Strategic Dynamic Pricing with Network Effects

36 Pages Posted: 13 Jun 2017 Last revised: 26 Mar 2020

See all articles by Ali Makhdoumi

Ali Makhdoumi

Fuqua School of Business; Massachusetts Institute of Technology (MIT)

Azarakhsh Malekian

University of Toronto - Rotman School of Management; Massachusetts Institute of Technology (MIT) - Electrical Engineering and Computer Science

Asuman E. Ozdaglar

Massachusetts Institute of Technology (MIT) - Department of Electrical Engineering and Computer Science

Date Written: June 7, 2017

Abstract

We study the optimal pricing strategy of a monopolist selling homogeneous goods to multiple buyers over multiple periods. The customers choose their time of purchase to maximize their payoff that depends on their valuation of the product, the purchase price, and the utility they derive from past purchases of others, termed the network effect. We first show that the optimal price sequence is non-decreasing. Therefore, by postponing purchase to future rounds, customers trade-off a higher utility from the network effects with a higher price.

We then show that a customer's equilibrium strategy can be characterized by a threshold rule in which at each round a customer purchases the product when her valuation exceeds a certain threshold. This implies that customers face an inference problem regarding the valuations of others, i.e., observing that a customer has not yet purchased the product, signals that her valuation is below a threshold. Building on this characterization, we fully characterize the optimal price sequence asymptotically as the number of buyers goes to infinity. Notably, the optimal price sequence is linearly increasing in time with a slope that depends on the network structure through a novel scalar term given by the sum of entries of the inverse of the network weight matrix.

Our characterization shows that increasing the ``imbalance'' in the network defined as the difference between the in-degree and out-degree of the nodes increases the revenue of the monopolist.

Keywords: Positive Network Externality, Dynamic Pricing, Revenue Management, Strategic Buyers, Bernstein Polynomials

JEL Classification: D42, D62, D85

Suggested Citation

Makhdoumi, Ali and Malekian, Azarakhsh and Ozdaglar, Asuman E., Strategic Dynamic Pricing with Network Effects (June 7, 2017). Rotman School of Management Working Paper No. 2980109. Available at SSRN: https://ssrn.com/abstract=2980109 or http://dx.doi.org/10.2139/ssrn.2980109

Ali Makhdoumi (Contact Author)

Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States

HOME PAGE: http://https://www.fuqua.duke.edu/faculty/ali-makhdoumi

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Azarakhsh Malekian

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

Massachusetts Institute of Technology (MIT) - Electrical Engineering and Computer Science ( email )

77 Massachusetts Avenue
Cambridge, MA 02139-4307
United States

Asuman E. Ozdaglar

Massachusetts Institute of Technology (MIT) - Department of Electrical Engineering and Computer Science ( email )

50 Memorial Drive
Cambridge, MA 02139-4307
United States
617-324-0058 (Phone)

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