Smart Data Pricing: To Share or Not to Share

CTN Issue: September 2014

Authors: Yue Jin (Bell Labs, Alcatel-Lucent, Ireland) and Zhan Pang (Lancaster University, UK)
Title: “Smart Data Pricing: To Share or Not to Share?”
Publication: 2014 IEEE INFOCOM Workshop on Smart Data Pricing

A shared data plan is one where the usage price and/or quota for a single account covers data consumed across multiple devices and/or multiple users.  “Family plans” currently advertised by service providers are a representative example, and offer an appealing (to some) alternative to the conventional model of one data plan per device.   It is natural to ask under what conditions a service provider finds profit in offering such plans to its customer base. 

This paper compares “bundled” (shared) data plans with “partitioned” data plans in a simplified market environment with a single (monopolist) service provider, servicing an idealized population of independent users, each of which owns two wireless devices (say, a smart phone and a tablet). 

The objective of the service provider is to maximize profits by selecting prices.  In the case of partitioned data plans, the service provider selects separate prices per time period, one price for smart phone, and a second price for tablet.  In the case of bundled data plans, the service provider selects a single price for the pair of devices.

The two types of devices (smart phones and tablets) are assumed to have different maximum data usages, and each user’s usage of each device is modeled as a random variable, uniformly distributed between zero and the maximum data usage.  This randomness is included to capture the heterogeneity of user data consumption within the population, and the authors assume this usage equals the user’s utility for the device. 

Once the ISP has advertised its price or prices, each user now subscribes to the service if  its net utility (usage minus cost) is positive.  In the case of a partitioned data plan, each user will make two separate decisions, i.e., whether or not to subscribe to the plan for each of the two devices, based on whether or not the user’s usage on that device exceeds the set cost.  Likewise, in the case of a bundled data plan, each user will make a single decision, i.e., whether or not to subscribe to the plan for both devices, based on whether or not the user’s sum usage over both devices exceeds the set cost. 

With this basic model, the natural question is how to set the prices under each of the two plans so as to maximize the profit to the ISP, and to compute the corresponding profits under those optimal prices.  The prices and profits for both data plans are given in terms of the model parameters, i.e., the maximum data usage on each device and the operating costs per unit of data faced by the ISP.  With these in hand, the authors can then compare both the optimal prices and the profits across the two pricing schemes.  Theorem 1 asserts that the maximum profit under bundling exceeds that under partitioned data plans if and only if the operating costs per unit of data faced by the ISP is sufficiently small (less than one-half), and that the optimal price under bundling is less than the sum of the two optimal prices for the services under partitioning. 

The authors have several additional results beyond Theorem 1 that further characterize these two data models which we don’t discuss here, and for which a precise nonmathematical characterization of the results is more difficult. 

Overall, the paper presents an elegant abstraction of the question of data plan sharing from the perspective of a monopoly service provider.  The (idealized) findings state that optimized bundling yields superior profit to optimized partitioning when the operating costs of the service provider are sufficiently low.  

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