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Dynamic Learning and Pricing with Model Misspecification

Author

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  • 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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    3. 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.
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