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Pricing Problems under the Markov Chain Choice Model

Author

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  • James Dong
  • A. Serdar Simsek
  • Huseyin Topaloglu

Abstract

We consider pricing problems when customers choose under the Markov chain choice model. In this choice model, a customer arriving into the system is interested in a certain product with a certain probability. Depending on the price charged for this product, the customer decides whether to purchase the product. If the customer purchases the product, then she leaves the system. Otherwise, the customer transitions to another product or to the no purchase option with certain transition probabilities. In this way, the customer transitions between the products until she purchases a product or reaches the no purchase option. We study three fundamental pricing problems under this choice model. First, for the monopolistic pricing problem, we show how to compute the optimal prices efficiently. Second, for the competitive pricing problem, we show that a Nash equilibrium exists, prove that Nash equilibrium prices are no larger than the prices computed by a central planner controlling all prices and characterize a Nash equilibrium that Pareto dominates all other Nash equilibria. Third, for the dynamic pricing problem with a single resource, we show that the optimal prices decrease as we have more resource capacity or as we get closer to the end of the selling horizon. We also consider a deterministic approximation formulated under the assumption that the demand for each product takes on its expected value. Although the objective function and constraints in this approximation do not have explicit expressions, we develop an equivalent reformulation with explicit expressions for the objective function and constraints.

Suggested Citation

  • James Dong & A. Serdar Simsek & Huseyin Topaloglu, 2019. "Pricing Problems under the Markov Chain Choice Model," Production and Operations Management, Production and Operations Management Society, vol. 28(1), pages 157-175, January.
  • Handle: RePEc:bla:popmgt:v:28:y:2019:i:1:p:157-175
    DOI: 10.1111/poms.12903
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    Citations

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    Cited by:

    1. 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.
    2. Ruben van de Geer & Arnoud V. den Boer, 2022. "Price Optimization Under the Finite-Mixture Logit Model," Management Science, INFORMS, vol. 68(10), pages 7480-7496, October.
    3. Anton J. Kleywegt & Hongzhang Shao, 2022. "Revenue Management Under the Markov Chain Choice Model with Joint Price and Assortment Decisions," Papers 2204.04774, arXiv.org.
    4. Kameng Nip & Changjun Wang & Zizhuo Wang, 2022. "Competitive and Cooperative Assortment Games under Markov Chain Choice Model," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1033-1051, March.
    5. Kevin K. Wang & Michael D. Wittman & Thomas Fiig, 2023. "Dynamic offer creation for airline ancillaries using a Markov chain choice model," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 22(2), pages 103-121, April.
    6. Schlicher, Loe & Lurkin, Virginie, 2024. "Fighting pickpocketing using a choice-based resource allocation model," European Journal of Operational Research, Elsevier, vol. 315(2), pages 580-595.
    7. Woonghee T. Huh & Hongmin Li, 2023. "Product‐line pricing with dual objective of profit and consumer surplus," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1223-1242, April.

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