Dynamic Pricing Under a General Parametric Choice Model

Josef Broder () and Paat Rusmevichientong ()
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Josef Broder: Center for Applied Mathematics, Cornell University, Ithaca, New York 14850
Paat Rusmevichientong: Marshall School of Business, University of Southern California, Los Angeles, California 90089

Operations Research, 2012, vol. 60, issue 4, 965-980

Abstract: We consider a stylized dynamic pricing model in which a monopolist prices a product to a sequence of T customers who independently make purchasing decisions based on the price offered according to a general parametric choice model. The parameters of the model are unknown to the seller, whose objective is to determine a pricing policy that minimizes the regret , which is the expected difference between the seller's revenue and the revenue of a clairvoyant seller who knows the values of the parameters in advance and always offers the revenue-maximizing price. We show that the regret of the optimal pricing policy in this model is \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$\Theta(\sqrt T)$\end{document} , by establishing an \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$\Omega(\sqrt T)$\end{document} lower bound on the worst-case regret under an arbitrary policy, and presenting a pricing policy based on maximum-likelihood estimation whose regret is \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$\mathcal{O}(\sqrt T)$\end{document} across all problem instances. Furthermore, we show that when the demand curves satisfy a “well-separated” condition, the T -period regret of the optimal policy is (Theta)(log T ). Numerical experiments show that our policies perform well.

Keywords: dynamic pricing; customer choice model (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (78)

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