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Dynamic pricing under nested logit demand

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  • David Muller
  • Yurii Nesterov
  • Vladimir Shikhman

Abstract

Recently, there is growing interest and need for dynamic pricing algorithms, especially, in the field of online marketplaces by offering smart pricing options for big online stores. We present an approach to adjust prices based on the observed online market data. The key idea is to characterize optimal prices as minimizers of a total expected revenue function, which turns out to be convex. We assume that consumers face information processing costs, hence, follow a discrete choice demand model, and suppliers are equipped with quantity adjustment costs. We prove the strong smoothness of the total expected revenue function by deriving the strong convexity modulus of its dual. Our gradient-based pricing schemes outbalance supply and demand at the convergence rates of $\mathcal{O}(\frac{1}{t})$ and $\mathcal{O}(\frac{1}{t^2})$, respectively. This suggests that the imperfect behavior of consumers and suppliers helps to stabilize the market.

Suggested Citation

  • David Muller & Yurii Nesterov & Vladimir Shikhman, 2021. "Dynamic pricing under nested logit demand," Papers 2101.04486, arXiv.org.
  • Handle: RePEc:arx:papers:2101.04486
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    References listed on IDEAS

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    Cited by:

    1. David Müller & Vladimir Shikhman, 2022. "Network manipulation algorithm based on inexact alternating minimization," Computational Management Science, Springer, vol. 19(4), pages 627-664, October.

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