Original Article

Journal of Revenue and Pricing Management (2009) 8, 42–66. doi:10.1057/rpm.2008.48; published online 5 December 2008

Dynamic pricing when customers strategically time their purchase: Asymptotic optimality of a two-price policy

Matulya Bansal1 and Costis Maglaras2

Correspondence: Costis Maglaras, Graduate School of Business, Columbia University, 3022 Broadway, New York, NY 10027, USA. E-mail: c.maglaras@gsb.columbia.edu

1did his Ph.D. at the Graduate School of Business at Columbia University in the Division of Decision, Risk & Operations. His research interests lie in the areas of Revenue Management, Quantitative Finance and Distributed Systems. Presently, he works in Quantitative Research at JPMorgan.

2is a Professor at the Graduate School of Business at Columbia University in the Division of Decision, Risk & Operations. His research focuses on quantitative pricing and revenue management, and the economics, design, and operations of service systems. He has authored over 20 scientific articles, spanning theory and applications, most recently focusing on the application of quantitative pricing models in real estate and in the design of portfolio trading systems. He holds editorial positions is most of the flagship journals of his fields of study, he is the recipient of several research and teaching awards, he is a frequent speaker in academic and industry forums, and a frequent consultant to industry.

Received 3 November 2008; Revised 3 November 2008; Published online 5 December 2008.

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Abstract

We study the dynamic pricing problem of a monopolist firm in presence of strategic customers that differ in their valuations and risk preferences. We show that this problem can be formulated as a static mechanism design problem, which is more amenable to analysis. We highlight several structural properties of the optimal solution, and solve the problem for several special cases. Focusing on settings with low risk-aversion, we show through an asymptotic analysis that the 'two-price point' strategy is near-optimal, offering partial validation for its wide use in practice, but also highlighting when it is indeed suitable to adopt it.

Keywords:

strategic behaviour, mechanism design, asymptotic optimality, revenue optimisation, risk-aversion, nonlinear programming

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