Publications

Working Papers

Optimal Pricing and Introduction Timing of New Virtual Machines

Authors: Zoumpoulis Spyros

Cloud service providers can provide increasingly powerful upgrades of their virtual machines to their customers, but at a launching cost, and at the expense of the sales of existing products. The authors propose a model of product introduction and characterize the optimal pricing and timing of introductions of new virtual machines for a cloud service provider in the face of customers who are averse to upgrading to improved offerings. Overall, they show that a simple policy of Myerson (i.e., myopic) pricing and periodic introductions is near-optimal.

The authors first show that under a Myerson pricing rule, there is no loss of optimality with a periodic schedule of introductions, and that under periodic introductions, the potential additional revenue of any pricing policy over Myerson pricing decays to zero after sufficiently many introductions. They then show that, given arbitrary fixed introduction times, Myerson pricing is approximately optimal. To do so, the authors characterize the prices that achieve optimal revenue in a single introduction period and provide a bound for the competitive ratio of Myerson pricing over the optimal single-period pricing. This bound shows that Myerson pricing is approximately optimal when switching costs for the customers who upgrade are small or large.

Following this analysis, the authors examine their analytical bounds for Myerson pricing with simulations and show that they can provide strong guarantees for all values of the switching cost, for several natural distributions for the customer type. Furthermore, when numerically computing optimal prices, rather than using its bounds, the authors find that Myerson pricing is often several orders of magnitude closer to optimal than their analytical bounds suggest.

Download PDF