Internet services are traditionally priced at flat rates; however, many Internet service providers (ISPs) have recently shifted towards two-part tariffs where a data cap is imposed to restrain data demand from heavy users. Although the two-part tariff could generally increase the revenue for ISPs and has been supported by the US FCC, the role of data cap and its optimal pricing structures are not well understood. In this article, we study the impact of data cap on the optimal two-part pricing schemes for congestion-prone service markets. We model users' demand and preferences over pricing and congestion alternatives and derive the market share and congestion of service providers under a market equilibrium. Based on the equilibrium model, we characterize the two-part structures of the revenue- and welfare-optimal pricing schemes. Our results reveal that 1) the data cap provides a mechanism for ISPs to transition from the flat-rate to pay-as-you-go type of schemes, 2) both the revenue and welfare objectives of the ISP will drive the optimal pricing towards usage-based schemes with diminishing data caps, and 3) the welfare-optimal tariff comprises lower fees than the revenue-optimal counterpart, suggesting that regulators might want to promote usage-based pricing but regulate the lump-sum and per-unit fees.
Early studies of two-part tariff came from economics. Oi @cite_4 first studied the price discrimination via quantity discounts in the monopoly Disneyland market. Calem @cite_7 examined and compared the revenue-optimal prices by a multi-product monopoly and a differentiated oligopoly. Littlechild @cite_25 studied the explicit characterizations of welfare-optimal pricing and the effect of consumption externalities. Scotchmer @cite_2 explored the nature of Nash equilibrium among profit-maximizing shared facilities. However, all of these work were confined to a special case where the data usage cap is set to be zero. Our work studies the impact and dynamic of data cap on the two-part pricing, which generalizes the special case.
@cite_4 @cite_25 @cite_7 @cite_2
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This paper provides explicit characteristics of those two-part tariffs which maximize profit and consumers' plus producer's surplus. The effect of consumption externalities (as in telecommunications systems) is then explored. The characterizations are in terms of elasticities of demand with respect to price, income, and the number of other customers in the system. Abstract Two part pricing by a multiproduct monopoly and a differentiated oligopoly are examined and compared. Two part pricing policies are seen to depend on whether products are complements or substitutes and on whether or not the market is segmented. A principle result is that although competition tends to lower unit prices, there is no corresponding tendency for competition to reduce entry fees. The unit pricing rule is related to the Ramsey pricing rule. Oligopoly equilibrium unit prices equal marginal cost when there is one consumer type. We consider the problem of pricing n items to maximize revenue when faced with a series of unknown buyers with complex preferences, and show that a simple pricing scheme achieves surprisingly strong guarantees. We show that in the unlimited supply setting, a random single price achieves expected revenue within a logarithmic factor of the total social welfare for customers with general valuation functions, which may not even necessarily be monotone. This generalizes work of Guruswami et. al [18], who show a logarithmic factor for only the special cases of single-minded and unit-demand customers. In the limited supply setting, we show that for subadditive valuations, a random single price achieves revenue within a factor of 2O(√(log n loglog n) of the total social welfare, i.e., the optimal revenue the seller could hope to extract even if the seller could price each bundle differently for every buyer. This is the best approximation known for any item pricing scheme for subadditive (or even submodular) valuations, even using multiple prices. We complement this result with a lower bound showing a sequence of subadditive (in fact, XOS) buyers for which any single price has approximation ratio 2Ω(log1 4 n), thus showing that single price schemes cannot achieve a polylogarithmic ratio. This lower bound demonstrates a clear distinction between revenue maximization and social welfare maximization in this setting, for which [12,10] show that a fixed price achieves a logarithmic approximation in the case of XOS [12], and more generally subadditive [10], customers. We also consider the multi-unit case examined by [1111] in the context of social welfare, and show that so long as no buyer requires more than a 1 -- e fraction of the items, a random single price now does in fact achieve revenue within an O(log n) factor of the maximum social welfare. I. Two-part tariffs and a discriminating monopoly, 78.—II. Determination of a uniform two-part tariff, 81.—III. Applications of two-part tariffs, 88.—Appendix: Mathematical derivation of a uniform two-part tariff, 93.