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 nonincreasing, 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 nondiscriminatory setting, a simple policy of Myerson (i.e., myopic) pricing and periodic introductions enjoys good performance guarantees. Funding: This material is based upon work supported by INSEAD and University Pierre et Marie Curie [Grant ELICIT], as well as by the National Science Foundation [Grant 2110707]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2364 .
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Technical Note—Static Pricing: Universal Guarantees for Reusable Resources
We consider a fundamental pricing model in which a fixed number of units of a reusable resource are used to serve customers. Customers arrive to the system according to a stochastic process and, upon arrival, decide whether to purchase the service, depending on their willingness to pay and the current price. The service time during which the resource is used by the customer is stochastic, and the firm may incur a service cost. This model represents various markets for reusable resources, such as cloud computing, shared vehicles, rotable parts, and hotel rooms. In the present paper, we analyze this pricing problem when the firm attempts to maximize a weighted combination of three central metrics: profit, market share, and service level. Under Poisson arrivals, exponential service times, and standard assumptions on the willingness-to-pay distribution, we establish a series of results that characterize the performance of static pricing in such environments. In particular, although an optimal policy is fully dynamic in such a context, we prove that a static pricing policy simultaneously guarantees 78.9% of the profit, market share, and service level from the optimal policy. Notably, this result holds for any service rate and number of units the firm operates. Our proof technique relies on a judicious construction of a static price that is derived directly from the optimal dynamic pricing policy. In the special case in which there are two units and the induced demand is linear, we also prove that the static policy guarantees 95.5% of the profit from the optimal policy. Our numerical findings on a large test bed of instances suggest that the latter result is quite indicative of the profit obtained by the static pricing policy across all parameters.
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- Award ID(s):
- 1944428
- PAR ID:
- 10359507
- Date Published:
- Journal Name:
- Operations Research
- Volume:
- 70
- Issue:
- 2
- ISSN:
- 0030-364X
- Page Range / eLocation ID:
- 1143 to 1152
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract We study optimal pricing for tandem queueing systems with finite buffers. The service provider dynamically quotes prices to incoming price sensitive customers to maximize the long‐run average revenue. We present a Markov decision process model for the optimization problem. For systems with two stations, general‐sized buffers, and two or more prices, we describe the structure of the optimal dynamic pricing policy and develop tailored policy iteration algorithms to find an optimal pricing policy. For systems with two stations but no intermediate buffer, we characterize conditions under which quoting either a high or a low price to all customers is optimal and provide an easy‐to‐implement algorithm to solve the problem. Numerical experiments are conducted to compare the developed algorithms with the regular policy iteration algorithm. The work also discusses possible extensions of the obtained results to both three‐station systems and two‐station systems with price and congestion sensitive customers using numerical analysis.
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Problem definition: Inspired by new developments in dynamic spectrum access, we study the dynamic pricing of wireless Internet access when demand and capacity (bandwidth) are stochastic. Academic/practical relevance: The demand for wireless Internet access has increased enormously. However, the spectrum available to wireless service providers is limited. The industry has, thus, altered conventional license-based spectrum access policies through unlicensed spectrum operations. The additional spectrum obtained through these operations has stochastic capacity. Thus, the pricing of this service by the service provider has novel challenges. The problem considered in this paper is, therefore, of high practical relevance and new to the academic literature. Methodology: We study this pricing problem using a Markov decision process model in which customers are posted dynamic prices based on their bandwidth requirement and the available capacity. Results: We characterize the structure of the optimal pricing policy as a function of the system state and of the input parameters. Because it is impossible to solve this problem for practically large state spaces, we propose a heuristic dynamic pricing policy that performs very well, particularly when the ratio of capacity to demand rate is low. Managerial implications: We demonstrate the value of using a dynamic heuristic pricing policy compared with the myopic and optimal static policies. The previous literature has studied similar systems with fixed capacity and has characterized conditions under which myopic policies perform well. In contrast, our setting has dynamic (stochastic) capacity, and we find that identifying good state-dependent heuristic pricing policies is of greater importance. Our heuristic policy is computationally more tractable and easier to implement than the optimal dynamic and static pricing policies. It also provides a significant performance improvement relative to the myopic and optimal static policies when capacity is scarce, a condition that holds for the practical setting that motivated this research.more » « less
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Characterizing the Efficiency of Static Pricing Schemes as a Function of the Supply
The problem of selling a supply of k units to a stream of customers constitutes one of the cornerstones in revenue management. Static pricing schemes (that output the same price to all customers) are commonly used because of their simplicity and their many desirable properties; they are anonymous, nonadaptive, and order oblivious. Although the efficiency of those schemes should improve as the supply k increases, prior work has only focused either on algorithms that aim for a constant approximation that is independent of k or on the setting where k becomes really large. In contrast, this paper characterizes the efficiency of static pricing schemes as a function of the supply. Our approach stems from identifying a “sweet spot” between selling enough items and obtaining enough utility from customers with high valuations. Subsequent work shows that our pricing scheme is the optimal static pricing for every value of k.
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Debates over paid peering and usage fees have expanded from the United States to Europe and South Korea. ISPs argue that content providers should pay fees based on the amount of downstream traffic they generate. In contrast, content providers contend that customers already pay ISPs for delivering the content they request, and therefore that peering agreements should be settlement-free. The issue has arisen in debates in the United States, Europe, and South Korea over net neutrality, universal service, and infrastructure funding. Regulatory entities are considering whether to regulate peering prices and/or impose usage fees. A key part of the debate concerns whether the market determines the socially beneficial peering price, and if not, how much of a difference there is between the socially beneficial peering price and the market-determined peering price. Our objective here is to understand the range from a cost-based peering price to a profit-maximizing peering price. First, we determine an ISP’s cost for directly peering with a content provider, by analyzing the incremental cost for transporting the content provider’s traffic when it directly peers with the ISP versus when it sends its traffic through a transit provider. We find that this cost-based peering price is positive if there is little localization of content, but it is zero (i.e., settlement-free peering) if there is sufficient localization of content. We also find that the required amount of localization varies with the number of interconnection points. Next, we determine the peering price that maximizes an ISP’s profit using a two-sided market model in which a profit-maximizing ISP determines broadband prices and the peering price, and in which content providers determine their service prices based on the peering price. We find that the profit-maximizing peering price decreases with content localization. These prices establish a range if the peering price is unregulated, from the cost-based peering price (at the low end) to the profit-maximizing peering price (at the high end). Regulatory oversight of peering prices may be warranted when there is a substantial difference between cost-based and profit-maximizing prices.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/opre.2020.2054
