Optimal Pricing and Introduction Timing of Technology Upgrades in Subscription-Based Services

In the context of subscription-based services, many technologies improve over time and service providers can provide increasingly powerful service upgrades to their customers, but at a launching cost, and the expense of the sales of existing products. We propose a model of technology upgrades and characterize the optimal pricing and timing of technology introductions for a service provider who price-discriminates among customers based on their upgrade experience, in the face of customers who are averse to switching to improved offerings. We first characterize optimal discriminatory pricing for the infinite horizon pricing problem with fixed introduction times. We reduce the optimal pricing problem to a tractable optimization problem and propose an efficient algorithm for solving it. Our algorithm computes optimal discriminatory prices within a fraction of a second, even for large problem instances. We then show that periodic introduction times, combined with optimal pricing, enjoy optimality guarantees. In particular, we first show that as long as the introduction intervals are constrained to be non-increasing, it is optimal to have periodic introductions after an initial warm-up phase. When allowing general introduction intervals, we show that periodic introduction intervals after some time are optimal in a more restricted sense. Numerical experiments suggest that it is generally optimal to have periodic introductions after an initial warm-up phase. Finally, we focus on a setting in which the firm does not price-discriminate based on customers' experience. We show both analytically and numerically that in the non-discriminatory setting, a simple policy of Myerson (i.e., myopic) pricing and periodic introductions enjoys good performance guarantees.