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Dynamic pricing under first order Markovian competition

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  • Benny Mantin
  • Daniel Granot
  • Frieda Granot
Abstract
We evaluate the effect of competition on prices, profits, and consumers' surplus in multiperiod, finite horizon, dynamic pricing settings. In our base model, a single myopic consumer visits two competing retailers, who offer identical goods, in a (first order Markovian) probabilistic fashion—if the posted price exceeds the consumer's valuation for the good, he returns to the same store in the following period with a certain probability. We find that even a small reduction in the return probability from one—which corresponds to the monopoly case at which prices decline linearly—is sufficient to revert the price decline from a linear into an exponential shape. Each retailer's profit is particularly sensitive to changes in his return probability when it is relatively high, and is maximized under complete loyalty behavior (i.e., return probability is one). On the other hand, consumer surplus is maximized under complete switching behavior (i.e., return probability is zero). In the presence of many similar consumers, the insights remain valid. We further focus on the extreme scenario where all consumers follow a complete switching behavior, to derive sharp bounds, and also consider the instance where, in this setting, myopic consumers are replaced with strategic consumers. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

Suggested Citation

  • Benny Mantin & Daniel Granot & Frieda Granot, 2011. "Dynamic pricing under first order Markovian competition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 608-617, September.
    • Handle: RePEc:wly:navres:v:58:y:2011:i:6:p:608-617
    DOI: 10.1002/nav.20470
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    References listed on IDEAS

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    3. Qi Feng & Yuanchen Li & J. George Shanthikumar, 2020. "Competitive Revenue Management with Sequential Bargaining," Production and Operations Management, Production and Operations Management Society, vol. 29(5), pages 1307-1324, May.
    4. Gisches, Eyran J. & Qi, Hang & Becker, William J. & Rapoport, Amnon, 2021. "Strategic retailers and myopic consumers: Competitive pricing of perishable goods," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 92(C).
    5. Narayan Mishra & Sri Vanamalla Venkataraman, 2022. "Optimal order quantity in the presence of strategic customers," Annals of Operations Research, Springer, vol. 315(2), pages 1871-1894, August.
    6. Yi Zheng & Zehao Li & Peng Jiang & Yijie Peng, 2024. "Dual-Agent Deep Reinforcement Learning for Dynamic Pricing and Replenishment," Papers 2410.21109, arXiv.org.
    7. 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.
    8. Moutaz Khouja & Jing Zhou, 2016. "The effect of a temporary product distribution channel on supply chain performance," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(7), pages 505-528, October.

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