing with Models That Do Not Explicitly Incorporate Competition," Operations Research, INFORMS, vol. 63(1), pages 86-103, February.
    • Handle: RePEc:inm:oropre:v:63:y:2015:i:1:p:86-103
    DOI: 10.1287/opre.2014.1341
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    References listed on IDEAS

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    Cited by:

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    3. den Boer, Arnoud V., 2015. "Tracking the market: Dynamic pricing and learning in a changing environment," European Journal of Operational Research, Elsevier, vol. 247(3), pages 914-927.
    4. Stephanie Assad & Robert Clark & Daniel Ershov & Lei Xu, 2020. "Algorithmic Pricing and Competition: Empirical Evidence from the German Retail Gasoline Market," CESifo Working Paper Series 8521, CESifo.
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    7. Adam J. Mersereau, 2015. "Demand Estimation from Censored Observations with Inventory Record Inaccuracy," Manufacturing & Service Operations Management, INFORMS, vol. 17(3), pages 335-349, July.
    8. Joseph E. Harrington, 2022. "The Effect of Outsourcing Pricing Algorithms on Market Competition," Management Science, INFORMS, vol. 68(9), pages 6889-6906, September.
    9. Thomas Loots & Arnoud V. den Boer, 2023. "Data‐driven collusion and competition in a pricing duopoly with multinomial logit demand," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1169-1186, April.
    10. Joseph Jiaqi Xu & Peter S. Fader & Senthil Veeraraghavan, 2019. "Designing and Evaluating Dynamic Pricing Policies for Major League Baseball Tickets," Service Science, INFORMS, vol. 21(1), pages 121-138, January.
    11. Timo Klein, 2021. "Autonomous algorithmic collusion: Q‐learning under sequential pricing," RAND Journal of Economics, RAND Corporation, vol. 52(3), pages 538-558, September.
    12. Guillaume Coqueret & Romain Deguest, 2024. "Unexpected opportunities in misspecified predictive regressions," Post-Print hal-04595355, HAL.
    13. 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.
    14. Alexandru CONSTÃNGIOARÃ & Gyula-Laszlo FLORIAN, 2019. "Pricing Optimization Using R," Proceedings of the INTERNATIONAL MANAGEMENT CONFERENCE, Faculty of Management, Academy of Economic Studies, Bucharest, Romania, vol. 13(1), pages 142-149, November.
    15. Pai, Mallesh & Hansen, Karsten, 2020. "Algorithmic Collusion: Supra-competitive Prices via Independent Algorithms," CEPR Discussion Papers 14372, C.E.P.R. Discussion Papers.
    16. Nur Aini Masruroh & Yun Prihantina Mulyani, 2016. "Mathematical model for revenue management under oligopolistic competition," International Journal of Revenue Management, Inderscience Enterprises Ltd, vol. 9(1), pages 17-39.
    17. Ravi Kumar & Wei Wang & Ahmed Simrin & Sivarama Krishnan Arunachalam & Bhaskara Rao Guntreddy & Darius Walczak, 2021. "Competitive revenue management models with loyal and fully flexible customers," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 20(3), pages 256-275, June.
    18. Karsten T. Hansen & Kanishka Misra & Mallesh M. Pai, 2021. "Frontiers: Algorithmic Collusion: Supra-competitive Prices via," Marketing Science, INFORMS, vol. 40(1), pages 1-12, January.
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    20. Mila Nambiar & David Simchi-Levi & He Wang, 2019. "Dynamic Learning and Pricing with Model Misspecification," Management Science, INFORMS, vol. 65(11), pages 4980-5000, November.

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