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Dynamic Learning and Pricing with Model Misspecification

Author

Listed:
  • Mila Nambiar

    (Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • David Simchi-Levi

    (Institute for Data, Systems, and Society, Department of Civil and Environmental Engineering, and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • He Wang

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

Abstract
We study a multiperiod dynamic pricing problem with contextual information, where the seller uses a misspecified demand model. The seller sequentially observes past demand, updates model parameters, and then chooses the price for the next period based on time-varying features. We show that model misspecification leads to a correlation between price and prediction error of demand per period, which, in turn, leads to inconsistent price elasticity estimates and hence suboptimal pricing decisions. We propose a “random price shock” (RPS) algorithm that dynamically generates randomized price shocks to estimate price elasticity, while maximizing revenue. We show that the RPS algorithm has strong theoretical performance guarantees, that it is robust to model misspecification, and that it can be adapted to a number of business settings, including (1) when the feasible price set is a price ladder and (2) when the contextual information is not IID. We also perform offline simulations to gauge the performance of RPS on a large fashion retail data set and find that is expected to earn 8%–20% more revenue on average than competing algorithms that do not account for price endogeneity.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ormnsc:v:65:y:2019:i:11:p:4980-5000
    DOI: 10.1287/mnsc.2018.3194
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    References listed on IDEAS

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    Cited by:

    1. Gah-Yi Ban & N. Bora Keskin, 2021. "Personalized Dynamic Pricing with Machine Learning: High-Dimensional Features and Heterogeneous Elasticity," Management Science, INFORMS, vol. 67(9), pages 5549-5568, September.
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    4. Sentao Miao & Xi Chen & Xiuli Chao & Jiaxi Liu & Yidong Zhang, 2022. "Context‐based dynamic pricing with online clustering," Production and Operations Management, Production and Operations Management Society, vol. 31(9), pages 3559-3575, September.
    5. Daniel Garcia & Juha Tolvanen & Alexander K. Wagner, 2022. "Demand Estimation Using Managerial Responses to Automated Price Recommendations," Management Science, INFORMS, vol. 68(11), pages 7918-7939, November.
    6. Coqueret, Guillaume & Deguest, Romain, 2024. "Unexpected opportunities in misspecified predictive regressions," European Journal of Operational Research, Elsevier, vol. 318(2), pages 686-700.
    7. Zikun Ye & Dennis J. Zhang & Heng Zhang & Renyu Zhang & Xin Chen & Zhiwei Xu, 2023. "Cold Start to Improve Market Thickness on Online Advertising Platforms: Data-Driven Algorithms and Field Experiments," Management Science, INFORMS, vol. 69(7), pages 3838-3860, July.
    8. Pathikrit Basu, 2023. "Mechanism design with model specification," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 263-276, August.
    9. Woonghee Tim Huh & Michael Jong Kim & Meichun Lin, 2022. "Bayesian dithering for learning: Asymptotically optimal policies in dynamic pricing," Production and Operations Management, Production and Operations Management Society, vol. 31(9), pages 3576-3593, September.
    10. Ausseil, Rosemonde & Ulmer, Marlin W. & Pazour, Jennifer A., 2024. "Online acceptance probability approximation in peer-to-peer transportation," Omega, Elsevier, vol. 123(C).
    11. Jianqing Fan & Yongyi Guo & Mengxin Yu, 2021. "Policy Optimization Using Semi-parametric Models for Dynamic Pricing," Papers 2109.06368, arXiv.org, revised May 2022.
    12. Stefan Wager & Kuang Xu, 2021. "Experimenting in Equilibrium," Management Science, INFORMS, vol. 67(11), pages 6694-6715, November.
    13. Jin Li & Ye Luo & Xiaowei Zhang, 2021. "Causal Reinforcement Learning: An Instrumental Variable Approach," Papers 2103.04021, arXiv.org, revised Sep 2022.
    14. Guillaume Coqueret & Romain Deguest, 2024. "Unexpected opportunities in misspecified predictive regressions," Post-Print hal-04595355, HAL.
    15. Ye, Yuan & Lu, Yonggang & Robinson, Powell & Narayanan, Arunachalam, 2022. "An empirical Bayes approach to incorporating demand intermittency and irregularity into inventory control," European Journal of Operational Research, Elsevier, vol. 303(1), pages 255-272.
    16. Wayne Taylor & Brett Hollenbeck, 2021. "Leveraging loyalty programs using competitor based targeting," Quantitative Marketing and Economics (QME), Springer, vol. 19(3), pages 417-455, December.
    17. Qi Feng & J. George Shanthikumar, 2022. "Developing operations management data analytics," Production and Operations Management, Production and Operations Management Society, vol. 31(12), pages 4544-4557, December.
    18. Boxiao Chen & David Simchi-Levi & Yining Wang & Yuan Zhou, 2022. "Dynamic Pricing and Inventory Control with Fixed Ordering Cost and Incomplete Demand Information," Management Science, INFORMS, vol. 68(8), pages 5684-5703, August.

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