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Personalized Dynamic Pricing Based on Improved Thompson Sampling

Author

Listed:
  • Wenjie Bi

    (Business School, Central South University, No. 932, Lushan South Road, Changsha 410083, China)

  • Bing Wang

    (Business School, Central South University, No. 932, Lushan South Road, Changsha 410083, China)

  • Haiying Liu

    (School of Accounting, Hunan University of Finance and Economics, No. 139, Fenglin Second Road, Changsha 410205, China)

Abstract

This study investigates personalized pricing with demand learning. We first encode consumer-personalized feature information into high-dimensional vectors, then establish the relationship between this feature vector and product demand using a logit model, and finally learn demand parameters through historical transaction data. To address the balance between learning and revenue, we introduce the Thompson Sampling algorithm. Considering the difficulty of Bayesian inference in Thompson Sampling owing to high-dimensional feature vectors, we improve the basic Thompson Sampling by approximating the likelihood function of the logit model with the Pólya-Gamma (PG) distribution and by proposing a Thompson Sampling algorithm based on the PG distribution. To validate the proposed algorithm’s effectiveness, we conduct experiments using both simulated data and real loan data provided by the Columbia University Revenue Management Center. The study results demonstrate that the Thompson Sampling algorithm based on the PG distribution proposed outperforms traditional Laplace approximation methods regarding convergence speed and regret value in both real and simulated data experiments. The real-time personalized pricing algorithm developed here not only enriches the theoretical research of personalized dynamic pricing, but also provides a theoretical basis and guidance for enterprises to implement personalized pricing.

Suggested Citation

  • Wenjie Bi & Bing Wang & Haiying Liu, 2024. "Personalized Dynamic Pricing Based on Improved Thompson Sampling," Mathematics, MDPI, vol. 12(8), pages 1-14, April.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1123-:d:1372350
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    References listed on IDEAS

    as
    1. Peter Seele & Claus Dierksmeier & Reto Hofstetter & Mario D. Schultz, 2021. "Mapping the Ethicality of Algorithmic Pricing: A Review of Dynamic and Personalized Pricing," Journal of Business Ethics, Springer, vol. 170(4), pages 697-719, May.
    2. Cao, Ping & Zhao, Nenggui & Wu, Jie, 2019. "Dynamic pricing with Bayesian demand learning and reference price effect," European Journal of Operational Research, Elsevier, vol. 279(2), pages 540-556.
    3. Steinberg, Etye, 2020. "Big Data and Personalized Pricing," Business Ethics Quarterly, Cambridge University Press, vol. 30(1), pages 97-117, January.
    4. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    5. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    6. Patrick Bajari & Denis Nekipelov & Stephen P. Ryan & Miaoyu Yang, 2015. "Machine Learning Methods for Demand Estimation," American Economic Review, American Economic Association, vol. 105(5), pages 481-485, May.
    7. Jean-Pierre Dubé & Sanjog Misra, 2023. "Personalized Pricing and Consumer Welfare," Journal of Political Economy, University of Chicago Press, vol. 131(1), pages 131-189.
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